TSTP Solution File: SET037-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:05:03 EDT 2022
% Result : Unsatisfiable 0.16s 0.41s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 67
% Syntax : Number of formulae : 150 ( 40 unt; 14 typ; 0 def)
% Number of atoms : 616 ( 121 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 869 ( 413 ~; 395 |; 0 &)
% ( 61 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 11 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 234 ( 212 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(a_function_type,type,
a_function: $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(f2_type,type,
f2: $i > $i ).
tff(first_type,type,
first: $i > $i ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(ordered_pair_predicate_type,type,
ordered_pair_predicate: $i > $o ).
tff(little_set_type,type,
little_set: $i > $o ).
tff(function_type,type,
function: $i > $o ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( member(a,domain_of(a_function))
<=> member(a,domain_of(a_function)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_function_domain) ).
tff(3,plain,
member(a,domain_of(a_function)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,X: $i] :
refl(
( ( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
<=> ( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain3) ).
tff(8,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
| ~ member(a,domain_of(a_function))
| ( a = first(f8(a,a_function)) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
| ~ member(a,domain_of(a_function))
| ( a = first(f8(a,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
| ~ member(a,domain_of(a_function))
| ( a = first(f8(a,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ( Z = first(f8(Z,X)) ) )
| ~ member(a,domain_of(a_function))
| ( a = first(f8(a,a_function)) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
a = first(f8(a,a_function)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
first(f8(a,a_function)) = a,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [Z: $i,X: $i] :
refl(
( ( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
<=> ( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
<=> ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
<=> ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [Z: $i,X: $i] :
rewrite(
( ( ~ member(Z,domain_of(X))
| ordered_pair_predicate(f8(Z,X)) )
<=> ( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ordered_pair_predicate(f8(Z,X)) )
<=> ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| ordered_pair_predicate(f8(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain1) ).
tff(22,plain,
! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
| ordered_pair_predicate(f8(a,a_function))
| ~ member(a,domain_of(a_function)) )
<=> ( ~ ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
| ordered_pair_predicate(f8(a,a_function))
| ~ member(a,domain_of(a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
| ordered_pair_predicate(f8(a,a_function))
| ~ member(a,domain_of(a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [Z: $i,X: $i] :
( ordered_pair_predicate(f8(Z,X))
| ~ member(Z,domain_of(X)) )
| ordered_pair_predicate(f8(a,a_function))
| ~ member(a,domain_of(a_function)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
ordered_pair_predicate(f8(a,a_function)),
inference(unit_resolution,[status(thm)],[28,25,3]) ).
tff(30,plain,
^ [X: $i] :
refl(
( ( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
<=> ( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
<=> ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
<=> ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).
tff(34,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
| ~ ordered_pair_predicate(f8(a,a_function))
| ( f8(a,a_function) = ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) ) )
<=> ( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
| ~ ordered_pair_predicate(f8(a,a_function))
| ( f8(a,a_function) = ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
| ~ ordered_pair_predicate(f8(a,a_function))
| ( f8(a,a_function) = ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| ( X = ordered_pair(f2(X),f3(X)) ) )
| ~ ordered_pair_predicate(f8(a,a_function))
| ( f8(a,a_function) = ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
f8(a,a_function) = ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) = f8(a,a_function),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = first(f8(a,a_function)),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
^ [X: $i] :
refl(
( ( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
<=> ( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
<=> ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
<=> ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).
tff(47,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
| ~ ordered_pair_predicate(f8(a,a_function))
| little_set(f3(f8(a,a_function))) )
<=> ( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
| ~ ordered_pair_predicate(f8(a,a_function))
| little_set(f3(f8(a,a_function))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
| ~ ordered_pair_predicate(f8(a,a_function))
| little_set(f3(f8(a,a_function))) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f3(X)) )
| ~ ordered_pair_predicate(f8(a,a_function))
| little_set(f3(f8(a,a_function))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
little_set(f3(f8(a,a_function))),
inference(unit_resolution,[status(thm)],[52,49,29]) ).
tff(54,plain,
^ [X: $i] :
refl(
( ( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
<=> ( little_set(f2(X))
| ~ ordered_pair_predicate(X) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
<=> ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
<=> ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [X: $i] :
rewrite(
( ( ~ ordered_pair_predicate(X)
| little_set(f2(X)) )
<=> ( little_set(f2(X))
| ~ ordered_pair_predicate(X) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f2(X)) )
<=> ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [X: $i] :
( ~ ordered_pair_predicate(X)
| little_set(f2(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).
tff(60,plain,
! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
| little_set(f2(f8(a,a_function)))
| ~ ordered_pair_predicate(f8(a,a_function)) )
<=> ( ~ ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
| little_set(f2(f8(a,a_function)))
| ~ ordered_pair_predicate(f8(a,a_function)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
| little_set(f2(f8(a,a_function)))
| ~ ordered_pair_predicate(f8(a,a_function)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X: $i] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) )
| little_set(f2(f8(a,a_function)))
| ~ ordered_pair_predicate(f8(a,a_function)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
little_set(f2(f8(a,a_function))),
inference(unit_resolution,[status(thm)],[66,63,29]) ).
tff(68,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
<=> ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
<=> ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ little_set(X)
| ~ little_set(Y)
| ( first(ordered_pair(X,Y)) = X ) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [Y: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ( first(ordered_pair(X,Y)) = X ) )
<=> ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [Y: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ( first(ordered_pair(X,Y)) = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
tff(74,plain,
! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) )
<=> ( ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ( first(ordered_pair(X,Y)) = X ) )
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))) = f2(f8(a,a_function)),
inference(unit_resolution,[status(thm)],[83,77,67,53]) ).
tff(85,plain,
f2(f8(a,a_function)) = first(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function)))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
f2(f8(a,a_function)) = a,
inference(transitivity,[status(thm)],[85,42,15]) ).
tff(87,plain,
apply(a_function,f2(f8(a,a_function))) = apply(a_function,a),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function)
<=> member(f8(a,a_function),a_function) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(89,plain,
( member(f8(a,a_function),a_function)
<=> member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
^ [Z: $i,X: $i] :
refl(
( ( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
<=> ( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain2) ).
tff(94,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
| ~ member(a,domain_of(a_function))
| member(f8(a,a_function),a_function) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
| ~ member(a,domain_of(a_function))
| member(f8(a,a_function),a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
| ~ member(a,domain_of(a_function))
| member(f8(a,a_function),a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,domain_of(X))
| member(f8(Z,X),X) )
| ~ member(a,domain_of(a_function))
| member(f8(a,a_function),a_function) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
member(f8(a,a_function),a_function),
inference(unit_resolution,[status(thm)],[99,96,3]) ).
tff(101,plain,
member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function),
inference(modus_ponens,[status(thm)],[100,89]) ).
tff(102,plain,
( function(a_function)
<=> function(a_function) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
function(a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_function) ).
tff(104,plain,
function(a_function),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
^ [Y: $i,Xf: $i,X: $i] :
refl(
( ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
<=> ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
<=> ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [Y: $i,Xf: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) ) )),
rewrite(
( ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) ) )),
rewrite(
( ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) )),
( ( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) )
<=> ( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) )
<=> ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(X)
| ~ little_set(Y)
| ~ function(Xf)
| ~ member(ordered_pair(X,Y),Xf)
| ( apply(Xf,X) = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_functions1) ).
tff(111,plain,
! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) )
<=> ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ~ function(a_function)
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) )
<=> ( ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ~ function(a_function)
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) )
<=> ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ~ function(a_function)
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) )
<=> ( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ little_set(f3(f8(a,a_function)))
| ~ little_set(f2(f8(a,a_function)))
| ~ function(a_function)
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [Y: $i,Xf: $i,X: $i] :
( ~ little_set(Y)
| ~ little_set(X)
| ~ function(Xf)
| ( apply(Xf,X) = Y )
| ~ member(ordered_pair(X,Y),Xf) )
| ~ function(a_function)
| ~ little_set(f2(f8(a,a_function)))
| ~ little_set(f3(f8(a,a_function)))
| ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ( apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)) )
| ~ member(ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))),a_function) ),
inference(unit_resolution,[status(thm)],[120,114,104,67,53]) ).
tff(122,plain,
apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)),
inference(unit_resolution,[status(thm)],[121,101]) ).
tff(123,plain,
f3(f8(a,a_function)) = apply(a_function,f2(f8(a,a_function))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
f3(f8(a,a_function)) = apply(a_function,a),
inference(transitivity,[status(thm)],[123,87]) ).
tff(125,plain,
ordered_pair(f2(f8(a,a_function)),f3(f8(a,a_function))) = ordered_pair(a,apply(a_function,a)),
inference(monotonicity,[status(thm)],[86,124]) ).
tff(126,plain,
f8(a,a_function) = ordered_pair(a,apply(a_function,a)),
inference(transitivity,[status(thm)],[40,125]) ).
tff(127,plain,
( member(f8(a,a_function),a_function)
<=> member(ordered_pair(a,apply(a_function,a)),a_function) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( member(ordered_pair(a,apply(a_function,a)),a_function)
<=> member(f8(a,a_function),a_function) ),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ~ member(ordered_pair(a,apply(a_function,a)),a_function)
<=> ~ member(f8(a,a_function),a_function) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ~ member(ordered_pair(a,b),a_function)
<=> ~ member(ordered_pair(a,apply(a_function,a)),a_function) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ member(ordered_pair(a,b),a_function)
<=> ~ member(ordered_pair(a,b),a_function) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
~ member(ordered_pair(a,b),a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_in_function) ).
tff(133,plain,
~ member(ordered_pair(a,b),a_function),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
~ member(ordered_pair(a,apply(a_function,a)),a_function),
inference(modus_ponens,[status(thm)],[133,130]) ).
tff(135,plain,
~ member(f8(a,a_function),a_function),
inference(modus_ponens,[status(thm)],[134,129]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[100,135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.31 % Computer : n026.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Sat Sep 3 01:50:53 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 0.16/0.41 % SZS status Unsatisfiable
% 0.16/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------