TSTP Solution File: ALG069-10 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 6 16:07:44 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 60
% Syntax : Number of formulae : 148 ( 97 unt; 12 typ; 0 def)
% Number of atoms : 207 ( 190 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 87 ( 32 ~; 14 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 187 ( 165 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i ) > $i ).
tff(sorti2_type,type,
sorti2: $i > $i ).
tff(sK1_ax4_U_type,type,
sK1_ax4_U: $i ).
tff(h_type,type,
h: $i > $i ).
tff(sK2_ax3_V_type,type,
sK2_ax3_V: $i > $i ).
tff(j_type,type,
j: $i > $i ).
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(sorti1_type,type,
sorti1: $i > $i ).
tff(true_type,type,
true: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(1,plain,
^ [U: $i] :
refl(
( ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [U: $i] :
rewrite(
( ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
<=> ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
<=> ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
<=> ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(7,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti2(h(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
| ( ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = sorti1(sK2_ax3_V(j(sK1_ax4_U))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U)) = sorti1(j(sK1_ax4_U)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U)) = sorti1(j(sK1_ax4_U)),
inference(unit_resolution,[status(thm)],[22,19]) ).
tff(24,plain,
^ [V: $i] :
refl(
( ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [V: $i] :
rewrite(
( ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true )
<=> ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true )
<=> ! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true )
<=> ! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(30,plain,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ ! [V: $i] : ( ifeq(sorti2(V),sorti2(sK1_ax4_U),sorti1(j(V)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
| ( ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
sorti2(sK1_ax4_U) = ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
sorti2(sK1_ax4_U) = sorti1(j(sK1_ax4_U)),
inference(transitivity,[status(thm)],[36,23]) ).
tff(38,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = ifeq(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
ifeq(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [U: $i] :
refl(
( ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
<=> ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [U: $i] :
rewrite(
( ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true )
<=> ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true )
<=> ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true )
<=> ! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).
tff(46,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(U)),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) )
| ( ifeq(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
ifeq(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)) = sorti2(sK1_ax4_U),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
sorti2(sK1_ax4_U) = ifeq(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
sorti2(sK1_ax4_U) = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(transitivity,[status(thm)],[52,39,21]) ).
tff(54,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)) = ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)) = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)) = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(unit_resolution,[status(thm)],[55,19]) ).
tff(57,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = sorti2(sK1_ax4_U),
inference(transitivity,[status(thm)],[57,54,12]) ).
tff(59,plain,
^ [X1: $i] :
refl(
( ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 )
<=> ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 )
<=> ! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [X1: $i] :
rewrite(
( ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
<=> ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
<=> ! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
<=> ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(65,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ),
inference(modus_ponens,[status(thm)],[65,62]) ).
tff(67,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ~ ! [X1: $i] : ( ifeq2(sorti2(X1),sorti2(sK1_ax4_U),h(j(X1)),X1) = X1 )
| ( ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(75,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U) = h(j(sK1_ax4_U)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U) = h(j(sK1_ax4_U)),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
h(j(sK1_ax4_U)) = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
^ [U: $i] :
refl(
( ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [U: $i] :
rewrite(
( ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(87,plain,
! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(modus_ponens,[status(thm)],[87,84]) ).
tff(89,plain,
! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ~ ! [U: $i] : ( ifeq2(sorti1(U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
| ( ifeq2(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = j(sK1_ax4_U) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
ifeq2(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = j(sK1_ax4_U),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = ifeq2(sorti1(j(sK1_ax4_U)),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(monotonicity,[status(thm)],[37]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),
inference(unit_resolution,[status(thm)],[94,77]) ).
tff(96,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U),
inference(transitivity,[status(thm)],[96,93,92]) ).
tff(98,plain,
h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))) = h(j(sK1_ax4_U)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
^ [W: $i,X: $i] :
refl(
( ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
<=> ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
<=> ! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [W: $i,X: $i] :
rewrite(
( ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
<=> ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [W: $i,X: $i] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
<=> ! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [W: $i,X: $i] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
<=> ! [W: $i,X: $i] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
! [W: $i,X: $i] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(105,plain,
! [W: $i,X: $i] : ( ifeq2(sorti1(X),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
inference(modus_ponens,[status(thm)],[105,102]) ).
tff(107,plain,
! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ~ ! [W: $i,X: $i] : ( ifeq2(sorti1(X),sorti2(sK1_ax4_U),ifeq2(sorti1(W),sorti2(sK1_ax4_U),op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) )
| ( ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
h(j(sK1_ax4_U)) = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(symmetry,[status(thm)],[98]) ).
tff(112,plain,
sK1_ax4_U = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),h(j(sK1_ax4_U)),sK1_ax4_U),
inference(symmetry,[status(thm)],[70]) ).
tff(113,plain,
sK1_ax4_U = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(transitivity,[status(thm)],[112,79,111]) ).
tff(114,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),sK1_ax4_U) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),
inference(monotonicity,[status(thm)],[53,113]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),sK1_ax4_U) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),sK1_ax4_U) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),
inference(unit_resolution,[status(thm)],[115,77]) ).
tff(117,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))) = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),sK1_ax4_U),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))))),
inference(monotonicity,[status(thm)],[53,113]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U) = op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U) = op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(unit_resolution,[status(thm)],[119,77]) ).
tff(121,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = sK1_ax4_U,
inference(transitivity,[status(thm)],[121,118,117,114,110,98,80,70]) ).
tff(123,plain,
tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))) = tuple(sK1_ax4_U,sorti2(sK1_ax4_U)),
inference(monotonicity,[status(thm)],[122,58]) ).
tff(124,plain,
^ [V: $i] :
refl(
( ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) )
<=> ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) )
<=> ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
^ [V: $i] :
rewrite(
( ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) )
<=> ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ) )),
inference(bind,[status(th)],]) ).
tff(127,plain,
( ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) )
<=> ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) )
<=> ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,axiom,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_1) ).
tff(130,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ),
inference(modus_ponens,[status(thm)],[130,127]) ).
tff(132,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ~ ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) )
| ( tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))) != tuple(sK1_ax4_U,sorti2(sK1_ax4_U)),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[135,123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 13:20:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------