%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET688+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:43:48 PM UTC 2026
% Result : Theorem 32.12s 9.58s
% Output : Proof 32.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 25 |; 23 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 21 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f11,conjecture,
! [A,B,C] :
( ( ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) )
=> ~ equal_set(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI04) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B,C] :
( ( ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) )
=> ~ equal_set(A,C) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B,C] :
( equal_set(A,C)
& ~ equal_set(B,C)
& subset(B,C)
& ~ equal_set(A,B)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( equal_set(sk3,sk5)
& ~ equal_set(sk4,sk5)
& subset(sk4,sk5)
& ~ equal_set(sk3,sk4)
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f11_nnf]) ).
cnf(c29,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p51,plain,
( ~ subset(sk4,sk3)
| equal_set(sk3,sk4) ),
inference(resolution,[status(thm)],[c5,c29]) ).
cnf(c4,plain,
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c33,plain,
equal_set(sk3,sk5),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p44,plain,
subset(sk5,sk3),
inference(resolution,[status(thm)],[c4,c33]) ).
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,X] :
( ( ( ~ member(sk0(A,B),B)
& member(sk0(A,B),A) )
| subset(A,B) )
& ( member(X,B)
| ~ member(X,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p45,plain,
( member(X0,sk3)
| ~ member(X0,sk5) ),
inference(resolution,[status(thm)],[p44,c0]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c31,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p35,plain,
( member(X0,sk5)
| ~ member(X0,sk4) ),
inference(resolution,[status(thm)],[c0,c31]) ).
cnf(p38,plain,
( member(sk0(sk4,X0),sk5)
| subset(sk4,X0) ),
inference(resolution,[status(thm)],[c1,p35]) ).
cnf(p47,plain,
( subset(sk4,X0)
| member(sk0(sk4,X0),sk3) ),
inference(resolution,[status(thm)],[p45,p38]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p49,plain,
( subset(sk4,sk3)
| subset(sk4,sk3) ),
inference(resolution,[status(thm)],[p47,c2]) ).
cnf(p55,plain,
subset(sk4,sk3),
inference(factoring,[status(thm)],[p49]) ).
cnf(p58,plain,
equal_set(sk3,sk4),
inference(resolution,[status(thm)],[p51,p55]) ).
cnf(c30,plain,
~ equal_set(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p59,plain,
$false,
inference(resolution,[status(thm)],[p58,c30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET688+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n003.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 11:41:57 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.12/9.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.12/9.58 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------