%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET083-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 02:42:04 PM UTC 2026
% Result : Unsatisfiable 8.48s 1.57s
% Output : Proof 8.48s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t93,axiom,
sF1 = member(x,universal_class),
introduced(definition) ).
cnf(f92,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_2) ).
fof(f92_nnf,plain,
member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f92]) ).
cnf(c92,plain,
member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f92_nnf]) ).
cnf(t7,plain,
member(x,universal_class) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t104,plain,
member(x,universal_class) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t2479,plain,
sF1 = true,
inference(step,[status(thm)],[t93,t104]) ).
cnf(t120,plain,
true = sF1,
inference(orient,[status(thm)],[t2479]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t57,plain,
ifeq(member(X1,unordered_pair(X2,X3)),true,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t2751,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(step,[status(thm)],[t57,t120]) ).
cnf(t2752,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = true,
inference(step,[status(thm)],[t2751,t120]) ).
cnf(t2753,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = sF1,
inference(step,[status(thm)],[t2752,t120]) ).
cnf(t747,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = sF1,
inference(orient,[status(thm)],[t2753]) ).
cnf(f93,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_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(t102,plain,
eq(x,y) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t92,axiom,
sF0 = eq(x,y),
introduced(definition) ).
cnf(t2471,plain,
sF0 = false,
inference(step,[status(thm)],[t92,t102]) ).
cnf(t111,plain,
false = sF0,
inference(orient,[status(thm)],[t2471]) ).
cnf(t2475,plain,
eq(x,y) = sF0,
inference(step,[status(thm)],[t102,t111]) ).
cnf(t115,plain,
eq(x,y) = sF0,
inference(orient,[status(thm)],[t2475]) ).
cnf(t750,plain,
sF1 = ifeq(member(x,unordered_pair(y,X1)),sF1,or(sF0,eq(x,X1)),sF1),
inference(cp,[status(thm)],[t747,t115]) ).
cnf(t10,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t107,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t2478,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t107,t111]) ).
cnf(t118,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t2478]) ).
cnf(t145,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t118]) ).
cnf(t3016,plain,
sF1 = ifeq(member(x,unordered_pair(y,X1)),sF1,eq(x,X1),sF1),
inference(step,[status(thm)],[t750,t145]) ).
cnf(t2104,plain,
ifeq(member(x,unordered_pair(y,X1)),sF1,eq(x,X1),sF1) = sF1,
inference(orient,[status(thm)],[t3016]) ).
cnf(t2105,plain,
sF1 = ifeq(member(x,unordered_pair(y,y)),sF1,sF0,sF1),
inference(cp,[status(thm)],[t2104,t115]) ).
cnf(t95,axiom,
sF3 = unordered_pair(y,y),
introduced(definition) ).
cnf(t139,plain,
unordered_pair(y,y) = sF3,
inference(orient,[status(thm)],[t95]) ).
cnf(t3017,plain,
sF1 = ifeq(member(x,sF3),sF1,sF0,sF1),
inference(step,[status(thm)],[t2105,t139]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/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(t43,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t2574,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t43,t120]) ).
cnf(t2575,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = true,
inference(step,[status(thm)],[t2574,t120]) ).
cnf(t2576,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = sF1,
inference(step,[status(thm)],[t2575,t120]) ).
cnf(t295,plain,
ifeq(member(X1,universal_class),sF1,member(X1,unordered_pair(X1,X2)),sF1) = sF1,
inference(orient,[status(thm)],[t2576]) ).
cnf(f91,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_1) ).
fof(f91_nnf,plain,
singleton(x) = singleton(y),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
singleton(x) = singleton(y),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(u8,axiom,
singleton(x) = singleton(y),
inference(equality_encoding,[status(esa)],[c91]) ).
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(t18,plain,
unordered_pair(y,y) = unordered_pair(x,x),
inference(definition_unfolding,[status(thm)],[u8,d0]) ).
cnf(t110,plain,
unordered_pair(x,x) = unordered_pair(y,y),
inference(orient,[status(thm)],[t18]) ).
cnf(t2495,plain,
unordered_pair(x,x) = sF3,
inference(step,[status(thm)],[t110,t139]) ).
cnf(t140,plain,
unordered_pair(x,x) = sF3,
inference(orient,[status(thm)],[t2495]) ).
cnf(t298,plain,
sF1 = ifeq(member(x,universal_class),sF1,member(x,sF3),sF1),
inference(cp,[status(thm)],[t295,t140]) ).
cnf(t2489,plain,
member(x,universal_class) = sF1,
inference(step,[status(thm)],[t104,t120]) ).
cnf(t130,plain,
member(x,universal_class) = sF1,
inference(orient,[status(thm)],[t2489]) ).
cnf(t2577,plain,
sF1 = ifeq(sF1,sF1,member(x,sF3),sF1),
inference(step,[status(thm)],[t298,t130]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t144,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t2578,plain,
sF1 = member(x,sF3),
inference(step,[status(thm)],[t2577,t144]) ).
cnf(t302,plain,
member(x,sF3) = sF1,
inference(orient,[status(thm)],[t2578]) ).
cnf(t3018,plain,
sF1 = ifeq(sF1,sF1,sF0,sF1),
inference(step,[status(thm)],[t3017,t302]) ).
cnf(t3019,plain,
sF1 = sF0,
inference(step,[status(thm)],[t3018,t144]) ).
cnf(t2106,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t3019]) ).
cnf(t3034,plain,
true = sF0,
inference(step,[status(thm)],[t120,t2106]) ).
cnf(t2121,plain,
true = sF0,
inference(orient,[status(thm)],[t3034]) ).
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,c93]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t2121]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t111]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET083-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 09:46:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.48/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.48/1.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------