%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:22 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.80s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 45
% Syntax : Number of formulae : 186 ( 144 unt; 0 typ; 0 def)
% Number of atoms : 238 ( 232 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 78 ( 31 ~; 27 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 133 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(not_type,type,
not: $i > $i ).
tff(1,plain,
( ( x = implies(truth,x) )
<=> ( implies(truth,x) = x ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
^ [X: $i] :
refl(( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(3,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(6,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(y,y)) = implies(y,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(10,plain,
implies(truth,implies(y,y)) = implies(y,y),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = implies(Y,X) )
<=> ( implies(X,Y) = implies(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_antecedent) ).
tff(15,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(y,x),implies(y,x)),implies(y,y)) = implies(implies(y,y),implies(implies(y,x),implies(y,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
implies(implies(implies(y,x),implies(y,x)),implies(y,y)) = implies(implies(y,y),implies(implies(y,x),implies(y,x))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
implies(implies(y,y),implies(implies(y,x),implies(y,x))) = implies(implies(implies(y,x),implies(y,x)),implies(y,y)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(y,y),implies(implies(y,x),implies(y,x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
implies(implies(y,y),implies(implies(y,x),implies(y,x))) = truth,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
truth = implies(implies(y,y),implies(implies(y,x),implies(y,x))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
truth = implies(implies(implies(y,x),implies(y,x)),implies(y,y)),
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
implies(truth,implies(y,y)) = implies(implies(implies(implies(y,x),implies(y,x)),implies(y,y)),implies(y,y)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
implies(implies(implies(implies(y,x),implies(y,x)),implies(y,y)),implies(y,y)) = implies(truth,implies(y,y)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
tff(38,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(y,y),implies(implies(y,x),implies(y,x))),implies(implies(y,x),implies(y,x))) = implies(implies(implies(implies(y,x),implies(y,x)),implies(y,y)),implies(y,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
implies(implies(implies(y,y),implies(implies(y,x),implies(y,x))),implies(implies(y,x),implies(y,x))) = implies(implies(implies(implies(y,x),implies(y,x)),implies(y,y)),implies(y,y)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(y,x) = implies(x,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
implies(y,x) = implies(x,y),
inference(unit_resolution,[status(thm)],[43,17]) ).
tff(45,plain,
implies(x,y) = implies(y,x),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
implies(implies(x,y),implies(x,y)) = implies(implies(y,x),implies(y,x)),
inference(monotonicity,[status(thm)],[45,45]) ).
tff(47,plain,
implies(implies(y,x),implies(y,x)) = implies(implies(x,y),implies(x,y)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
implies(implies(not(x),not(y)),implies(x,y)) = implies(implies(not(x),not(y)),implies(y,x)),
inference(monotonicity,[status(thm)],[45]) ).
tff(49,plain,
implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(not(x),not(y)),implies(x,y)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
tff(54,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(x),not(y)),implies(y,x)) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
implies(implies(not(x),not(y)),implies(y,x)) = truth,
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
truth = implies(implies(not(x),not(y)),implies(y,x)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
implies(implies(y,y),implies(implies(y,x),implies(y,x))) = implies(implies(not(x),not(y)),implies(x,y)),
inference(transitivity,[status(thm)],[29,59,49]) ).
tff(61,plain,
implies(implies(implies(y,y),implies(implies(y,x),implies(y,x))),implies(implies(y,x),implies(y,x))) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y))),
inference(monotonicity,[status(thm)],[60,47]) ).
tff(62,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y))) = implies(implies(implies(y,y),implies(implies(y,x),implies(y,x))),implies(implies(y,x),implies(y,x))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
implies(truth,implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y))),
inference(unit_resolution,[status(thm)],[63,8]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(x,y),implies(not(x),not(y))) = implies(implies(not(x),not(y)),implies(x,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
implies(implies(x,y),implies(not(x),not(y))) = implies(implies(not(x),not(y)),implies(x,y)),
inference(unit_resolution,[status(thm)],[65,17]) ).
tff(67,plain,
implies(implies(not(x),not(y)),implies(x,y)) = implies(implies(x,y),implies(not(x),not(y))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
truth = implies(implies(x,y),implies(not(x),not(y))),
inference(transitivity,[status(thm)],[59,49,67]) ).
tff(69,plain,
implies(truth,implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = implies(implies(implies(x,y),implies(not(x),not(y))),implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
implies(implies(implies(x,y),implies(not(x),not(y))),implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = implies(truth,implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(implies(x,y),implies(not(x),not(y))),implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
implies(implies(implies(x,y),implies(not(x),not(y))),implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))) = truth,
inference(unit_resolution,[status(thm)],[71,27]) ).
tff(73,plain,
truth = implies(implies(implies(x,y),implies(not(x),not(y))),implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
truth = implies(y,y),
inference(transitivity,[status(thm)],[73,70,64,62,42,33,10]) ).
tff(75,plain,
implies(truth,x) = implies(implies(y,y),x),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
implies(implies(y,y),x) = implies(truth,x),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(x,implies(y,y)) = implies(implies(y,y),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
implies(x,implies(y,y)) = implies(implies(y,y),x),
inference(unit_resolution,[status(thm)],[77,17]) ).
tff(79,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y))) = implies(truth,implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(x,y),implies(x,y)))),
inference(symmetry,[status(thm)],[64]) ).
tff(80,plain,
implies(implies(implies(implies(y,x),implies(y,x)),implies(y,y)),implies(y,y)) = implies(implies(implies(y,y),implies(implies(y,x),implies(y,x))),implies(implies(y,x),implies(y,x))),
inference(symmetry,[status(thm)],[42]) ).
tff(81,plain,
implies(y,y) = implies(truth,implies(y,y)),
inference(symmetry,[status(thm)],[10]) ).
tff(82,plain,
implies(y,y) = truth,
inference(transitivity,[status(thm)],[81,32,80,61,79,69,72]) ).
tff(83,plain,
implies(x,implies(y,y)) = implies(x,truth),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
implies(x,truth) = implies(x,implies(y,y)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(implies(y,x),x)) = implies(implies(y,x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
implies(truth,implies(implies(y,x),x)) = implies(implies(y,x),x),
inference(unit_resolution,[status(thm)],[85,8]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(y,implies(x,y)) = implies(implies(x,y),y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
implies(y,implies(x,y)) = implies(implies(x,y),y),
inference(unit_resolution,[status(thm)],[87,17]) ).
tff(89,plain,
implies(implies(x,y),y) = implies(y,implies(x,y)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(x,y),y) = implies(implies(y,x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
implies(implies(x,y),y) = implies(implies(y,x),x),
inference(unit_resolution,[status(thm)],[90,40]) ).
tff(92,plain,
implies(implies(y,x),x) = implies(implies(x,y),y),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
implies(implies(y,x),x) = implies(y,implies(x,y)),
inference(transitivity,[status(thm)],[92,89]) ).
tff(94,plain,
truth = implies(implies(not(x),not(y)),implies(x,y)),
inference(transitivity,[status(thm)],[59,49]) ).
tff(95,plain,
implies(truth,implies(implies(y,x),x)) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(y,implies(x,y))),
inference(monotonicity,[status(thm)],[94,93]) ).
tff(96,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(y,implies(x,y))) = implies(truth,implies(implies(y,x),x)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
implies(y,implies(x,y)) = implies(implies(y,x),x),
inference(transitivity,[status(thm)],[88,91]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)) = implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)) = implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),
inference(unit_resolution,[status(thm)],[98,17]) ).
tff(100,plain,
implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
implies(implies(x,y),x) = implies(implies(y,x),x),
inference(monotonicity,[status(thm)],[45]) ).
tff(102,plain,
implies(implies(y,x),x) = implies(implies(x,y),x),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))) = truth,
inference(unit_resolution,[status(thm)],[105,27]) ).
tff(107,plain,
truth = implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
implies(implies(not(x),not(y)),implies(x,y)) = implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),
inference(transitivity,[status(thm)],[48,58,107,104,100]) ).
tff(109,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(y,implies(x,y))) = implies(implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),implies(implies(y,x),x)),
inference(monotonicity,[status(thm)],[108,97]) ).
tff(110,plain,
implies(implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),implies(implies(y,x),x)) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(y,implies(x,y))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),implies(implies(y,x),x)) = implies(implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),implies(implies(x,y),implies(implies(x,y),y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
implies(implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),implies(implies(y,x),x)) = implies(implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),implies(implies(x,y),implies(implies(x,y),y))),
inference(unit_resolution,[status(thm)],[111,40]) ).
tff(113,plain,
implies(implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(implies(x,y),implies(implies(x,y),y)),implies(implies(y,x),x)),implies(implies(y,x),x)),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(y,x),x),implies(x,y)) = implies(implies(x,y),implies(implies(y,x),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
implies(implies(implies(y,x),x),implies(x,y)) = implies(implies(x,y),implies(implies(y,x),x)),
inference(unit_resolution,[status(thm)],[114,17]) ).
tff(116,plain,
implies(implies(x,y),implies(implies(y,x),x)) = implies(implies(implies(y,x),x),implies(x,y)),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
implies(implies(x,y),implies(implies(y,x),x)) = implies(implies(x,y),implies(implies(x,y),y)),
inference(monotonicity,[status(thm)],[92]) ).
tff(118,plain,
implies(implies(x,y),implies(implies(x,y),y)) = implies(implies(x,y),implies(implies(y,x),x)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
implies(implies(x,y),implies(implies(x,y),y)) = implies(implies(implies(y,x),x),implies(x,y)),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(not(x),not(y)),implies(x,y)),
inference(transitivity,[status(thm)],[103,106,59,49]) ).
tff(121,plain,
implies(implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(monotonicity,[status(thm)],[120,119]) ).
tff(122,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))) = implies(implies(implies(implies(y,x),x),implies(implies(x,y),implies(implies(x,y),y))),implies(implies(x,y),implies(implies(x,y),y))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
implies(implies(implies(y,x),x),implies(x,y)) = implies(implies(x,y),implies(implies(x,y),y)),
inference(transitivity,[status(thm)],[115,117]) ).
tff(124,plain,
implies(implies(not(x),not(y)),implies(x,y)) = truth,
inference(transitivity,[status(thm)],[48,58]) ).
tff(125,plain,
implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))) = implies(truth,implies(implies(x,y),implies(implies(x,y),y))),
inference(monotonicity,[status(thm)],[124,123]) ).
tff(126,plain,
implies(truth,implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(implies(not(x),not(y)),implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(x,y),implies(implies(x,y),y)),truth) = implies(truth,implies(implies(x,y),implies(implies(x,y),y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
implies(implies(implies(x,y),implies(implies(x,y),y)),truth) = implies(truth,implies(implies(x,y),implies(implies(x,y),y))),
inference(unit_resolution,[status(thm)],[127,17]) ).
tff(129,plain,
implies(implies(implies(x,y),implies(implies(x,y),y)),truth) = implies(implies(implies(implies(y,x),x),implies(x,y)),implies(implies(not(x),not(y)),implies(x,y))),
inference(monotonicity,[status(thm)],[119,94]) ).
tff(130,plain,
implies(implies(implies(implies(y,x),x),implies(x,y)),implies(implies(not(x),not(y)),implies(x,y))) = implies(implies(implies(x,y),implies(implies(x,y),y)),truth),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(x,implies(x,y)) = implies(implies(x,y),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
implies(x,implies(x,y)) = implies(implies(x,y),x),
inference(unit_resolution,[status(thm)],[131,17]) ).
tff(133,plain,
implies(x,implies(x,y)) = implies(y,implies(x,y)),
inference(transitivity,[status(thm)],[132,101,92,89]) ).
tff(134,plain,
implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))) = implies(implies(y,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
implies(implies(y,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))) = implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
implies(y,implies(x,y)) = implies(implies(x,y),x),
inference(transitivity,[status(thm)],[88,91,102]) ).
tff(137,plain,
implies(implies(y,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))) = implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))),
inference(monotonicity,[status(thm)],[136,123]) ).
tff(138,plain,
implies(implies(implies(x,y),x),implies(implies(x,y),implies(implies(x,y),y))) = implies(implies(y,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
implies(implies(not(x),not(y)),implies(x,y)) = implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y))),
inference(transitivity,[status(thm)],[48,58,107,138,135]) ).
tff(140,plain,
implies(implies(implies(y,x),x),x) = implies(implies(implies(x,y),x),x),
inference(monotonicity,[status(thm)],[102]) ).
tff(141,plain,
implies(implies(implies(x,y),x),x) = implies(implies(implies(y,x),x),x),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(x,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
implies(implies(x,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),x),x),
inference(unit_resolution,[status(thm)],[142,40]) ).
tff(144,plain,
implies(x,implies(x,y)) = implies(implies(x,y),y),
inference(transitivity,[status(thm)],[132,101,92]) ).
tff(145,plain,
implies(implies(x,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),y),implies(x,y)),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
implies(implies(implies(x,y),y),implies(x,y)) = implies(implies(x,implies(x,y)),implies(x,y)),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
implies(implies(implies(x,y),y),implies(x,y)) = implies(implies(implies(y,x),x),implies(x,y)),
inference(monotonicity,[status(thm)],[91]) ).
tff(148,plain,
implies(implies(implies(y,x),x),implies(x,y)) = implies(implies(implies(x,y),y),implies(x,y)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
implies(implies(implies(y,x),x),implies(x,y)) = implies(implies(implies(y,x),x),x),
inference(transitivity,[status(thm)],[148,146,143,141]) ).
tff(150,plain,
implies(implies(implies(implies(y,x),x),implies(x,y)),implies(implies(not(x),not(y)),implies(x,y))) = implies(implies(implies(implies(y,x),x),x),implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y)))),
inference(monotonicity,[status(thm)],[149,139]) ).
tff(151,plain,
implies(implies(implies(implies(y,x),x),x),implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y)))) = implies(implies(implies(implies(y,x),x),implies(x,y)),implies(implies(not(x),not(y)),implies(x,y))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(implies(implies(y,x),x),x),implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
implies(implies(implies(implies(y,x),x),x),implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y)))) = truth,
inference(unit_resolution,[status(thm)],[152,27]) ).
tff(154,plain,
truth = implies(implies(implies(implies(y,x),x),x),implies(implies(x,implies(x,y)),implies(implies(implies(y,x),x),implies(x,y)))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
truth = implies(implies(y,x),x),
inference(transitivity,[status(thm)],[154,151,130,128,126,122,113,110,96,86]) ).
tff(156,plain,
implies(x,truth) = implies(x,implies(implies(y,x),x)),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
implies(x,implies(implies(y,x),x)) = implies(x,truth),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(y,x),x),x) = implies(x,implies(implies(y,x),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
implies(implies(implies(y,x),x),x) = implies(x,implies(implies(y,x),x)),
inference(unit_resolution,[status(thm)],[158,17]) ).
tff(160,plain,
implies(implies(y,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),y),implies(x,y)),
inference(monotonicity,[status(thm)],[88]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(y,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),y),y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
implies(implies(y,implies(x,y)),implies(x,y)) = implies(implies(implies(x,y),y),y),
inference(unit_resolution,[status(thm)],[161,40]) ).
tff(163,plain,
implies(implies(implies(x,y),y),y) = implies(implies(y,implies(x,y)),implies(x,y)),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
implies(implies(implies(y,x),x),y) = implies(implies(implies(x,y),y),y),
inference(monotonicity,[status(thm)],[92]) ).
tff(165,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(implies(y,x),x),y) = implies(y,implies(implies(y,x),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
implies(implies(implies(y,x),x),y) = implies(y,implies(implies(y,x),x)),
inference(unit_resolution,[status(thm)],[165,17]) ).
tff(167,plain,
implies(y,implies(implies(y,x),x)) = implies(implies(implies(y,x),x),y),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
implies(y,truth) = implies(y,implies(implies(y,x),x)),
inference(monotonicity,[status(thm)],[155]) ).
tff(169,plain,
implies(y,implies(y,y)) = implies(y,truth),
inference(monotonicity,[status(thm)],[82]) ).
tff(170,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = implies(Y,X) )
| ( implies(implies(y,y),y) = implies(y,implies(y,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
implies(implies(y,y),y) = implies(y,implies(y,y)),
inference(unit_resolution,[status(thm)],[170,17]) ).
tff(172,plain,
implies(truth,y) = implies(implies(y,y),y),
inference(monotonicity,[status(thm)],[74]) ).
tff(173,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,y) = y ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
implies(truth,y) = y,
inference(unit_resolution,[status(thm)],[173,8]) ).
tff(175,plain,
y = implies(truth,y),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
y = implies(truth,x),
inference(transitivity,[status(thm)],[175,172,171,169,168,167,164,163,160,146,143,141,159,157,84,78,76]) ).
tff(177,plain,
( ( x = y )
<=> ( x = implies(truth,x) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( x = y )
<=> ( implies(truth,x) = x ) ),
inference(transitivity,[status(thm)],[177,1]) ).
tff(179,plain,
( ( implies(truth,x) = x )
<=> ( x = y ) ),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,x) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
implies(truth,x) = x,
inference(unit_resolution,[status(thm)],[180,8]) ).
tff(182,plain,
x = y,
inference(modus_ponens,[status(thm)],[181,179]) ).
tff(183,plain,
( ( x != y )
<=> ( x != y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
tff(185,plain,
x != y,
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E %s %d THM
% 0.16/0.41 % Computer : n029.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 5 08:08:26 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.57/0.80 % SZS status Unsatisfiable
% 0.57/0.80 % SZS output start Proof
% See solution above
% 0.57/0.83 % E exiting
%------------------------------------------------------------------------------