%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG030-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 04:57:55 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 50
% Syntax : Number of formulae : 161 ( 121 unt; 0 typ; 0 def)
% Number of atoms : 215 ( 207 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 74 ( 27 ~; 23 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 182 ( 168 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(sK2_ax3_U_type,type,
sK2_ax3_U: $i ).
tff(sK1_ax3_V_type,type,
sK1_ax3_V: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(j_type,type,
j: $i > $i ).
tff(h_type,type,
h: $i > $i ).
tff(true_type,type,
true: $i ).
tff(sorti1_type,type,
sorti1: $i > $i ).
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(sorti2_type,type,
sorti2: $i > $i ).
tff(1,plain,
^ [X2: $i] :
refl(( ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 )
<=> ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 )
<=> ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 )
<=> ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(5,plain,
! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 )
| ( ifeq2(sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = op1(sK1_ax3_V,sK2_ax3_U) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq2(sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = op1(sK1_ax3_V,sK2_ax3_U),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(14,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)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,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_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = h(op1(sK1_ax3_V,sK2_ax3_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( sorti1(sK2_ax3_U) = true )
<=> ( sorti1(sK2_ax3_U) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
sorti1(sK2_ax3_U) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(21,plain,
sorti1(sK2_ax3_U) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = sorti1(sK2_ax3_U),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq2(true,true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
ifeq2(true,true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(true,true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( sorti1(sK1_ax3_V) = true )
<=> ( sorti1(sK1_ax3_V) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_1) ).
tff(36,plain,
sorti1(sK1_ax3_V) = true,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
true = sorti1(sK1_ax3_V),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(unit_resolution,[status(thm)],[39,30]) ).
tff(41,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(transitivity,[status(thm)],[41,38,33,23,18]) ).
tff(43,plain,
j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) = j(h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [V: $i,U: $i] :
refl(( ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true )
<=> ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true )
<=> ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true )
<=> ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(49,plain,
! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true )
| ( ifeq(sorti1(sK2_ax3_U),true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
ifeq(sorti1(sK2_ax3_U),true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true) = true,
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
ifeq(true,true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true) = ifeq(sorti1(sK2_ax3_U),true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(58,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true) = ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ifeq(true,true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true) = ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) = ifeq(true,true,ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),true),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
ifeq(true,true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) = ifeq(sorti1(sK1_ax3_V),true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) = sorti1(op1(sK1_ax3_V,sK2_ax3_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
ifeq(true,true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) = sorti1(op1(sK1_ax3_V,sK2_ax3_U)),
inference(unit_resolution,[status(thm)],[66,61]) ).
tff(68,plain,
sorti1(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq(true,true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
sorti1(op1(sK1_ax3_V,sK2_ax3_U)) = true,
inference(transitivity,[status(thm)],[68,65,64,54,53]) ).
tff(70,plain,
ifeq2(sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)),
inference(monotonicity,[status(thm)],[69,44]) ).
tff(71,plain,
ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),
inference(unit_resolution,[status(thm)],[72,30]) ).
tff(74,plain,
j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) = ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,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(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK2_ax3_U,sK1_ax3_V)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(unit_resolution,[status(thm)],[75,16]) ).
tff(77,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(monotonicity,[status(thm)],[37]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(unit_resolution,[status(thm)],[78,30]) ).
tff(80,plain,
ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(monotonicity,[status(thm)],[22]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = op2(h(sK2_ax3_U),h(sK1_ax3_V)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = op2(h(sK2_ax3_U),h(sK1_ax3_V)),
inference(unit_resolution,[status(thm)],[82,30]) ).
tff(84,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
^ [V: $i,U: $i] :
refl(( ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) )
<=> ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) )
<=> ! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) )
<=> ! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(89,plain,
! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] : ( ifeq2(sorti2(V),true,ifeq2(sorti2(U),true,op2(U,V),op2(V,U)),op2(V,U)) = op2(V,U) )
| ( ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),op2(h(sK2_ax3_U),h(sK1_ax3_V))) = op2(h(sK2_ax3_U),h(sK1_ax3_V)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),op2(h(sK2_ax3_U),h(sK1_ax3_V))) = op2(h(sK2_ax3_U),h(sK1_ax3_V)),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[81]) ).
tff(95,plain,
ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(true,true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[77]) ).
tff(96,plain,
h(op1(sK2_ax3_U,sK1_ax3_V)) = ifeq2(sorti1(sK1_ax3_V),true,ifeq2(sorti1(sK2_ax3_U),true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[76]) ).
tff(97,plain,
h(op1(sK2_ax3_U,sK1_ax3_V)) = op2(h(sK2_ax3_U),h(sK1_ax3_V)),
inference(transitivity,[status(thm)],[96,95,79,94,83]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = sorti2(h(sK2_ax3_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = sorti2(h(sK2_ax3_U)),
inference(unit_resolution,[status(thm)],[98,61]) ).
tff(100,plain,
ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = ifeq(sorti1(sK2_ax3_U),true,sorti2(h(sK2_ax3_U)),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(101,plain,
ifeq(sorti1(sK2_ax3_U),true,sorti2(h(sK2_ax3_U)),true) = ifeq(true,true,sorti2(h(sK2_ax3_U)),true),
inference(symmetry,[status(thm)],[100]) ).
tff(102,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(103,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)],[102]) ).
tff(104,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(105,axiom,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(106,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
| ( ifeq(sorti1(sK2_ax3_U),true,sorti2(h(sK2_ax3_U)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
ifeq(sorti1(sK2_ax3_U),true,sorti2(h(sK2_ax3_U)),true) = true,
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
true = ifeq(sorti1(sK2_ax3_U),true,sorti2(h(sK2_ax3_U)),true),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
true = sorti2(h(sK2_ax3_U)),
inference(transitivity,[status(thm)],[111,101,99]) ).
tff(113,plain,
ifeq2(true,true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),op2(h(sK2_ax3_U),h(sK1_ax3_V))),
inference(monotonicity,[status(thm)],[112,97]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
ifeq2(true,true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),
inference(unit_resolution,[status(thm)],[114,30]) ).
tff(116,plain,
ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))) = ifeq2(true,true,ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[38]) ).
tff(118,plain,
ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(true,true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[23]) ).
tff(119,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(sorti1(sK2_ax3_U),true,ifeq2(sorti1(sK1_ax3_V),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[18]) ).
tff(120,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(transitivity,[status(thm)],[119,118,32,117,40]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = sorti2(h(sK1_ax3_V)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = sorti2(h(sK1_ax3_V)),
inference(unit_resolution,[status(thm)],[121,61]) ).
tff(123,plain,
ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = ifeq(sorti1(sK1_ax3_V),true,sorti2(h(sK1_ax3_V)),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(124,plain,
ifeq(sorti1(sK1_ax3_V),true,sorti2(h(sK1_ax3_V)),true) = ifeq(true,true,sorti2(h(sK1_ax3_V)),true),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [U: $i] : ( ifeq(sorti1(U),true,sorti2(h(U)),true) = true )
| ( ifeq(sorti1(sK1_ax3_V),true,sorti2(h(sK1_ax3_V)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
ifeq(sorti1(sK1_ax3_V),true,sorti2(h(sK1_ax3_V)),true) = true,
inference(unit_resolution,[status(thm)],[125,108]) ).
tff(127,plain,
true = ifeq(sorti1(sK1_ax3_V),true,sorti2(h(sK1_ax3_V)),true),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
true = sorti2(h(sK1_ax3_V)),
inference(transitivity,[status(thm)],[127,124,122]) ).
tff(129,plain,
ifeq2(true,true,h(op1(sK1_ax3_V,sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),op2(h(sK2_ax3_U),h(sK1_ax3_V))),
inference(monotonicity,[status(thm)],[128,120,97]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,h(op1(sK1_ax3_V,sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK1_ax3_V,sK2_ax3_U)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
ifeq2(true,true,h(op1(sK1_ax3_V,sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(unit_resolution,[status(thm)],[130,30]) ).
tff(132,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(true,true,h(op1(sK1_ax3_V,sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(transitivity,[status(thm)],[132,129,116,113,93,84,81,80,77,76]) ).
tff(134,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = j(h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = j(h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),
inference(monotonicity,[status(thm)],[97]) ).
tff(137,plain,
j(op2(h(sK2_ax3_U),h(sK1_ax3_V))) = j(h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = j(op2(h(sK2_ax3_U),h(sK1_ax3_V))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
ifeq2(true,true,j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),
inference(unit_resolution,[status(thm)],[138,30]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) = sorti1(op1(sK2_ax3_U,sK1_ax3_V)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
ifeq(true,true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) = sorti1(op1(sK2_ax3_U,sK1_ax3_V)),
inference(unit_resolution,[status(thm)],[140,61]) ).
tff(142,plain,
ifeq(true,true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) = ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(143,plain,
ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) = ifeq(true,true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
ifeq(true,true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),
inference(unit_resolution,[status(thm)],[144,61]) ).
tff(146,plain,
ifeq(true,true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(147,plain,
ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = ifeq(true,true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [V: $i,U: $i] : ( ifeq(sorti1(V),true,ifeq(sorti1(U),true,sorti1(op1(U,V)),true),true) = true )
| ( ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true) = true,
inference(unit_resolution,[status(thm)],[148,51]) ).
tff(150,plain,
true = ifeq(sorti1(sK1_ax3_V),true,ifeq(sorti1(sK2_ax3_U),true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true),true),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
true = sorti1(op1(sK2_ax3_U,sK1_ax3_V)),
inference(transitivity,[status(thm)],[150,147,145,143,141]) ).
tff(152,plain,
ifeq2(true,true,j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = ifeq2(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)),
inference(monotonicity,[status(thm)],[151,137]) ).
tff(153,plain,
ifeq2(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = ifeq2(true,true,j(op2(h(sK2_ax3_U),h(sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [X2: $i] : ( ifeq2(sorti1(X2),true,j(h(X2)),X2) = X2 )
| ( ifeq2(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = op1(sK2_ax3_U,sK1_ax3_V) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
ifeq2(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = op1(sK2_ax3_U,sK1_ax3_V),
inference(unit_resolution,[status(thm)],[154,7]) ).
tff(156,plain,
op1(sK2_ax3_U,sK1_ax3_V) = ifeq2(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
op1(sK2_ax3_U,sK1_ax3_V) = op1(sK1_ax3_V,sK2_ax3_U),
inference(transitivity,[status(thm)],[156,153,139,137,135,44,74,71,9]) ).
tff(158,plain,
( ( op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U) )
<=> ( op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_2) ).
tff(160,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
$false,
inference(unit_resolution,[status(thm)],[160,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG030-10 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 10:43:01 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------