%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 3.30s 0.84s
% Output : Proof 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 101 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 51 ~; 34 |; 29 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f6,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B,C] :
( ( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c11,plain,
( in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f8,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != unordered_pair(sk2,sk3)
& set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk3)
& set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2)
& set_difference(unordered_pair(sk2,sk3),sk4) != empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c18,plain,
set_difference(unordered_pair(sk2,sk3),sk4) != unordered_pair(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p32,plain,
( in(sk3,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[c11,c18]) ).
fof(f3,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p44,plain,
( in(X0,sk4)
| set_difference(unordered_pair(X0,sk3),sk4) = singleton(X0)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p32,c5]) ).
cnf(c16,plain,
set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p49,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p44,c16]) ).
cnf(p56,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p49]) ).
cnf(p60,plain,
( in(X0,sk4)
| set_difference(unordered_pair(X0,sk2),sk4) = singleton(X0) ),
inference(resolution,[status(thm)],[p56,c5]) ).
cnf(p63,plain,
( in(X0,sk4)
| set_difference(unordered_pair(sk2,X0),sk4) = singleton(X0) ),
inference(superposition,[status(thm)],[c1,p60]) ).
cnf(c17,plain,
set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p71,plain,
in(sk3,sk4),
inference(resolution,[status(thm)],[p63,c17]) ).
fof(f7,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f7_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)],[f7]) ).
fof(f7_sk,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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c14,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p58,plain,
( ~ in(X0,sk4)
| set_difference(unordered_pair(sk2,X0),sk4) = empty_set ),
inference(resolution,[status(thm)],[p56,c14]) ).
cnf(p77,plain,
set_difference(unordered_pair(sk2,sk3),sk4) = empty_set,
inference(resolution,[status(thm)],[p71,p58]) ).
cnf(c15,plain,
set_difference(unordered_pair(sk2,sk3),sk4) != empty_set,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p78,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p77,c15]) ).
cnf(p82,plain,
$false,
inference(equality_resolution,[status(thm)],[p78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n020.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 12:25:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.30/0.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.30/0.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------