%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET025-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 7.15s 1.45s
% Output : Proof 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 29 unt; 0 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 38 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 57 ( 8 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f141,negated_conjecture,
~ little_set(ordered_pair(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).
fof(f141_nnf,plain,
~ little_set(ordered_pair(a,b)),
inference(nnf_transformation,[status(thm)],[f141]) ).
fof(f141_sk,plain,
~ little_set(ordered_pair(a,b)),
inference(skolemisation,[status(esa)],[f141_nnf]) ).
cnf(c141,plain,
~ little_set(ordered_pair(a,b)),
inference(cnf_transformation,[status(esa)],[f141_sk]) ).
cnf(hi140,negated_conjecture,
ifeq(little_set(ordered_pair(a,b)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(f7,axiom,
little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/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(hi7,axiom,
little_set(non_ordered_pair(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f9,axiom,
ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/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(hi11,axiom,
ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
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(hi12,axiom,
singleton_set(X0) = non_ordered_pair(X0,X0),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi140,hi7,hi11,hi12]) ).
cnf(t711,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c141]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t711]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET025-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 09:16:00 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.15/1.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.15/1.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------