%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET931+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 : n014.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 11.17s 2.11s
% Output : Proof 11.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 188 ( 168 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 193 ( 59 ~; 101 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 59 ( 7 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C] :
( ( ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set )
& set_difference(A,unordered_pair(B,C)) != empty_set )
| ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set
& set_difference(A,unordered_pair(B,C)) = empty_set ) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ( ( sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set )
& set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set )
| ( sk2 != unordered_pair(sk3,sk4)
& sk2 != singleton(sk4)
& sk2 != singleton(sk3)
& sk2 != empty_set
& set_difference(sk2,unordered_pair(sk3,sk4)) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f7_nnf]) ).
cnf(c13,plain,
( sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set
| set_difference(sk2,unordered_pair(sk3,sk4)) = empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f6,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/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(c10,plain,
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p59,plain,
( subset(sk2,unordered_pair(sk3,sk4))
| sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[c13,c10]) ).
fof(f2,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = unordered_pair(X1,X2)
| X0 = singleton(X2)
| X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p378,plain,
( sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p59,c2]) ).
cnf(p1467,plain,
( sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p378]) ).
cnf(p2399,plain,
( sk2 = singleton(sk4)
| sk2 = empty_set
| sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p1467]) ).
cnf(p2402,plain,
( sk2 = empty_set
| sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p2399]) ).
cnf(p2409,plain,
( sk2 = unordered_pair(sk3,sk4)
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p2402]) ).
cnf(c20,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 != unordered_pair(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p2436,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p2409,c20]) ).
cnf(c6,plain,
( X0 != unordered_pair(X1,X2)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f0_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p43,plain,
subset(unordered_pair(X0,X1),unordered_pair(X1,X0)),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(c11,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p45,plain,
set_difference(unordered_pair(X0,X1),unordered_pair(X1,X0)) = empty_set,
inference(resolution,[status(thm)],[p43,c11]) ).
cnf(p2434,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) = empty_set
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p2409,p45]) ).
cnf(p3348,plain,
( sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p2436,p2434]) ).
cnf(p5895,plain,
( sk2 = singleton(sk4)
| sk2 = empty_set
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p3348]) ).
cnf(p5898,plain,
( sk2 = empty_set
| sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p5895]) ).
cnf(p5899,plain,
( sk2 = singleton(sk4)
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p5898]) ).
cnf(c18,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 != singleton(sk4) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p5912,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p5899,c18]) ).
cnf(c4,plain,
( X0 != singleton(X1)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p39,plain,
subset(singleton(X0),unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(p40,plain,
subset(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c0,p39]) ).
cnf(p42,plain,
set_difference(singleton(X0),unordered_pair(X1,X0)) = empty_set,
inference(resolution,[status(thm)],[p40,c11]) ).
cnf(p5911,plain,
( set_difference(sk2,unordered_pair(X0,sk4)) = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p5899,p42]) ).
cnf(p6435,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p5912,p5911]) ).
cnf(p6440,plain,
( sk2 = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p6435]) ).
cnf(p6441,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p6440]) ).
cnf(c16,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 != singleton(sk3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p6450,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p6441,c16]) ).
cnf(p41,plain,
set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(resolution,[status(thm)],[p39,c11]) ).
cnf(p6448,plain,
( set_difference(sk2,unordered_pair(sk3,X0)) = empty_set
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p6441,p41]) ).
cnf(p6920,plain,
( sk2 = empty_set
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p6450,p6448]) ).
cnf(p6921,plain,
sk2 = empty_set,
inference(factoring,[status(thm)],[p6920]) ).
cnf(c14,plain,
( set_difference(sk2,unordered_pair(sk3,sk4)) != empty_set
| sk2 != empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p6922,plain,
( set_difference(empty_set,unordered_pair(sk3,sk4)) != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p6921,c14]) ).
cnf(p6932,plain,
empty_set != empty_set,
inference(equality_resolution,[status(thm)],[p6922]) ).
cnf(p6933,plain,
$false,
inference(equality_resolution,[status(thm)],[p6932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.55 % Computer : n014.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Thu Sep 24 12:24:03 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.10/0.55 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.17/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.17/2.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------