%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 34
% Syntax : Number of formulae : 85 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 116 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 13 ~; 9 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 102 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(and_star_type,type,
and_star: ( $i * $i ) > $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(not_type,type,
not: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( and_star(X,truth) = X )
<=> ( and_star(X,truth) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( and_star(X,truth) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
tff(5,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(x,truth) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
and_star(x,truth) = x,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( xor(X,falsehood) = X )
<=> ( xor(X,falsehood) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( xor(X,falsehood) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
tff(14,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( xor(X,falsehood) = X )
| ( xor(and_star(x,truth),falsehood) = and_star(x,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
xor(and_star(x,truth),falsehood) = and_star(x,truth),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(( ( not(X) = xor(X,truth) )
<=> ( not(X) = xor(X,truth) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : ( not(X) = xor(X,truth) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
tff(23,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ( not(X) = xor(X,truth) )
| ( not(truth) = xor(truth,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
not(truth) = xor(truth,truth),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ( not(truth) = falsehood )
<=> ( not(truth) = falsehood ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
tff(30,plain,
not(truth) = falsehood,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
falsehood = xor(truth,truth),
inference(transitivity,[status(thm)],[31,27]) ).
tff(33,plain,
xor(and_star(x,truth),falsehood) = xor(x,xor(truth,truth)),
inference(monotonicity,[status(thm)],[9,32]) ).
tff(34,plain,
xor(x,xor(truth,truth)) = xor(and_star(x,truth),falsehood),
inference(symmetry,[status(thm)],[33]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,axiom,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
tff(39,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,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(43,plain,
xor(x,xor(truth,truth)) = xor(xor(x,truth),truth),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
xor(xor(x,truth),truth) = xor(x,xor(truth,truth)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,axiom,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
tff(49,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,x),truth) = and_star(truth,xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
and_star(xor(truth,x),truth) = and_star(truth,xor(truth,x)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(truth,x),truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
and_star(xor(truth,x),truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[54,7]) ).
tff(56,plain,
xor(truth,x) = and_star(xor(truth,x),truth),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [Y: $i,X: $i] :
refl(( ( xor(X,Y) = xor(Y,X) )
<=> ( xor(X,Y) = xor(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(58,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)],[57]) ).
tff(59,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(60,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
tff(61,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(x,truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
xor(x,truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
xor(x,truth) = and_star(truth,xor(truth,x)),
inference(transitivity,[status(thm)],[65,56,53]) ).
tff(67,plain,
xor(xor(x,truth),truth) = xor(and_star(truth,xor(truth,x)),truth),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
xor(and_star(truth,xor(truth,x)),truth) = xor(xor(x,truth),truth),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(truth,xor(truth,x)),truth) = xor(truth,and_star(truth,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
xor(and_star(truth,xor(truth,x)),truth) = xor(truth,and_star(truth,xor(truth,x))),
inference(unit_resolution,[status(thm)],[69,63]) ).
tff(71,plain,
xor(truth,and_star(truth,xor(truth,x))) = xor(and_star(truth,xor(truth,x)),truth),
inference(symmetry,[status(thm)],[70]) ).
tff(72,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(73,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)],[72]) ).
tff(74,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(75,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
tff(76,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(truth,x) = xor(truth,and_star(truth,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
implies(truth,x) = xor(truth,and_star(truth,xor(truth,x))),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
implies(truth,x) = x,
inference(transitivity,[status(thm)],[80,71,68,44,34,18,9]) ).
tff(82,plain,
( ( implies(truth,x) != x )
<=> ( implies(truth,x) != x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
implies(truth,x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
tff(84,plain,
implies(truth,x) != x,
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 08:59:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42 % SZS output start Proof
% See solution above
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------