%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET059-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 02:41:46 PM UTC 2026
% Result : Unsatisfiable 3.13s 6.17s
% Output : Proof 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 47 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 23 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t93,axiom,
sF1 = ifeq(x,y,false,true),
introduced(definition) ).
cnf(t92,axiom,
sF0 = eq(x,y),
introduced(definition) ).
cnf(f93,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality4_3) ).
fof(f93_nnf,plain,
x != y,
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
x != y,
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
x != y,
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(t5,plain,
eq(x,y) = false,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t103,plain,
eq(x,y) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t522,plain,
sF0 = false,
inference(step,[status(thm)],[t92,t103]) ).
cnf(t110,plain,
false = sF0,
inference(orient,[status(thm)],[t522]) ).
cnf(t533,plain,
sF1 = ifeq(x,y,sF0,true),
inference(step,[status(thm)],[t93,t110]) ).
cnf(t13,plain,
ifeq(x,y,false,true) = true,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t530,plain,
ifeq(x,y,sF0,true) = true,
inference(step,[status(thm)],[t13,t110]) ).
cnf(t124,plain,
ifeq(x,y,sF0,true) = true,
inference(orient,[status(thm)],[t530]) ).
cnf(t534,plain,
sF1 = true,
inference(step,[status(thm)],[t533,t124]) ).
cnf(t130,plain,
true = sF1,
inference(orient,[status(thm)],[t534]) ).
cnf(t526,plain,
eq(x,y) = sF0,
inference(step,[status(thm)],[t103,t110]) ).
cnf(t114,plain,
eq(x,y) = sF0,
inference(orient,[status(thm)],[t526]) ).
cnf(t388,plain,
eq(y,y) = sF0,
inference(rw,[status(thm)],[t114]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t102,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t540,plain,
eq(X1,X1) = sF1,
inference(step,[status(thm)],[t102,t130]) ).
cnf(t136,plain,
eq(X1,X1) = sF1,
inference(orient,[status(thm)],[t540]) ).
cnf(t671,plain,
sF1 = sF0,
inference(step,[status(thm)],[t388,t136]) ).
cnf(t403,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t671]) ).
cnf(t692,plain,
true = sF0,
inference(step,[status(thm)],[t130,t403]) ).
cnf(t424,plain,
true = sF0,
inference(orient,[status(thm)],[t692]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c93]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t424]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t110]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET059-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n008.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 09:29:32 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.13/6.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/6.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------