%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET078-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:42:00 PM UTC 2026
% Result : Unsatisfiable 6.07s 1.25s
% Output : Proof 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 49 unt; 0 def)
% Number of atoms : 73 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 27 ~; 12 |; 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 : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 51 ( 14 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f9_nnf,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t41,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t309,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X2,X1)),true) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t91,axiom,
sF1 = unordered_pair(x,unordered_pair(y,y)),
introduced(definition) ).
cnf(t90,axiom,
sF0 = unordered_pair(y,y),
introduced(definition) ).
cnf(t105,plain,
unordered_pair(y,y) = sF0,
inference(orient,[status(thm)],[t90]) ).
cnf(t427,plain,
sF1 = unordered_pair(x,sF0),
inference(step,[status(thm)],[t91,t105]) ).
cnf(t112,plain,
unordered_pair(x,sF0) = sF1,
inference(orient,[status(thm)],[t427]) ).
cnf(t313,plain,
true = ifeq(member(sF0,universal_class),true,member(sF0,sF1),true),
inference(cp,[status(thm)],[t309,t112]) ).
cnf(f10,axiom,
member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/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(t12,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t107,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t108,plain,
true = member(sF0,universal_class),
inference(cp,[status(thm)],[t107,t105]) ).
cnf(t109,plain,
member(sF0,universal_class) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(t472,plain,
true = ifeq(true,true,member(sF0,sF1),true),
inference(step,[status(thm)],[t313,t109]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t106,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t473,plain,
true = member(sF0,sF1),
inference(step,[status(thm)],[t472,t106]) ).
cnf(f91,negated_conjecture,
~ member(singleton(y),unordered_pair(x,singleton(y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_singletons_are_sets_1) ).
fof(f91_nnf,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
~ member(singleton(y),unordered_pair(x,singleton(y))),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(u11,axiom,
member(singleton(y),unordered_pair(x,singleton(y))) = false,
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(t32,plain,
member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))) = false,
inference(definition_unfolding,[status(thm)],[u11,d0]) ).
cnf(t429,plain,
member(sF0,unordered_pair(x,unordered_pair(y,y))) = false,
inference(step,[status(thm)],[t32,t105]) ).
cnf(t430,plain,
member(sF0,unordered_pair(x,sF0)) = false,
inference(step,[status(thm)],[t429,t105]) ).
cnf(t431,plain,
member(sF0,sF1) = false,
inference(step,[status(thm)],[t430,t112]) ).
cnf(t163,plain,
member(sF0,sF1) = false,
inference(orient,[status(thm)],[t431]) ).
cnf(t92,axiom,
sF2 = member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))),
introduced(definition) ).
cnf(t432,plain,
sF2 = member(sF0,unordered_pair(x,unordered_pair(y,y))),
inference(step,[status(thm)],[t92,t105]) ).
cnf(t433,plain,
sF2 = member(sF0,unordered_pair(x,sF0)),
inference(step,[status(thm)],[t432,t105]) ).
cnf(t434,plain,
sF2 = member(sF0,sF1),
inference(step,[status(thm)],[t433,t112]) ).
cnf(t435,plain,
sF2 = false,
inference(step,[status(thm)],[t434,t163]) ).
cnf(t165,plain,
false = sF2,
inference(orient,[status(thm)],[t435]) ).
cnf(t441,plain,
member(sF0,sF1) = sF2,
inference(step,[status(thm)],[t163,t165]) ).
cnf(t173,plain,
member(sF0,sF1) = sF2,
inference(orient,[status(thm)],[t441]) ).
cnf(t474,plain,
true = sF2,
inference(step,[status(thm)],[t473,t173]) ).
cnf(t315,plain,
true = sF2,
inference(orient,[status(thm)],[t474]) ).
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,c91]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t315]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t165]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET078-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 09:41:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.07/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------