%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET024-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:41:33 PM UTC 2026
% Result : Unsatisfiable 12.03s 5.20s
% Output : Proof 12.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 73 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 46 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 61 ( 8 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f5_nnf,plain,
! [U,X,Y] :
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [U,X,Y] :
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 != X1
| ~ little_set(X0)
| member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t179,plain,
ifeq(little_set(X1),true,ifeq(X1,X2,member(X1,non_ordered_pair(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t835,plain,
ifeq(little_set(X1),true,ifeq(X1,X2,member(X1,non_ordered_pair(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t179]) ).
cnf(f150,negated_conjecture,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_membership_of_singleton_set) ).
fof(f150_nnf,plain,
~ member(a,singleton_set(a)),
inference(nnf_transformation,[status(thm)],[f150]) ).
fof(f150_sk,plain,
~ member(a,singleton_set(a)),
inference(skolemisation,[status(esa)],[f150_nnf]) ).
cnf(c150,plain,
~ member(a,singleton_set(a)),
inference(cnf_transformation,[status(esa)],[f150_sk]) ).
cnf(u3,axiom,
member(a,singleton_set(a)) = false,
inference(equality_encoding,[status(esa)],[c150]) ).
cnf(f8,axiom,
singleton_set(X) = non_ordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f8_nnf,plain,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
singleton_set(X0) = non_ordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(d0,axiom,
singleton_set(X0) = non_ordered_pair(X0,X0),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t17,plain,
member(a,non_ordered_pair(a,a)) = false,
inference(definition_unfolding,[status(thm)],[u3,d0]) ).
cnf(t1355,plain,
member(a,non_ordered_pair(a,a)) = false,
inference(orient,[status(thm)],[t17]) ).
cnf(t1367,plain,
true = ifeq(little_set(a),true,ifeq(a,a,false,true),true),
inference(cp,[status(thm)],[t835,t1355]) ).
cnf(f149,hypothesis,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
fof(f149_nnf,plain,
little_set(a),
inference(nnf_transformation,[status(thm)],[f149]) ).
cnf(c149,plain,
little_set(a),
inference(cnf_transformation,[status(esa)],[f149_nnf]) ).
cnf(t1,plain,
little_set(a) = true,
inference(equality_encoding,[status(esa)],[c149]) ).
cnf(t1788,plain,
little_set(a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t7054,plain,
true = ifeq(true,true,ifeq(a,a,false,true),true),
inference(step,[status(thm)],[t1367,t1788]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t250,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t7055,plain,
true = ifeq(a,a,false,true),
inference(step,[status(thm)],[t7054,t250]) ).
cnf(t7056,plain,
true = false,
inference(step,[status(thm)],[t7055,t250]) ).
cnf(t6860,plain,
false = true,
inference(orient,[status(thm)],[t7056]) ).
cnf(f30,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f30_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f57,axiom,
~ member(Z,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f57_nnf,plain,
! [Z] : ~ member(Z,empty_set),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [Z] : ~ member(Z,empty_set),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f70,axiom,
( X != Y
| ~ proper_subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
fof(f70_nnf,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f94,axiom,
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
fof(f94_nnf,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c30,c57,c70,c94,c150]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6860]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:21:08 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.03/5.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.03/5.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------