%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG069-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 04:58:05 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 43
% Syntax : Number of formulae : 123 ( 90 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 164 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 69 ( 27 ~; 14 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 155 ( 141 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(sK1_ax4_U_type,type,
sK1_ax4_U: $i ).
tff(sorti2_type,type,
sorti2: $i > $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(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),true,sorti2(h(U)),true) = true )
<=> ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
<=> ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,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(4,axiom,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(5,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
| ( ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = sorti1(sK2_ax3_V(j(sK1_ax4_U))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti1(j(sK1_ax4_U)),true) = sorti1(j(sK1_ax4_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
ifeq(true,true,sorti1(j(sK1_ax4_U)),true) = sorti1(j(sK1_ax4_U)),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
( ( sorti2(sK1_ax4_U) = true )
<=> ( sorti2(sK1_ax4_U) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
sorti2(sK1_ax4_U) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(23,plain,
sorti2(sK1_ax4_U) = true,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
true = sorti2(sK1_ax4_U),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
ifeq(true,true,sorti1(j(sK1_ax4_U)),true) = ifeq(sorti2(sK1_ax4_U),true,sorti1(j(sK1_ax4_U)),true),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
ifeq(sorti2(sK1_ax4_U),true,sorti1(j(sK1_ax4_U)),true) = ifeq(true,true,sorti1(j(sK1_ax4_U)),true),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [V: $i] :
refl(( ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true )
<=> ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ) )),
inference(bind,[status(th)],[]) ).
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(quant_intro,[status(thm)],[27]) ).
tff(29,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(30,axiom,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(31,plain,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [V: $i] : ( ifeq(sorti2(V),true,sorti1(j(V)),true) = true )
| ( ifeq(sorti2(sK1_ax4_U),true,sorti1(j(sK1_ax4_U)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
ifeq(sorti2(sK1_ax4_U),true,sorti1(j(sK1_ax4_U)),true) = true,
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
true = ifeq(sorti2(sK1_ax4_U),true,sorti1(j(sK1_ax4_U)),true),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
true = sorti1(j(sK1_ax4_U)),
inference(transitivity,[status(thm)],[36,26,20]) ).
tff(38,plain,
ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
^ [U: $i] :
refl(( ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true )
<=> ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(41,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(quant_intro,[status(thm)],[40]) ).
tff(42,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(43,axiom,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).
tff(44,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),true,sorti1(sK2_ax3_V(U)),true) = true )
| ( ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) = true,
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
true = ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
true = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(transitivity,[status(thm)],[49,39,18]) ).
tff(51,plain,
ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(unit_resolution,[status(thm)],[52,16]) ).
tff(54,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = true,
inference(transitivity,[status(thm)],[54,51,9]) ).
tff(56,plain,
^ [X1: $i] :
refl(( ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
<=> ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
<=> ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,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(59,axiom,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(60,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [X1: $i] : ( ifeq2(sorti2(X1),true,h(j(X1)),X1) = X1 )
| ( ifeq2(sorti2(sK1_ax4_U),true,h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
ifeq2(sorti2(sK1_ax4_U),true,h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U,
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U) = ifeq2(sorti2(sK1_ax4_U),true,h(j(sK1_ax4_U)),sK1_ax4_U),
inference(monotonicity,[status(thm)],[24]) ).
tff(66,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(67,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)],[66]) ).
tff(68,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(69,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U) = h(j(sK1_ax4_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U) = h(j(sK1_ax4_U)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
h(j(sK1_ax4_U)) = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
^ [U: $i] :
refl(( ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
<=> ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ) )),
inference(bind,[status(th)],[]) ).
tff(77,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(quant_intro,[status(thm)],[76]) ).
tff(78,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(79,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(80,plain,
! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [U: $i] : ( ifeq2(sorti1(U),true,op1(sK2_ax3_V(U),sK2_ax3_V(U)),U) = U )
| ( ifeq2(sorti1(j(sK1_ax4_U)),true,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(84,plain,
ifeq2(sorti1(j(sK1_ax4_U)),true,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)],[83,82]) ).
tff(85,plain,
ifeq2(true,true,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)),true,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(86,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,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(87,plain,
ifeq2(true,true,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)],[86,72]) ).
tff(88,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U),
inference(transitivity,[status(thm)],[88,85,84]) ).
tff(90,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)],[89]) ).
tff(91,plain,
^ [W: $i,X: $i] :
refl(( ( 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),true,ifeq2(sorti1(W),true,op2(h(W),h(X)),h(op1(W,X))),h(op1(W,X))) = h(op1(W,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(92,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(quant_intro,[status(thm)],[91]) ).
tff(93,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(94,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(95,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)],[94,93]) ).
tff(96,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(skolemize,[status(sab)],[95]) ).
tff(97,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)],[96,92]) ).
tff(98,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)) )
| ( ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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(99,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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)],[98,97]) ).
tff(100,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)],[90]) ).
tff(101,plain,
ifeq2(sorti2(sK1_ax4_U),true,h(j(sK1_ax4_U)),sK1_ax4_U) = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U),
inference(symmetry,[status(thm)],[65]) ).
tff(102,plain,
sK1_ax4_U = ifeq2(sorti2(sK1_ax4_U),true,h(j(sK1_ax4_U)),sK1_ax4_U),
inference(symmetry,[status(thm)],[64]) ).
tff(103,plain,
sK1_ax4_U = h(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))),
inference(transitivity,[status(thm)],[102,101,74,100]) ).
tff(104,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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)],[50,103]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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))),true,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(106,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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))),true,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)],[105,72]) ).
tff(107,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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(true,true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,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)],[106]) ).
tff(108,plain,
ifeq2(true,true,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))),true,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)],[50,103]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,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(110,plain,
ifeq2(true,true,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)],[109,72]) ).
tff(111,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),
inference(symmetry,[status(thm)],[110]) ).
tff(112,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)],[111,108,107,104,99,90,75,65,64]) ).
tff(113,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,true),
inference(monotonicity,[status(thm)],[112,55]) ).
tff(114,plain,
^ [V: $i] :
refl(( ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) )
<=> ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ) )),
inference(bind,[status(th)],[]) ).
tff(115,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(quant_intro,[status(thm)],[114]) ).
tff(116,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(117,axiom,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_1) ).
tff(118,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [V: $i] : ( tuple(op2(V,V),sorti2(V)) != tuple(sK1_ax4_U,true) )
| ( 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,true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,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,true),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG069-10 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 10:46:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.39 % SZS status Unsatisfiable
% 0.22/0.39 % SZS output start Proof
% See solution above
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------