%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET117-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:42:21 PM UTC 2026
% Result : Unsatisfiable 8.29s 1.57s
% Output : Proof 8.29s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t92,axiom,
sF1 = ifeq(member(x,universal_class),true,false,true),
introduced(definition) ).
cnf(f92,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_2) ).
fof(f92_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(t6,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t107,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t91,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t1041,plain,
sF0 = false,
inference(step,[status(thm)],[t91,t107]) ).
cnf(t113,plain,
false = sF0,
inference(orient,[status(thm)],[t1041]) ).
cnf(t1045,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t107,t113]) ).
cnf(t117,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t1045]) ).
cnf(t1057,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t92,t117]) ).
cnf(t1058,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t1057,t113]) ).
cnf(t20,plain,
ifeq(member(x,universal_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t1055,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t20,t117]) ).
cnf(t1056,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t1055,t113]) ).
cnf(t150,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t1056]) ).
cnf(t1059,plain,
sF1 = true,
inference(step,[status(thm)],[t1058,t150]) ).
cnf(t161,plain,
true = sF1,
inference(orient,[status(thm)],[t1059]) ).
cnf(f10,axiom,
member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f10_nnf,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t13,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t125,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t1073,plain,
member(unordered_pair(X1,X2),universal_class) = sF1,
inference(step,[status(thm)],[t125,t161]) ).
cnf(t177,plain,
member(unordered_pair(X1,X2),universal_class) = sF1,
inference(orient,[status(thm)],[t1073]) ).
cnf(f91,negated_conjecture,
ordered_pair(first(x),second(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_1) ).
fof(f91_nnf,plain,
ordered_pair(first(x),second(x)) = x,
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
ordered_pair(first(x),second(x)) = x,
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(u25,axiom,
ordered_pair(first(x),second(x)) = x,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f12_nnf,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(d0,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(d1,axiom,
unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = ordered_pair(X0,X1),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t54,plain,
unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x,
inference(definition_unfolding,[status(thm)],[u25,d1]) ).
cnf(t93,axiom,
sF2 = first(x),
introduced(definition) ).
cnf(t103,plain,
first(x) = sF2,
inference(orient,[status(thm)],[t93]) ).
cnf(t1318,plain,
unordered_pair(unordered_pair(sF2,first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x,
inference(step,[status(thm)],[t54,t103]) ).
cnf(t1319,plain,
unordered_pair(unordered_pair(sF2,sF2),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x,
inference(step,[status(thm)],[t1318,t103]) ).
cnf(t94,axiom,
sF3 = unordered_pair(first(x),first(x)),
introduced(definition) ).
cnf(t1049,plain,
sF3 = unordered_pair(sF2,first(x)),
inference(step,[status(thm)],[t94,t103]) ).
cnf(t1050,plain,
sF3 = unordered_pair(sF2,sF2),
inference(step,[status(thm)],[t1049,t103]) ).
cnf(t128,plain,
unordered_pair(sF2,sF2) = sF3,
inference(orient,[status(thm)],[t1050]) ).
cnf(t1320,plain,
unordered_pair(sF3,unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x,
inference(step,[status(thm)],[t1319,t128]) ).
cnf(t1321,plain,
unordered_pair(sF3,unordered_pair(sF2,unordered_pair(second(x),second(x)))) = x,
inference(step,[status(thm)],[t1320,t103]) ).
cnf(t95,axiom,
sF4 = second(x),
introduced(definition) ).
cnf(t104,plain,
second(x) = sF4,
inference(orient,[status(thm)],[t95]) ).
cnf(t1322,plain,
unordered_pair(sF3,unordered_pair(sF2,unordered_pair(sF4,second(x)))) = x,
inference(step,[status(thm)],[t1321,t104]) ).
cnf(t1323,plain,
unordered_pair(sF3,unordered_pair(sF2,unordered_pair(sF4,sF4))) = x,
inference(step,[status(thm)],[t1322,t104]) ).
cnf(t96,axiom,
sF5 = unordered_pair(second(x),second(x)),
introduced(definition) ).
cnf(t1051,plain,
sF5 = unordered_pair(sF4,second(x)),
inference(step,[status(thm)],[t96,t104]) ).
cnf(t1052,plain,
sF5 = unordered_pair(sF4,sF4),
inference(step,[status(thm)],[t1051,t104]) ).
cnf(t131,plain,
unordered_pair(sF4,sF4) = sF5,
inference(orient,[status(thm)],[t1052]) ).
cnf(t1324,plain,
unordered_pair(sF3,unordered_pair(sF2,sF5)) = x,
inference(step,[status(thm)],[t1323,t131]) ).
cnf(t97,axiom,
sF6 = unordered_pair(first(x),unordered_pair(second(x),second(x))),
introduced(definition) ).
cnf(t1112,plain,
sF6 = unordered_pair(sF2,unordered_pair(second(x),second(x))),
inference(step,[status(thm)],[t97,t103]) ).
cnf(t1113,plain,
sF6 = unordered_pair(sF2,unordered_pair(sF4,second(x))),
inference(step,[status(thm)],[t1112,t104]) ).
cnf(t1114,plain,
sF6 = unordered_pair(sF2,unordered_pair(sF4,sF4)),
inference(step,[status(thm)],[t1113,t104]) ).
cnf(t1115,plain,
sF6 = unordered_pair(sF2,sF5),
inference(step,[status(thm)],[t1114,t131]) ).
cnf(t241,plain,
unordered_pair(sF2,sF5) = sF6,
inference(orient,[status(thm)],[t1115]) ).
cnf(t1325,plain,
unordered_pair(sF3,sF6) = x,
inference(step,[status(thm)],[t1324,t241]) ).
cnf(t801,plain,
unordered_pair(sF3,sF6) = x,
inference(orient,[status(thm)],[t1325]) ).
cnf(t802,plain,
sF1 = member(x,universal_class),
inference(cp,[status(thm)],[t177,t801]) ).
cnf(t1326,plain,
sF1 = sF0,
inference(step,[status(thm)],[t802,t117]) ).
cnf(t818,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t1326]) ).
cnf(t1353,plain,
true = sF0,
inference(step,[status(thm)],[t161,t818]) ).
cnf(t845,plain,
true = sF0,
inference(orient,[status(thm)],[t1353]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/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,c92]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t845]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t113]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET117-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:52:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.29/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.29/1.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------