%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET906+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 : n005.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 02:44:15 PM UTC 2026
% Result : Theorem 27.38s 4.56s
% Output : Proof 27.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 113 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 130 ( 47 ~; 45 |; 30 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 9 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
| in(D,A) )
& ~ in(D,C) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk1(A,B,C),B)
| in(sk1(A,B,C),A) )
& ~ in(sk1(A,B,C),C) )
| ( ~ in(sk1(A,B,C),B)
& ~ in(sk1(A,B,C),A)
& in(sk1(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c13,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p79,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c13]) ).
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D = B
| D = A )
& ~ in(D,C) )
| ( D != B
& D != A
& in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( ( sk0(A,B,C) = B
| sk0(A,B,C) = A )
& ~ in(sk0(A,B,C),C) )
| ( sk0(A,B,C) != B
& sk0(A,B,C) != A
& in(sk0(A,B,C),C) )
| C = unordered_pair(A,B) )
& ( ( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c4,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p38,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(p42,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p38]) ).
cnf(p85,plain,
in(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(resolution,[status(thm)],[p79,p42]) ).
cnf(p93,plain,
in(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c2,p85]) ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk2(A,B),B)
& in(sk2(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c21,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f12,conjecture,
! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f12_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [A,B,C] :
( ~ in(A,C)
& subset(set_union2(unordered_pair(A,B),C),C) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ~ in(sk5,sk7)
& subset(set_union2(unordered_pair(sk5,sk6),sk7),sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f12_nnf]) ).
cnf(c30,plain,
subset(set_union2(unordered_pair(sk5,sk6),sk7),sk7),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p75,plain,
( in(X0,sk7)
| ~ in(X0,set_union2(sk7,unordered_pair(sk5,sk6))) ),
inference(resolution,[status(thm)],[c21,c30]) ).
cnf(p99,plain,
in(sk5,sk7),
inference(resolution,[status(thm)],[p93,p75]) ).
cnf(c31,plain,
~ in(sk5,sk7),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p101,plain,
$false,
inference(resolution,[status(thm)],[p99,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 12:21:03 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.38/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.38/4.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------