%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET025-9 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:41:35 PM UTC 2026
% Result : Unsatisfiable 15.28s 2.37s
% Output : Proof 15.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 42 unt; 0 def)
% Number of atoms : 78 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 42 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 72 ( 16 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f7_nnf,plain,
! [X,Y] : little_set(non_ordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] : little_set(non_ordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t13,plain,
little_set(non_ordered_pair(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t447,plain,
little_set(non_ordered_pair(X1,X2)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f9,axiom,
ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f9_nnf,plain,
! [X,Y] : ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] : ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t44,plain,
non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)) = ordered_pair(X1,X2),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t615,plain,
non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)) = ordered_pair(X1,X2),
inference(orient,[status(thm)],[t44]) ).
cnf(t618,plain,
true = little_set(ordered_pair(X1,X2)),
inference(cp,[status(thm)],[t447,t615]) ).
cnf(t1186,plain,
little_set(ordered_pair(X1,X2)) = true,
inference(orient,[status(thm)],[t618]) ).
cnf(f12,axiom,
( X = ordered_pair(f2(X),f3(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
fof(f12_nnf,plain,
! [X] :
( X = ordered_pair(f2(X),f3(X))
| ~ ordered_pair_predicate(X) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] :
( X = ordered_pair(f2(X),f3(X))
| ~ ordered_pair_predicate(X) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( X0 = ordered_pair(f2(X0),f3(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t115,plain,
ifeq(ordered_pair_predicate(X1),true,X1,ordered_pair(f2(X1),f3(X1))) = ordered_pair(f2(X1),f3(X1)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t344,plain,
ifeq(ordered_pair_predicate(X1),true,X1,ordered_pair(f2(X1),f3(X1))) = ordered_pair(f2(X1),f3(X1)),
inference(orient,[status(thm)],[t115]) ).
cnf(f141,hypothesis,
ordered_pair_predicate(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
fof(f141_nnf,plain,
ordered_pair_predicate(a),
inference(nnf_transformation,[status(thm)],[f141]) ).
cnf(c141,plain,
ordered_pair_predicate(a),
inference(cnf_transformation,[status(esa)],[f141_nnf]) ).
cnf(t5,plain,
ordered_pair_predicate(a) = true,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(t664,plain,
ordered_pair_predicate(a) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t670,plain,
ordered_pair(f2(a),f3(a)) = ifeq(true,true,a,ordered_pair(f2(a),f3(a))),
inference(cp,[status(thm)],[t344,t664]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t158,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t2457,plain,
ordered_pair(f2(a),f3(a)) = a,
inference(step,[status(thm)],[t670,t158]) ).
cnf(t2364,plain,
ordered_pair(f2(a),f3(a)) = a,
inference(orient,[status(thm)],[t2457]) ).
cnf(t2365,plain,
true = little_set(a),
inference(cp,[status(thm)],[t1186,t2364]) ).
cnf(f142,negated_conjecture,
~ little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_predicate_is_small) ).
fof(f142_nnf,plain,
~ little_set(a),
inference(nnf_transformation,[status(thm)],[f142]) ).
fof(f142_sk,plain,
~ little_set(a),
inference(skolemisation,[status(esa)],[f142_nnf]) ).
cnf(c142,plain,
~ little_set(a),
inference(cnf_transformation,[status(esa)],[f142_sk]) ).
cnf(t1,plain,
little_set(a) = false,
inference(equality_encoding,[status(esa)],[c142]) ).
cnf(t535,plain,
little_set(a) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t2458,plain,
true = false,
inference(step,[status(thm)],[t2365,t535]) ).
cnf(t2381,plain,
false = true,
inference(orient,[status(thm)],[t2458]) ).
cnf(f30,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,c142]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2381]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET025-9 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:16:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.28/2.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.28/2.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------