%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.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 02:59:24 PM UTC 2026
% Result : Unsatisfiable 20.04s 20.30s
% Output : Proof 20.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 78
% Syntax : Number of formulae : 290 ( 224 unt; 0 typ; 0 def)
% Number of atoms : 376 ( 365 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 124 ( 48 ~; 44 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 234 ( 217 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(y_type,type,
y: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(and_star_type,type,
and_star: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(not_type,type,
not: $i > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(implies(y,x),x) = xor(truth,and_star(implies(y,x),xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(implies(y,x),x) = xor(truth,and_star(implies(y,x),xor(truth,x))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
xor(truth,and_star(implies(y,x),xor(truth,x))) = implies(implies(y,x),x),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( xor(X,Y) = xor(Y,X) )
<=> ( xor(X,Y) = xor(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
tff(15,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(implies(y,x),xor(truth,x)),truth) = xor(truth,and_star(implies(y,x),xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
xor(and_star(implies(y,x),xor(truth,x)),truth) = xor(truth,and_star(implies(y,x),xor(truth,x))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(y,x) = xor(truth,and_star(y,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
implies(y,x) = xor(truth,and_star(y,xor(truth,x))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
xor(truth,and_star(y,xor(truth,x))) = implies(y,x),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)) = and_star(implies(y,x),xor(truth,x)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
and_star(implies(y,x),xor(truth,x)) = and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
xor(and_star(implies(y,x),xor(truth,x)),truth) = xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth) = xor(and_star(implies(y,x),xor(truth,x)),truth),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(x,y) = xor(truth,and_star(x,xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
implies(x,y) = xor(truth,and_star(x,xor(truth,y))),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
and_star(implies(x,y),xor(truth,y)) = and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [X: $i] :
refl(( ( and_star(X,truth) = X )
<=> ( and_star(X,truth) = X ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X: $i] : ( and_star(X,truth) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
tff(34,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(x,truth) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
and_star(x,truth) = x,
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [X: $i] :
refl(( ( xor(X,falsehood) = X )
<=> ( xor(X,falsehood) = X ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [X: $i] : ( xor(X,falsehood) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
tff(43,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [X: $i] : ( xor(X,falsehood) = X )
| ( xor(and_star(x,truth),falsehood) = and_star(x,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
xor(and_star(x,truth),falsehood) = and_star(x,truth),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
^ [X: $i] :
refl(( ( not(X) = xor(X,truth) )
<=> ( not(X) = xor(X,truth) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X: $i] : ( not(X) = xor(X,truth) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
tff(52,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( not(X) = xor(X,truth) )
| ( not(truth) = xor(truth,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
not(truth) = xor(truth,truth),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( ( not(truth) = falsehood )
<=> ( not(truth) = falsehood ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
tff(59,plain,
not(truth) = falsehood,
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
falsehood = xor(truth,truth),
inference(transitivity,[status(thm)],[60,56]) ).
tff(62,plain,
xor(and_star(x,truth),falsehood) = xor(x,xor(truth,truth)),
inference(monotonicity,[status(thm)],[38,61]) ).
tff(63,plain,
xor(x,xor(truth,truth)) = xor(and_star(x,truth),falsehood),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [Y: $i,X: $i] :
refl(( ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
tff(68,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(x,xor(truth,truth)) = xor(xor(x,truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
xor(x,xor(truth,truth)) = xor(xor(x,truth),truth),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
xor(xor(x,truth),truth) = xor(x,xor(truth,truth)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(x,truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
xor(x,truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[74,17]) ).
tff(76,plain,
xor(xor(x,truth),truth) = xor(xor(truth,x),truth),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
xor(xor(truth,x),truth) = xor(xor(x,truth),truth),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(truth,x),truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
and_star(xor(truth,x),truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[78,36]) ).
tff(80,plain,
xor(truth,x) = and_star(xor(truth,x),truth),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
xor(xor(truth,x),truth) = xor(and_star(xor(truth,x),truth),truth),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
xor(and_star(xor(truth,x),truth),truth) = xor(xor(truth,x),truth),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(and_star(xor(truth,x),truth),truth),truth) = xor(and_star(xor(truth,x),truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
and_star(xor(and_star(xor(truth,x),truth),truth),truth) = xor(and_star(xor(truth,x),truth),truth),
inference(unit_resolution,[status(thm)],[83,36]) ).
tff(85,plain,
^ [Y: $i,X: $i] :
refl(( ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
<=> ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
<=> ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
<=> ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
tff(89,plain,
! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
| ( and_star(xor(and_star(xor(truth,truth),x),truth),x) = and_star(xor(and_star(xor(truth,x),truth),truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
and_star(xor(and_star(xor(truth,truth),x),truth),x) = and_star(xor(and_star(xor(truth,x),truth),truth),truth),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
^ [Y: $i,X: $i] :
refl(( ( and_star(X,Y) = and_star(Y,X) )
<=> ( and_star(X,Y) = and_star(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
tff(98,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,y),x) = and_star(x,xor(truth,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
and_star(xor(truth,y),x) = and_star(x,xor(truth,y)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
and_star(x,xor(truth,y)) = and_star(xor(truth,y),x),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))) = and_star(xor(truth,xor(truth,y)),and_star(xor(truth,y),x)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
and_star(xor(truth,xor(truth,y)),and_star(xor(truth,y),x)) = and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
<=> ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
tff(110,plain,
! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(truth,xor(truth,y)),xor(truth,y)),x) = and_star(xor(truth,xor(truth,y)),and_star(xor(truth,y),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
and_star(and_star(xor(truth,xor(truth,y)),xor(truth,y)),x) = and_star(xor(truth,xor(truth,y)),and_star(xor(truth,y),x)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
^ [X: $i] :
refl(( ( and_star(xor(truth,X),X) = falsehood )
<=> ( and_star(xor(truth,X),X) = falsehood ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
<=> ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
<=> ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
tff(119,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ~ ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
| ( and_star(xor(truth,xor(truth,y)),xor(truth,y)) = falsehood ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
and_star(xor(truth,xor(truth,y)),xor(truth,y)) = falsehood,
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
falsehood = and_star(xor(truth,xor(truth,y)),xor(truth,y)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
xor(truth,truth) = not(truth),
inference(symmetry,[status(thm)],[56]) ).
tff(126,plain,
xor(truth,truth) = and_star(xor(truth,xor(truth,y)),xor(truth,y)),
inference(transitivity,[status(thm)],[125,59,124]) ).
tff(127,plain,
and_star(xor(truth,truth),x) = and_star(and_star(xor(truth,xor(truth,y)),xor(truth,y)),x),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
and_star(xor(truth,truth),x) = and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),
inference(transitivity,[status(thm)],[127,114,105]) ).
tff(129,plain,
xor(and_star(xor(truth,truth),x),truth) = xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
and_star(xor(and_star(xor(truth,truth),x),truth),x) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x) = and_star(xor(and_star(xor(truth,truth),x),truth),x),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x) = x,
inference(transitivity,[status(thm)],[131,93,84,82,77,73,63,47,38]) ).
tff(133,plain,
implies(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),y) = implies(x,y),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),y) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
implies(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),y) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y))),
inference(unit_resolution,[status(thm)],[134,7]) ).
tff(136,plain,
xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y))) = implies(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),y),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),
inference(unit_resolution,[status(thm)],[137,112]) ).
tff(139,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))) = and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
| ( and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),
inference(unit_resolution,[status(thm)],[140,91]) ).
tff(142,plain,
and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)) = and_star(implies(x,y),xor(truth,y)),
inference(symmetry,[status(thm)],[29]) ).
tff(143,plain,
xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth) = xor(and_star(implies(x,y),xor(truth,y)),truth),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
xor(and_star(implies(x,y),xor(truth,y)),truth) = xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(implies(x,y),xor(truth,y)),truth) = xor(truth,and_star(implies(x,y),xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
xor(and_star(implies(x,y),xor(truth,y)),truth) = xor(truth,and_star(implies(x,y),xor(truth,y))),
inference(unit_resolution,[status(thm)],[145,17]) ).
tff(147,plain,
xor(truth,and_star(implies(x,y),xor(truth,y))) = xor(and_star(implies(x,y),xor(truth,y)),truth),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
xor(truth,and_star(implies(x,y),xor(truth,y))) = xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),
inference(transitivity,[status(thm)],[147,144]) ).
tff(149,plain,
and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y)) = and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)),
inference(transitivity,[status(thm)],[149,141,139]) ).
tff(151,plain,
xor(truth,and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y))) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y)),
inference(symmetry,[status(thm)],[149]) ).
tff(153,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))) = and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)),
inference(symmetry,[status(thm)],[141]) ).
tff(154,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))) = and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y)),
inference(transitivity,[status(thm)],[153,152]) ).
tff(155,plain,
xor(truth,and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y)))) = xor(truth,and_star(xor(truth,and_star(implies(x,y),xor(truth,y))),xor(truth,y))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),truth) = xor(truth,and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
xor(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),truth) = xor(truth,and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y)))),
inference(unit_resolution,[status(thm)],[156,17]) ).
tff(158,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))) = xor(truth,and_star(implies(x,y),xor(truth,y))),
inference(monotonicity,[status(thm)],[142]) ).
tff(159,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))) = xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),
inference(transitivity,[status(thm)],[158,147,144]) ).
tff(160,plain,
and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)) = and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),
inference(transitivity,[status(thm)],[160,141]) ).
tff(162,plain,
xor(and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)),truth) = xor(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),and_star(x,xor(truth,y))),truth),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
and_star(xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)),
inference(symmetry,[status(thm)],[160]) ).
tff(164,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,y),and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
and_star(xor(truth,y),and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),xor(truth,y)),
inference(unit_resolution,[status(thm)],[164,100]) ).
tff(166,plain,
and_star(xor(and_star(xor(truth,x),truth),truth),truth) = and_star(xor(and_star(xor(truth,truth),x),truth),x),
inference(symmetry,[status(thm)],[93]) ).
tff(167,plain,
xor(and_star(xor(truth,x),truth),truth) = and_star(xor(and_star(xor(truth,x),truth),truth),truth),
inference(symmetry,[status(thm)],[84]) ).
tff(168,plain,
and_star(x,truth) = xor(and_star(x,truth),falsehood),
inference(symmetry,[status(thm)],[47]) ).
tff(169,plain,
and_star(x,truth) = and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x),
inference(transitivity,[status(thm)],[168,62,72,76,81,167,166,130]) ).
tff(170,plain,
and_star(xor(truth,y),and_star(x,truth)) = and_star(xor(truth,y),and_star(xor(and_star(xor(truth,xor(truth,y)),and_star(x,xor(truth,y))),truth),x)),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(truth,y),x),truth) = and_star(xor(truth,y),and_star(x,truth)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
and_star(and_star(xor(truth,y),x),truth) = and_star(xor(truth,y),and_star(x,truth)),
inference(unit_resolution,[status(thm)],[171,112]) ).
tff(173,plain,
and_star(and_star(x,xor(truth,y)),truth) = and_star(and_star(xor(truth,y),x),truth),
inference(monotonicity,[status(thm)],[103]) ).
tff(174,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(and_star(x,xor(truth,y)),truth) = and_star(x,xor(truth,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
and_star(and_star(x,xor(truth,y)),truth) = and_star(x,xor(truth,y)),
inference(unit_resolution,[status(thm)],[174,36]) ).
tff(176,plain,
and_star(x,xor(truth,y)) = and_star(and_star(x,xor(truth,y)),truth),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(truth,x),truth) = xor(truth,xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
xor(xor(truth,x),truth) = xor(truth,xor(truth,x)),
inference(unit_resolution,[status(thm)],[177,17]) ).
tff(179,plain,
xor(truth,xor(truth,x)) = xor(xor(truth,x),truth),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
xor(truth,xor(truth,x)) = x,
inference(transitivity,[status(thm)],[179,77,73,63,47,38]) ).
tff(181,plain,
and_star(xor(truth,xor(truth,x)),xor(truth,y)) = and_star(x,xor(truth,y)),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
and_star(xor(truth,xor(truth,x)),xor(truth,y)) = and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)),
inference(transitivity,[status(thm)],[181,176,173,172,170,165,138,153,163]) ).
tff(183,plain,
xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth) = xor(and_star(xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))),xor(truth,y)),truth),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth) = implies(x,y),
inference(transitivity,[status(thm)],[183,162,157,155,151,136,133]) ).
tff(185,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth),xor(truth,y)) = and_star(implies(x,y),xor(truth,y)),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
| ( and_star(xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth),xor(truth,y)) = and_star(xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),xor(truth,x)),
inference(unit_resolution,[status(thm)],[186,91]) ).
tff(188,plain,
and_star(xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),xor(truth,y)),truth),xor(truth,y)),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
xor(truth,and_star(implies(y,x),xor(truth,x))) = xor(and_star(implies(y,x),xor(truth,x)),truth),
inference(symmetry,[status(thm)],[19]) ).
tff(190,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))) = xor(truth,and_star(implies(y,x),xor(truth,x))),
inference(monotonicity,[status(thm)],[23]) ).
tff(191,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))) = xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),
inference(transitivity,[status(thm)],[190,189,25]) ).
tff(192,plain,
and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)) = and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)) = and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
| ( and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),
inference(unit_resolution,[status(thm)],[194,91]) ).
tff(196,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))) = and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),
inference(unit_resolution,[status(thm)],[197,112]) ).
tff(199,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,x),and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
and_star(xor(truth,x),and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)),
inference(unit_resolution,[status(thm)],[199,100]) ).
tff(201,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,x),y) = and_star(y,xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
and_star(xor(truth,x),y) = and_star(y,xor(truth,x)),
inference(unit_resolution,[status(thm)],[201,100]) ).
tff(203,plain,
and_star(y,xor(truth,x)) = and_star(xor(truth,x),y),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))) = and_star(xor(truth,xor(truth,x)),and_star(xor(truth,x),y)),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
and_star(xor(truth,xor(truth,x)),and_star(xor(truth,x),y)) = and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(truth,xor(truth,x)),xor(truth,x)),y) = and_star(xor(truth,xor(truth,x)),and_star(xor(truth,x),y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
and_star(and_star(xor(truth,xor(truth,x)),xor(truth,x)),y) = and_star(xor(truth,xor(truth,x)),and_star(xor(truth,x),y)),
inference(unit_resolution,[status(thm)],[206,112]) ).
tff(208,plain,
( ~ ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
| ( and_star(xor(truth,xor(truth,x)),xor(truth,x)) = falsehood ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
and_star(xor(truth,xor(truth,x)),xor(truth,x)) = falsehood,
inference(unit_resolution,[status(thm)],[208,121]) ).
tff(210,plain,
falsehood = and_star(xor(truth,xor(truth,x)),xor(truth,x)),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
xor(truth,truth) = and_star(xor(truth,xor(truth,x)),xor(truth,x)),
inference(transitivity,[status(thm)],[125,59,210]) ).
tff(212,plain,
and_star(xor(truth,truth),y) = and_star(and_star(xor(truth,xor(truth,x)),xor(truth,x)),y),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
and_star(xor(truth,truth),y) = and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),
inference(transitivity,[status(thm)],[212,207,205]) ).
tff(214,plain,
xor(and_star(xor(truth,truth),y),truth) = xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
and_star(xor(and_star(xor(truth,truth),y),truth),y) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) )
| ( and_star(xor(and_star(xor(truth,truth),y),truth),y) = and_star(xor(and_star(xor(truth,y),truth),truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
and_star(xor(and_star(xor(truth,truth),y),truth),y) = and_star(xor(and_star(xor(truth,y),truth),truth),truth),
inference(unit_resolution,[status(thm)],[216,91]) ).
tff(218,plain,
and_star(xor(and_star(xor(truth,y),truth),truth),truth) = and_star(xor(and_star(xor(truth,truth),y),truth),y),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(and_star(xor(truth,y),truth),truth),truth) = xor(and_star(xor(truth,y),truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
and_star(xor(and_star(xor(truth,y),truth),truth),truth) = xor(and_star(xor(truth,y),truth),truth),
inference(unit_resolution,[status(thm)],[219,36]) ).
tff(221,plain,
xor(and_star(xor(truth,y),truth),truth) = and_star(xor(and_star(xor(truth,y),truth),truth),truth),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(truth,y),truth) = xor(truth,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
and_star(xor(truth,y),truth) = xor(truth,y),
inference(unit_resolution,[status(thm)],[222,36]) ).
tff(224,plain,
xor(truth,y) = and_star(xor(truth,y),truth),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
xor(xor(truth,y),truth) = xor(and_star(xor(truth,y),truth),truth),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(y,truth) = xor(truth,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
xor(y,truth) = xor(truth,y),
inference(unit_resolution,[status(thm)],[226,17]) ).
tff(228,plain,
xor(xor(y,truth),truth) = xor(xor(truth,y),truth),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(y,xor(truth,truth)) = xor(xor(y,truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
xor(y,xor(truth,truth)) = xor(xor(y,truth),truth),
inference(unit_resolution,[status(thm)],[229,70]) ).
tff(231,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(y,truth) = y ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
and_star(y,truth) = y,
inference(unit_resolution,[status(thm)],[231,36]) ).
tff(233,plain,
xor(and_star(y,truth),falsehood) = xor(y,xor(truth,truth)),
inference(monotonicity,[status(thm)],[232,61]) ).
tff(234,plain,
( ~ ! [X: $i] : ( xor(X,falsehood) = X )
| ( xor(and_star(y,truth),falsehood) = and_star(y,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
xor(and_star(y,truth),falsehood) = and_star(y,truth),
inference(unit_resolution,[status(thm)],[234,45]) ).
tff(236,plain,
and_star(y,truth) = xor(and_star(y,truth),falsehood),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
and_star(y,truth) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),
inference(transitivity,[status(thm)],[236,233,230,228,225,221,218,215]) ).
tff(238,plain,
and_star(xor(truth,x),and_star(y,truth)) = and_star(xor(truth,x),and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y)),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) )
| ( and_star(and_star(xor(truth,x),y),truth) = and_star(xor(truth,x),and_star(y,truth)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
and_star(and_star(xor(truth,x),y),truth) = and_star(xor(truth,x),and_star(y,truth)),
inference(unit_resolution,[status(thm)],[239,112]) ).
tff(241,plain,
and_star(and_star(y,xor(truth,x)),truth) = and_star(and_star(xor(truth,x),y),truth),
inference(monotonicity,[status(thm)],[203]) ).
tff(242,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(and_star(y,xor(truth,x)),truth) = and_star(y,xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
and_star(and_star(y,xor(truth,x)),truth) = and_star(y,xor(truth,x)),
inference(unit_resolution,[status(thm)],[242,36]) ).
tff(244,plain,
and_star(y,xor(truth,x)) = and_star(and_star(y,xor(truth,x)),truth),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
xor(y,xor(truth,truth)) = xor(and_star(y,truth),falsehood),
inference(symmetry,[status(thm)],[233]) ).
tff(246,plain,
xor(xor(y,truth),truth) = xor(y,xor(truth,truth)),
inference(symmetry,[status(thm)],[230]) ).
tff(247,plain,
xor(xor(truth,y),truth) = xor(xor(y,truth),truth),
inference(symmetry,[status(thm)],[228]) ).
tff(248,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(truth,y),truth) = xor(truth,xor(truth,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
xor(xor(truth,y),truth) = xor(truth,xor(truth,y)),
inference(unit_resolution,[status(thm)],[248,17]) ).
tff(250,plain,
xor(truth,xor(truth,y)) = xor(xor(truth,y),truth),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
xor(truth,xor(truth,y)) = y,
inference(transitivity,[status(thm)],[250,247,246,245,235,232]) ).
tff(252,plain,
and_star(xor(truth,xor(truth,y)),xor(truth,x)) = and_star(y,xor(truth,x)),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
and_star(xor(truth,xor(truth,y)),xor(truth,x)) = and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),
inference(transitivity,[status(thm)],[252,244,241,240,238,200,198,196,193]) ).
tff(254,plain,
xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth) = xor(and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),truth),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
xor(and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),truth) = xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),
inference(transitivity,[status(thm)],[192,195]) ).
tff(257,plain,
xor(and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),truth) = xor(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),truth),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
xor(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),truth) = xor(and_star(xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),xor(truth,x)),truth),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),truth) = xor(truth,and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
xor(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),truth) = xor(truth,and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x)))),
inference(unit_resolution,[status(thm)],[259,17]) ).
tff(261,plain,
xor(truth,and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x)))) = xor(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))),truth),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
xor(truth,and_star(implies(y,x),xor(truth,x))) = xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),
inference(transitivity,[status(thm)],[189,25]) ).
tff(263,plain,
and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x)) = and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
and_star(xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),xor(truth,x)) = and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))) = and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x)),
inference(transitivity,[status(thm)],[196,264]) ).
tff(266,plain,
xor(truth,and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x)))) = xor(truth,and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
xor(truth,and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x))) = xor(truth,and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x)))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),and_star(y,xor(truth,x))) = and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)),
inference(symmetry,[status(thm)],[198]) ).
tff(269,plain,
and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x)) = and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x)),
inference(transitivity,[status(thm)],[263,195,268]) ).
tff(270,plain,
xor(truth,and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x))) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x))) = xor(truth,and_star(xor(truth,and_star(implies(y,x),xor(truth,x))),xor(truth,x))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),x) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
implies(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),x) = xor(truth,and_star(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),xor(truth,x))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
xor(and_star(xor(truth,y),truth),truth) = xor(xor(truth,y),truth),
inference(symmetry,[status(thm)],[225]) ).
tff(275,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y) = and_star(xor(and_star(xor(truth,truth),y),truth),y),
inference(symmetry,[status(thm)],[215]) ).
tff(276,plain,
and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y) = y,
inference(transitivity,[status(thm)],[275,217,220,274,247,246,245,235,232]) ).
tff(277,plain,
implies(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),x) = implies(y,x),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
implies(y,x) = implies(and_star(xor(and_star(xor(truth,xor(truth,x)),and_star(y,xor(truth,x))),truth),y),x),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
implies(y,x) = xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),
inference(transitivity,[status(thm)],[278,273,271,267,261,258,255]) ).
tff(280,plain,
and_star(implies(y,x),xor(truth,x)) = and_star(xor(and_star(xor(truth,xor(truth,y)),xor(truth,x)),truth),xor(truth,x)),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)) = and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),
inference(transitivity,[status(thm)],[23,280,188,185,29]) ).
tff(282,plain,
xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth) = xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
xor(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y)),truth) = xor(and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x)),truth),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(implies(x,y),y) = xor(truth,and_star(implies(x,y),xor(truth,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
implies(implies(x,y),y) = xor(truth,and_star(implies(x,y),xor(truth,y))),
inference(unit_resolution,[status(thm)],[284,7]) ).
tff(286,plain,
implies(implies(x,y),y) = implies(implies(y,x),x),
inference(transitivity,[status(thm)],[285,147,144,283,26,19,10]) ).
tff(287,plain,
( ( implies(implies(x,y),y) != implies(implies(y,x),x) )
<=> ( implies(implies(x,y),y) != implies(implies(y,x),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(288,axiom,
implies(implies(x,y),y) != implies(implies(y,x),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
tff(289,plain,
implies(implies(x,y),y) != implies(implies(y,x),x),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
$false,
inference(unit_resolution,[status(thm)],[289,286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n028.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 4 17:32:30 UTC 2026
% 0.07/0.33 % CPUTime :
% 20.04/20.30 % SZS status Unsatisfiable
% 20.04/20.30 % SZS output start Proof
% See solution above
% 20.04/20.34 % E exiting
%------------------------------------------------------------------------------