%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET085-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:42:07 PM UTC 2026
% Result : Unsatisfiable 12.57s 2.15s
% Output : Proof 12.57s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t96,axiom,
sF2 = member(x,universal_class),
introduced(definition) ).
cnf(f92,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_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(t8,plain,
member(x,universal_class) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t109,plain,
member(x,universal_class) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t2485,plain,
sF2 = true,
inference(step,[status(thm)],[t96,t109]) ).
cnf(t128,plain,
true = sF2,
inference(orient,[status(thm)],[t2485]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/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(t59,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(t2763,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF2,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(step,[status(thm)],[t59,t128]) ).
cnf(t2764,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF2,or(eq(X1,X2),eq(X1,X3)),sF2) = true,
inference(step,[status(thm)],[t2763,t128]) ).
cnf(t2765,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF2,or(eq(X1,X2),eq(X1,X3)),sF2) = sF2,
inference(step,[status(thm)],[t2764,t128]) ).
cnf(t756,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF2,or(eq(X1,X2),eq(X1,X3)),sF2) = sF2,
inference(orient,[status(thm)],[t2765]) ).
cnf(f93,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_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(t106,plain,
eq(x,y) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t94,axiom,
sF0 = eq(x,y),
introduced(definition) ).
cnf(t2474,plain,
sF0 = false,
inference(step,[status(thm)],[t94,t106]) ).
cnf(t116,plain,
false = sF0,
inference(orient,[status(thm)],[t2474]) ).
cnf(t2478,plain,
eq(x,y) = sF0,
inference(step,[status(thm)],[t106,t116]) ).
cnf(t120,plain,
eq(x,y) = sF0,
inference(orient,[status(thm)],[t2478]) ).
cnf(t759,plain,
sF2 = ifeq(member(x,unordered_pair(y,X1)),sF2,or(sF0,eq(x,X1)),sF2),
inference(cp,[status(thm)],[t756,t120]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t112,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t2483,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t112,t116]) ).
cnf(t125,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t2483]) ).
cnf(t153,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t125]) ).
cnf(t3023,plain,
sF2 = ifeq(member(x,unordered_pair(y,X1)),sF2,eq(x,X1),sF2),
inference(step,[status(thm)],[t759,t153]) ).
cnf(t2100,plain,
ifeq(member(x,unordered_pair(y,X1)),sF2,eq(x,X1),sF2) = sF2,
inference(orient,[status(thm)],[t3023]) ).
cnf(f94,negated_conjecture,
x != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
fof(f94_nnf,plain,
x != z,
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
x != z,
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
x != z,
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t6,plain,
eq(x,z) = false,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t107,plain,
eq(x,z) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t2480,plain,
eq(x,z) = sF0,
inference(step,[status(thm)],[t107,t116]) ).
cnf(t122,plain,
eq(x,z) = sF0,
inference(orient,[status(thm)],[t2480]) ).
cnf(t2102,plain,
sF2 = ifeq(member(x,unordered_pair(y,z)),sF2,sF0,sF2),
inference(cp,[status(thm)],[t2100,t122]) ).
cnf(t99,axiom,
sF5 = unordered_pair(y,z),
introduced(definition) ).
cnf(t147,plain,
unordered_pair(y,z) = sF5,
inference(orient,[status(thm)],[t99]) ).
cnf(t3024,plain,
sF2 = ifeq(member(x,sF5),sF2,sF0,sF2),
inference(step,[status(thm)],[t2102,t147]) ).
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(t45,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t2586,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),true) = true,
inference(step,[status(thm)],[t45,t128]) ).
cnf(t2587,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = true,
inference(step,[status(thm)],[t2586,t128]) ).
cnf(t2588,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = sF2,
inference(step,[status(thm)],[t2587,t128]) ).
cnf(t313,plain,
ifeq(member(X1,universal_class),sF2,member(X1,unordered_pair(X1,X2)),sF2) = sF2,
inference(orient,[status(thm)],[t2588]) ).
cnf(f91,negated_conjecture,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
fof(f91_nnf,plain,
unordered_pair(y,z) = singleton(x),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
unordered_pair(y,z) = singleton(x),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(u8,axiom,
unordered_pair(y,z) = singleton(x),
inference(equality_encoding,[status(esa)],[c91]) ).
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(t20,plain,
unordered_pair(y,z) = unordered_pair(x,x),
inference(definition_unfolding,[status(thm)],[u8,d0]) ).
cnf(t115,plain,
unordered_pair(x,x) = unordered_pair(y,z),
inference(orient,[status(thm)],[t20]) ).
cnf(t2501,plain,
unordered_pair(x,x) = sF5,
inference(step,[status(thm)],[t115,t147]) ).
cnf(t148,plain,
unordered_pair(x,x) = sF5,
inference(orient,[status(thm)],[t2501]) ).
cnf(t316,plain,
sF2 = ifeq(member(x,universal_class),sF2,member(x,sF5),sF2),
inference(cp,[status(thm)],[t313,t148]) ).
cnf(t2495,plain,
member(x,universal_class) = sF2,
inference(step,[status(thm)],[t109,t128]) ).
cnf(t138,plain,
member(x,universal_class) = sF2,
inference(orient,[status(thm)],[t2495]) ).
cnf(t2589,plain,
sF2 = ifeq(sF2,sF2,member(x,sF5),sF2),
inference(step,[status(thm)],[t316,t138]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t150,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t2590,plain,
sF2 = member(x,sF5),
inference(step,[status(thm)],[t2589,t150]) ).
cnf(t320,plain,
member(x,sF5) = sF2,
inference(orient,[status(thm)],[t2590]) ).
cnf(t3025,plain,
sF2 = ifeq(sF2,sF2,sF0,sF2),
inference(step,[status(thm)],[t3024,t320]) ).
cnf(t3026,plain,
sF2 = sF0,
inference(step,[status(thm)],[t3025,t150]) ).
cnf(t2103,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t3026]) ).
cnf(t3041,plain,
true = sF0,
inference(step,[status(thm)],[t128,t2103]) ).
cnf(t2118,plain,
true = sF0,
inference(orient,[status(thm)],[t3041]) ).
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,c94]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t2118]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t116]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET085-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 09:41:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.57/2.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.57/2.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------