%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:44:19 PM UTC 2026
% Result : Theorem 5.09s 1.09s
% Output : Proof 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 81 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 32 ~; 31 |; 15 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 2 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( ( in(B,C)
& in(A,C)
& set_difference(unordered_pair(A,B),C) != empty_set )
| ( ( ~ in(B,C)
| ~ in(A,C) )
& set_difference(unordered_pair(A,B),C) = empty_set ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ( in(sk3,sk4)
& in(sk2,sk4)
& set_difference(unordered_pair(sk2,sk3),sk4) != empty_set )
| ( ( ~ in(sk3,sk4)
| ~ in(sk2,sk4) )
& set_difference(unordered_pair(sk2,sk3),sk4) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c13,plain,
( in(sk3,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f6,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p38,plain,
( subset(unordered_pair(sk2,sk3),sk4)
| in(sk3,sk4) ),
inference(resolution,[status(thm)],[c13,c6]) ).
fof(f7,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f7_nnf,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p39,plain,
( in(sk3,sk4)
| in(sk3,sk4) ),
inference(resolution,[status(thm)],[p38,c9]) ).
cnf(p40,plain,
in(sk3,sk4),
inference(factoring,[status(thm)],[p39]) ).
cnf(c12,plain,
( in(sk2,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p23,plain,
( subset(unordered_pair(sk2,sk3),sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[c12,c6]) ).
cnf(c8,plain,
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p24,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p23,c8]) ).
cnf(p26,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p24]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p31,plain,
( ~ in(X0,sk4)
| subset(unordered_pair(sk2,X0),sk4) ),
inference(resolution,[status(thm)],[p26,c10]) ).
cnf(p45,plain,
subset(unordered_pair(sk2,sk3),sk4),
inference(resolution,[status(thm)],[p40,p31]) ).
cnf(c7,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p47,plain,
set_difference(unordered_pair(sk2,sk3),sk4) = empty_set,
inference(resolution,[status(thm)],[p45,c7]) ).
cnf(c14,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != empty_set
| ~ in(sk3,sk4)
| ~ in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p41,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != empty_set
| ~ in(sk3,sk4) ),
inference(resolution,[status(thm)],[c14,p26]) ).
cnf(p48,plain,
( empty_set != empty_set
| ~ in(sk3,sk4) ),
inference(demodulation,[status(thm)],[p47,p41]) ).
cnf(p50,plain,
~ in(sk3,sk4),
inference(equality_resolution,[status(thm)],[p48]) ).
cnf(p51,plain,
$false,
inference(resolution,[status(thm)],[p50,p40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:23:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.09/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------