%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET950+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 : n010.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 02:44:21 PM UTC 2026
% Result : Theorem 5.14s 1.20s
% Output : Proof 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 19 unt; 0 def)
% Number of atoms : 120 ( 38 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 135 ( 54 ~; 43 |; 34 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 101 ( 0 sgn 55 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
& ~ in(D,C) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) )
| C = cartesian_product2(A,B) )
& ( ! [D] :
( ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
| in(D,C) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D,E,F] :
( ( ( sk2(A,B,C) = ordered_pair(sk3(A,B,C),sk4(A,B,C))
& in(sk4(A,B,C),B)
& in(sk3(A,B,C),A)
& ~ in(sk2(A,B,C),C) )
| ( ( sk2(A,B,C) != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(sk2(A,B,C),C) )
| C = cartesian_product2(A,B) )
& ( ( ( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| in(D,C) )
& ( ( D = ordered_pair(sk0(A,B,C,D),sk1(A,B,C,D))
& in(sk1(A,B,C,D),B)
& in(sk0(A,B,C,D),A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f2_nnf]) ).
cnf(c4,plain,
( X3 = ordered_pair(sk0(X0,X1,X2,X3),sk1(X0,X1,X2,X3))
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p52,plain,
( X0 = ordered_pair(sk0(X1,X2,cartesian_product2(X1,X2),X0),sk1(X1,X2,cartesian_product2(X1,X2),X0))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk5(A,B),B)
& in(sk5(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f3_nnf]) ).
cnf(c14,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f9,conjecture,
! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f9_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [A,B,C,D] :
( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,C)
| ~ in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
! [E,F] :
( ( sk11 != ordered_pair(E,F)
| ~ in(F,sk10)
| ~ in(E,sk9) )
& in(sk11,sk8)
& subset(sk8,cartesian_product2(sk9,sk10)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11])],[f9_nnf]) ).
cnf(c22,plain,
subset(sk8,cartesian_product2(sk9,sk10)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p51,plain,
( in(X0,cartesian_product2(sk9,sk10))
| ~ in(X0,sk8) ),
inference(resolution,[status(thm)],[c14,c22]) ).
cnf(c23,plain,
in(sk11,sk8),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p53,plain,
in(sk11,cartesian_product2(sk9,sk10)),
inference(resolution,[status(thm)],[p51,c23]) ).
cnf(p434,plain,
sk11 = ordered_pair(sk0(sk9,sk10,cartesian_product2(sk9,sk10),sk11),sk1(sk9,sk10,cartesian_product2(sk9,sk10),sk11)),
inference(resolution,[status(thm)],[p52,p53]) ).
fof(f4,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f4_nnf,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c17,plain,
ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
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]) ).
cnf(p32,plain,
unordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(X0,X1),
inference(superposition,[status(thm)],[c17,c1]) ).
cnf(p451,plain,
ordered_pair(sk0(sk9,sk10,cartesian_product2(sk9,sk10),sk11),sk1(sk9,sk10,cartesian_product2(sk9,sk10),sk11)) = sk11,
inference(superposition,[status(thm)],[p434,p32]) ).
cnf(c3,plain,
( in(sk1(X0,X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p38,plain,
( in(sk1(X1,X2,cartesian_product2(X1,X2),X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p381,plain,
in(sk1(sk9,sk10,cartesian_product2(sk9,sk10),sk11),sk10),
inference(resolution,[status(thm)],[p38,p53]) ).
cnf(c2,plain,
( in(sk0(X0,X1,X2,X3),X0)
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( in(sk0(X1,X2,cartesian_product2(X1,X2),X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p319,plain,
in(sk0(sk9,sk10,cartesian_product2(sk9,sk10),sk11),sk9),
inference(resolution,[status(thm)],[p30,p53]) ).
cnf(c24,plain,
( sk11 != ordered_pair(X4,X5)
| ~ in(X5,sk10)
| ~ in(X4,sk9) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p335,plain,
( sk11 != ordered_pair(sk0(sk9,sk10,cartesian_product2(sk9,sk10),sk11),X0)
| ~ in(X0,sk10) ),
inference(resolution,[status(thm)],[p319,c24]) ).
cnf(p410,plain,
sk11 != ordered_pair(sk0(sk9,sk10,cartesian_product2(sk9,sk10),sk11),sk1(sk9,sk10,cartesian_product2(sk9,sk10),sk11)),
inference(resolution,[status(thm)],[p381,p335]) ).
cnf(p452,plain,
sk11 != sk11,
inference(demodulation,[status(thm)],[p451,p410]) ).
cnf(p453,plain,
$false,
inference(equality_resolution,[status(thm)],[p452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:26:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.14/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.14/1.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------