%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 02:41:28 PM UTC 2026
% Result : Unsatisfiable 3.98s 1.31s
% Output : Proof 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 101 ( 41 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 30 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f8_nnf,plain,
complement(as) = bs,
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
complement(as) = bs,
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(f5,axiom,
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f5_nnf,plain,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f1,axiom,
( X = Y
| little_set(f1(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
fof(f1_nnf,plain,
! [X,Y] :
( X = Y
| little_set(f1(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( X = Y
| little_set(f1(X,Y)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = X1
| little_set(f1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p29,plain,
( X0 = X1
| member(f1(X0,X1),X2)
| member(f1(X0,X1),complement(X2)) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(p38,plain,
( X0 = X1
| member(f1(X0,X1),as)
| member(f1(X0,X1),bs) ),
inference(superposition,[status(thm)],[c8,p29]) ).
cnf(f2,axiom,
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f2_nnf,plain,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f4,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f4_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p17,plain,
( ~ member(f1(X0,complement(X1)),X1)
| X0 = complement(X1)
| member(f1(X0,complement(X1)),X0) ),
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(p51,plain,
( X0 = cs
| member(f1(X0,cs),X0)
| X0 = cs
| member(f1(X0,cs),as) ),
inference(resolution,[status(thm)],[p38,p17]) ).
cnf(p114,plain,
( as = cs
| as = cs
| member(f1(as,cs),as) ),
inference(factoring,[status(thm)],[p51]) ).
cnf(p116,plain,
( as = cs
| member(f1(as,cs),as) ),
inference(factoring,[status(thm)],[p114]) ).
cnf(f3,axiom,
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
fof(f3_nnf,plain,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p117,plain,
( as = cs
| ~ member(f1(as,cs),cs)
| as = cs ),
inference(resolution,[status(thm)],[p116,c3]) ).
cnf(p118,plain,
( ~ member(f1(as,cs),cs)
| as = cs ),
inference(factoring,[status(thm)],[p117]) ).
cnf(f9,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f9_nnf,plain,
complement(bs) = cs,
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
complement(bs) = cs,
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p39,plain,
( X0 = X1
| member(f1(X0,X1),bs)
| member(f1(X0,X1),cs) ),
inference(superposition,[status(thm)],[c9,p29]) ).
cnf(p119,plain,
( as = cs
| member(f1(as,cs),bs)
| as = cs ),
inference(resolution,[status(thm)],[p118,p39]) ).
cnf(p121,plain,
( member(f1(as,cs),bs)
| as = cs ),
inference(factoring,[status(thm)],[p119]) ).
cnf(p12,plain,
( ~ member(X0,as)
| ~ member(X0,bs) ),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(p122,plain,
( ~ member(f1(as,cs),as)
| as = cs ),
inference(resolution,[status(thm)],[p121,p12]) ).
cnf(p124,plain,
( as = cs
| as = cs ),
inference(resolution,[status(thm)],[p122,p116]) ).
cnf(p125,plain,
as = cs,
inference(factoring,[status(thm)],[p124]) ).
cnf(f10,negated_conjecture,
as != cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
fof(f10_nnf,plain,
as != cs,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
as != cs,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
as != cs,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p128,plain,
$false,
inference(resolution,[status(thm)],[p125,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.58 % Computer : n013.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 09:05:09 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.98/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.98/1.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------