%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET928+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 : n006.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 2.67s 0.77s
% Output : Proof 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 90 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 35 ~; 36 |; 13 &)
% ( 3 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 2 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(C,B)
| in(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(C,B)
| in(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f8,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f8_nnf,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c13,plain,
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p19,plain,
( set_difference(unordered_pair(X0,X2),X1) = unordered_pair(X0,X2)
| in(X2,X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[c6,c13]) ).
fof(f7,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_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)],[f7_neg]) ).
fof(f7_sk,plain,
( ( ~ in(sk3,sk4)
& ~ in(sk2,sk4)
& set_difference(unordered_pair(sk2,sk3),sk4) != unordered_pair(sk2,sk3) )
| ( ( in(sk3,sk4)
| in(sk2,sk4) )
& set_difference(unordered_pair(sk2,sk3),sk4) = unordered_pair(sk2,sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f7_nnf]) ).
cnf(c10,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != unordered_pair(sk2,sk3)
| in(sk3,sk4)
| in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p28,plain,
( in(sk3,sk4)
| in(sk2,sk4)
| in(sk3,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p19,c10]) ).
cnf(p30,plain,
( in(sk3,sk4)
| in(sk3,sk4)
| in(sk2,sk4) ),
inference(factoring,[status(thm)],[p28]) ).
cnf(p32,plain,
( in(sk3,sk4)
| in(sk2,sk4) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(c9,plain,
( ~ in(sk3,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = unordered_pair(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p33,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) = unordered_pair(sk2,sk3)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p32,c9]) ).
cnf(c14,plain,
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p35,plain,
( disjoint(unordered_pair(sk2,sk3),sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p33,c14]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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(f5,axiom,
! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p16,plain,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(p37,plain,
( ~ in(sk3,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p35,p16]) ).
cnf(p38,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p37,p32]) ).
cnf(p39,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p38]) ).
cnf(c8,plain,
( ~ in(sk2,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = unordered_pair(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p40,plain,
set_difference(unordered_pair(sk2,sk3),sk4) = unordered_pair(sk2,sk3),
inference(resolution,[status(thm)],[p39,c8]) ).
cnf(p42,plain,
disjoint(unordered_pair(sk2,sk3),sk4),
inference(resolution,[status(thm)],[p40,c14]) ).
cnf(p44,plain,
~ in(sk2,sk4),
inference(resolution,[status(thm)],[p42,c5]) ).
cnf(p46,plain,
$false,
inference(resolution,[status(thm)],[p44,p39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Thu Sep 24 12:23:26 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.67/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.67/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------