%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET024-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:41:33 PM UTC 2026
% Result : Unsatisfiable 4.62s 6.17s
% Output : Proof 4.62s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t91,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(f91,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_in_its_singleton_1) ).
fof(f91_nnf,plain,
member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t6,plain,
member(x,universal_class) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t101,plain,
member(x,universal_class) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t327,plain,
sF0 = true,
inference(step,[status(thm)],[t91,t101]) ).
cnf(t107,plain,
true = sF0,
inference(orient,[status(thm)],[t327]) ).
cnf(t93,axiom,
sF2 = member(x,unordered_pair(x,x)),
introduced(definition) ).
cnf(t92,axiom,
sF1 = unordered_pair(x,x),
introduced(definition) ).
cnf(t126,plain,
unordered_pair(x,x) = sF1,
inference(orient,[status(thm)],[t92]) ).
cnf(t349,plain,
sF2 = member(x,sF1),
inference(step,[status(thm)],[t93,t126]) ).
cnf(f92,negated_conjecture,
~ member(x,singleton(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_in_its_singleton_2) ).
fof(f92_nnf,plain,
~ member(x,singleton(x)),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
~ member(x,singleton(x)),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
~ member(x,singleton(x)),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(u11,axiom,
member(x,singleton(x)) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/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(t14,plain,
member(x,unordered_pair(x,x)) = false,
inference(definition_unfolding,[status(thm)],[u11,d0]) ).
cnf(t346,plain,
member(x,sF1) = false,
inference(step,[status(thm)],[t14,t126]) ).
cnf(t133,plain,
member(x,sF1) = false,
inference(orient,[status(thm)],[t346]) ).
cnf(t350,plain,
sF2 = false,
inference(step,[status(thm)],[t349,t133]) ).
cnf(t136,plain,
false = sF2,
inference(orient,[status(thm)],[t350]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t42,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t435,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t42,t107]) ).
cnf(t436,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = true,
inference(step,[status(thm)],[t435,t107]) ).
cnf(t437,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(step,[status(thm)],[t436,t107]) ).
cnf(t292,plain,
ifeq(member(X1,universal_class),sF0,member(X1,unordered_pair(X1,X2)),sF0) = sF0,
inference(orient,[status(thm)],[t437]) ).
cnf(t295,plain,
sF0 = ifeq(member(x,universal_class),sF0,member(x,sF1),sF0),
inference(cp,[status(thm)],[t292,t126]) ).
cnf(t339,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t101,t107]) ).
cnf(t119,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t339]) ).
cnf(t438,plain,
sF0 = ifeq(sF0,sF0,member(x,sF1),sF0),
inference(step,[status(thm)],[t295,t119]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t129,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t439,plain,
sF0 = member(x,sF1),
inference(step,[status(thm)],[t438,t129]) ).
cnf(t356,plain,
member(x,sF1) = sF2,
inference(step,[status(thm)],[t133,t136]) ).
cnf(t142,plain,
member(x,sF1) = sF2,
inference(orient,[status(thm)],[t356]) ).
cnf(t440,plain,
sF0 = sF2,
inference(step,[status(thm)],[t439,t142]) ).
cnf(t298,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t440]) ).
cnf(t445,plain,
false = sF0,
inference(step,[status(thm)],[t136,t298]) ).
cnf(t303,plain,
false = sF0,
inference(orient,[status(thm)],[t445]) ).
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,c92]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t107]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t303]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET024-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/5.48 % Computer : n012.cluster.edu
% 0.03/5.48 % Model : x86_64 x86_64
% 0.03/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.48 % Memory : 8046.5625MB
% 0.03/5.48 % OS : Linux 6.8.0-71-generic
% 0.03/5.48 % CPULimit : 300
% 0.03/5.48 % WCLimit : 300
% 0.03/5.48 % DateTime : Thu Sep 24 09:15:28 UTC 2026
% 0.03/5.49 % CPUTime :
% 0.03/5.49 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.62/6.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/6.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------