TSTP Solution File: SET034-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET034-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:05:02 EDT 2022
% Result : Unsatisfiable 0.17s 0.50s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 141
% Syntax : Number of formulae : 313 ( 71 unt; 15 typ; 0 def)
% Number of atoms : 1904 ( 351 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 2877 (1348 ~;1382 |; 0 &)
% ( 147 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 77 ( 77 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 798 ( 742 !; 0 ?; 798 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(a_function_type,type,
a_function: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(f30_type,type,
f30: ( $i * $i * $i ) > $i ).
tff(another_function_type,type,
another_function: $i ).
tff(f20_type,type,
f20: $i > $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(f19_type,type,
f19: $i > $i ).
tff(f31_type,type,
f31: ( $i * $i * $i ) > $i ).
tff(f21_type,type,
f21: $i > $i ).
tff(f29_type,type,
f29: ( $i * $i * $i ) > $i ).
tff(little_set_type,type,
little_set: $i > $o ).
tff(single_valued_set_type,type,
single_valued_set: $i > $o ).
tff(relation_type,type,
relation: $i > $o ).
tff(function_type,type,
function: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( relation(compose(Y,X))
<=> relation(compose(Y,X)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : relation(compose(Y,X))
<=> ! [Y: $i,X: $i] : relation(compose(Y,X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : relation(compose(Y,X))
<=> ! [Y: $i,X: $i] : relation(compose(Y,X)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : relation(compose(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_a_relation) ).
tff(5,plain,
! [Y: $i,X: $i] : relation(compose(Y,X)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : relation(compose(Y,X)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : relation(compose(Y,X)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : relation(compose(Y,X))
| relation(compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
relation(compose(another_function,a_function)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ function(compose(another_function,a_function))
<=> ~ function(compose(another_function,a_function)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ function(compose(another_function,a_function)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_their_composition_is_a_function) ).
tff(12,plain,
~ function(compose(another_function,a_function)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Xf: $i] :
refl(
( ( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
<=> ( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
<=> ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
<=> ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [Xf: $i] :
rewrite(
( ( function(Xf)
| ~ relation(Xf)
| ~ single_valued_set(Xf) )
<=> ( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Xf: $i] :
( function(Xf)
| ~ relation(Xf)
| ~ single_valued_set(Xf) )
<=> ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [Xf: $i] :
( function(Xf)
| ~ relation(Xf)
| ~ single_valued_set(Xf) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',function3) ).
tff(19,plain,
! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
| function(compose(another_function,a_function))
| ~ single_valued_set(compose(another_function,a_function))
| ~ relation(compose(another_function,a_function)) )
<=> ( ~ ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
| function(compose(another_function,a_function))
| ~ single_valued_set(compose(another_function,a_function))
| ~ relation(compose(another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
| function(compose(another_function,a_function))
| ~ single_valued_set(compose(another_function,a_function))
| ~ relation(compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Xf: $i] :
( function(Xf)
| ~ single_valued_set(Xf)
| ~ relation(Xf) )
| function(compose(another_function,a_function))
| ~ single_valued_set(compose(another_function,a_function))
| ~ relation(compose(another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ single_valued_set(compose(another_function,a_function))
| ~ relation(compose(another_function,a_function)) ),
inference(unit_resolution,[status(thm)],[25,22,12]) ).
tff(27,plain,
~ single_valued_set(compose(another_function,a_function)),
inference(unit_resolution,[status(thm)],[26,9]) ).
tff(28,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
<=> ( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
<=> ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
<=> ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set5) ).
tff(32,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f20(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)),
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
<=> ( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
rewrite(
( ( ~ member(Z,compose(Xf,Xg))
| little_set(f29(Z,Xf,Xg)) )
<=> ( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f29(Z,Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f29(Z,Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose1) ).
tff(45,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[51,48,38]) ).
tff(53,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
<=> ( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose4) ).
tff(57,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[62,59,38]) ).
tff(64,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| little_set(f19(X)) )
<=> ( single_valued_set(X)
| little_set(f19(X)) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set2) ).
tff(68,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f19(compose(another_function,a_function))) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f19(compose(another_function,a_function))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f19(compose(another_function,a_function))) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f19(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f19(compose(another_function,a_function))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
little_set(f19(compose(another_function,a_function))),
inference(unit_resolution,[status(thm)],[73,70,27]) ).
tff(75,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ little_set(X)
| ~ little_set(U)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
( ( ~ little_set(X)
| ~ little_set(U)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) )
<=> ( ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) )
<=> ( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
( ( ~ little_set(X)
| ~ little_set(U)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) )
<=> ( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(U)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(U)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( X = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
tff(81,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),
inference(unit_resolution,[status(thm)],[90,84,74,63,52]) ).
tff(92,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
<=> ( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
<=> ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
<=> ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set6) ).
tff(96,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| member(ordered_pair(f19(X),f21(X)),X) )
| single_valued_set(compose(another_function,a_function))
| member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)),
inference(unit_resolution,[status(thm)],[101,98,27]) ).
tff(103,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) )
| little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[105,48,102]) ).
tff(107,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| ( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)) ) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[109,59,102]) ).
tff(111,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ( X = U )
| ~ little_set(U)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
f19(compose(another_function,a_function)) = f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),
inference(unit_resolution,[status(thm)],[116,84,74,110,106]) ).
tff(118,plain,
f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) = f19(compose(another_function,a_function)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) = f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),
inference(transitivity,[status(thm)],[118,91]) ).
tff(120,plain,
ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) = ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
<=> member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
<=> member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
<=> ( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose5) ).
tff(127,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function),
inference(unit_resolution,[status(thm)],[132,129,38]) ).
tff(134,plain,
member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function),
inference(modus_ponens,[status(thm)],[133,122]) ).
tff(135,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
<=> ( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose3) ).
tff(139,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[144,141,38]) ).
tff(146,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f31(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[148,141,102]) ).
tff(150,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function),
inference(unit_resolution,[status(thm)],[152,129,102]) ).
tff(154,plain,
( function(another_function)
<=> function(another_function) ),
inference(rewrite,[status(thm)],]) ).
tff(155,axiom,
function(another_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_function) ).
tff(156,plain,
function(another_function),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
^ [Xf: $i] :
refl(
( ( ~ function(Xf)
| single_valued_set(Xf) )
<=> ( ~ function(Xf)
| single_valued_set(Xf) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
<=> ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
<=> ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,axiom,
! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',function2) ).
tff(161,plain,
! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
( ( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(another_function)
| single_valued_set(another_function) )
<=> ( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(another_function)
| single_valued_set(another_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(another_function)
| single_valued_set(another_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(another_function)
| single_valued_set(another_function) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
single_valued_set(another_function),
inference(unit_resolution,[status(thm)],[166,163,156]) ).
tff(168,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
inference(bind,[status(th)],]) ).
tff(169,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ single_valued_set(X)
| ~ little_set(U) )
<=> ( ~ little_set(U)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ single_valued_set(X)
| ~ little_set(V) ) )),
rewrite(
( ( ~ little_set(U)
| ~ single_valued_set(X)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ single_valued_set(X)
| ~ little_set(W) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(V)
| ~ single_valued_set(X)
| ~ little_set(W) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ single_valued_set(X)
| ~ member(ordered_pair(U,V),X) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ single_valued_set(X)
| ~ member(ordered_pair(U,V),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X)
| ~ member(ordered_pair(U,W),X) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X)
| ~ member(ordered_pair(U,W),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X)
| ( V = W ) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X)
| ( V = W ) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X)
| ( V = W ) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
( ( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X)
| ( V = W ) )
<=> ( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) )),
inference(bind,[status(th)],]) ).
tff(172,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ single_valued_set(X)
| ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ~ member(ordered_pair(U,V),X)
| ~ member(ordered_pair(U,W),X)
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set1) ).
tff(174,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) ),
inference(modus_ponens,[status(thm)],[176,169]) ).
tff(178,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) )
<=> ( ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function)
| ~ single_valued_set(another_function) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( ( f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),another_function) ),
inference(unit_resolution,[status(thm)],[183,177,167,153,149,106,145]) ).
tff(185,plain,
f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),
inference(unit_resolution,[status(thm)],[184,134]) ).
tff(186,plain,
f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) = f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) = ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
<=> member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
<=> member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
<=> ( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ) )),
inference(bind,[status(th)],]) ).
tff(191,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose6) ).
tff(194,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ),
inference(skolemize,[status(sab)],[194]) ).
tff(196,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) ),
inference(modus_ponens,[status(thm)],[195,191]) ).
tff(197,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function),
inference(unit_resolution,[status(thm)],[199,196,38]) ).
tff(201,plain,
member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function),
inference(modus_ponens,[status(thm)],[200,189]) ).
tff(202,plain,
^ [Xg: $i,Z: $i,Xf: $i] :
refl(
( ( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
<=> ( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ) )),
inference(bind,[status(th)],]) ).
tff(203,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
<=> ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,axiom,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',compose2) ).
tff(206,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ),
inference(skolemize,[status(sab)],[206]) ).
tff(208,plain,
! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(210,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[211,208,38]) ).
tff(213,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| little_set(f20(X)) )
<=> ( single_valued_set(X)
| little_set(f20(X)) ) )),
inference(bind,[status(th)],]) ).
tff(214,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(216,axiom,
! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set3) ).
tff(217,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f20(compose(another_function,a_function))) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f20(compose(another_function,a_function))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(221,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f20(compose(another_function,a_function))) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f20(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f20(compose(another_function,a_function))) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
little_set(f20(compose(another_function,a_function))),
inference(unit_resolution,[status(thm)],[222,219,27]) ).
tff(224,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(225,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(227,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(X) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(X)
| ~ little_set(V) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(X)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) ) )),
rewrite(
( ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) )
<=> ( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(228,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ~ little_set(U)
| ~ little_set(V)
| ( ordered_pair(X,Y) != ordered_pair(U,V) )
| ( Y = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_components_are_equal) ).
tff(230,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[230,226]) ).
tff(232,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) ),
inference(modus_ponens,[status(thm)],[232,225]) ).
tff(234,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(235,plain,
( ( ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(236,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(transitivity,[status(thm)],[236,234]) ).
tff(238,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f20(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function),
inference(unit_resolution,[status(thm)],[239,233,74,223,63,52,212]) ).
tff(241,plain,
( ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
<=> ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) ) ),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ( f20(compose(another_function,a_function)) != f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
<=> ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) != f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) ) ),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| little_set(f30(Z,Xf,Xg)) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),
inference(unit_resolution,[status(thm)],[245,208,102]) ).
tff(247,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| little_set(f21(X)) )
<=> ( single_valued_set(X)
| little_set(f21(X)) ) )),
inference(bind,[status(th)],]) ).
tff(248,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ) ),
inference(quant_intro,[status(thm)],[247]) ).
tff(249,plain,
( ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
<=> ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(250,axiom,
! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set4) ).
tff(251,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ),
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ),
inference(skolemize,[status(sab)],[251]) ).
tff(253,plain,
! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) ),
inference(modus_ponens,[status(thm)],[252,248]) ).
tff(254,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f21(compose(another_function,a_function))) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f21(compose(another_function,a_function))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f21(compose(another_function,a_function))) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| little_set(f21(X)) )
| single_valued_set(compose(another_function,a_function))
| little_set(f21(compose(another_function,a_function))) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
little_set(f21(compose(another_function,a_function))),
inference(unit_resolution,[status(thm)],[256,253,27]) ).
tff(258,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(259,plain,
( ( ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(260,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ) ),
inference(transitivity,[status(thm)],[260,258]) ).
tff(262,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f19(compose(another_function,a_function)))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(Y)
| ~ little_set(V)
| ~ little_set(X)
| ( Y = V )
| ( ordered_pair(X,Y) != ordered_pair(U,V) ) )
| ~ little_set(f21(compose(another_function,a_function)))
| ~ little_set(f19(compose(another_function,a_function)))
| ~ little_set(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ( ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))) != ordered_pair(f29(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
f21(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),
inference(unit_resolution,[status(thm)],[263,233,257,74,110,106,246]) ).
tff(265,plain,
( ( f20(compose(another_function,a_function)) = f21(compose(another_function,a_function)) )
<=> ( f20(compose(another_function,a_function)) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) ) ),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
( ( f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)) )
<=> ( f20(compose(another_function,a_function)) != f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) ) ),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
^ [X: $i] :
refl(
( ( single_valued_set(X)
| ( f20(X) != f21(X) ) )
<=> ( single_valued_set(X)
| ( f20(X) != f21(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(268,plain,
( ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
<=> ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,plain,
( ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
<=> ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(270,axiom,
! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',single_valued_set7) ).
tff(271,plain,
! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ),
inference(skolemize,[status(sab)],[271]) ).
tff(273,plain,
! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) ),
inference(modus_ponens,[status(thm)],[272,268]) ).
tff(274,plain,
( ( ~ ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
| single_valued_set(compose(another_function,a_function))
| ( f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)) ) )
<=> ( ~ ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
| single_valued_set(compose(another_function,a_function))
| ( f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(275,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
| single_valued_set(compose(another_function,a_function))
| ( f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
( ~ ! [X: $i] :
( single_valued_set(X)
| ( f20(X) != f21(X) ) )
| single_valued_set(compose(another_function,a_function))
| ( f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)) ) ),
inference(modus_ponens,[status(thm)],[275,274]) ).
tff(277,plain,
f20(compose(another_function,a_function)) != f21(compose(another_function,a_function)),
inference(unit_resolution,[status(thm)],[276,273,27]) ).
tff(278,plain,
f20(compose(another_function,a_function)) != f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),
inference(modus_ponens,[status(thm)],[277,266]) ).
tff(279,plain,
f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) != f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),
inference(modus_ponens,[status(thm)],[278,242]) ).
tff(280,plain,
( ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function) )
<=> ( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(281,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(282,plain,
( ~ ! [Xg: $i,Z: $i,Xf: $i] :
( ~ member(Z,compose(Xf,Xg))
| member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg) )
| ~ member(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),compose(another_function,a_function))
| member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function),
inference(unit_resolution,[status(thm)],[282,196,102]) ).
tff(284,plain,
( function(a_function)
<=> function(a_function) ),
inference(rewrite,[status(thm)],]) ).
tff(285,axiom,
function(a_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_function) ).
tff(286,plain,
function(a_function),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
( ( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(a_function)
| single_valued_set(a_function) )
<=> ( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(a_function)
| single_valued_set(a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(288,plain,
( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(a_function)
| single_valued_set(a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
( ~ ! [Xf: $i] :
( ~ function(Xf)
| single_valued_set(Xf) )
| ~ function(a_function)
| single_valued_set(a_function) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
single_valued_set(a_function),
inference(unit_resolution,[status(thm)],[289,163,286]) ).
tff(291,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(292,plain,
( ( ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) )
<=> ( ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(293,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ) ),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ) ),
inference(transitivity,[status(thm)],[293,291]) ).
tff(295,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ little_set(U)
| ~ little_set(V)
| ~ little_set(W)
| ( V = W )
| ~ member(ordered_pair(U,W),X)
| ~ member(ordered_pair(U,V),X)
| ~ single_valued_set(X) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ little_set(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function))
| ~ little_set(f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function))
| ( f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function) = f30(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function) )
| ~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function)
| ~ single_valued_set(a_function) ),
inference(modus_ponens,[status(thm)],[295,294]) ).
tff(297,plain,
~ member(ordered_pair(f31(ordered_pair(f19(compose(another_function,a_function)),f21(compose(another_function,a_function))),another_function,a_function),f30(ordered_pair(f19(compose(another_function,a_function)),f20(compose(another_function,a_function))),another_function,a_function)),a_function),
inference(unit_resolution,[status(thm)],[296,177,290,283,149,246,212,279]) ).
tff(298,plain,
$false,
inference(unit_resolution,[status(thm)],[297,201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SET034-3 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 01:35:35 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.50 % SZS status Unsatisfiable
% 0.17/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------