%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 08:37:21 AM UTC 2026
% Result : Theorem 0.26s 0.55s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 145 ( 49 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 137 ( 40 ~; 66 |; 25 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 81 ( 0 sgn 57 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t103_zfmisc_1,axiom,
! [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('theBenchmark.p',t103_zfmisc_1) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t110_zfmisc_1,conjecture,
! [A,B,C,D,E,F] :
( ( ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) )
& subset(D,cartesian_product2(E,F))
& subset(A,cartesian_product2(B,C)) )
=> A = D ),
file('theBenchmark.p',t110_zfmisc_1) ).
fof(t110_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) )
& subset(D,cartesian_product2(E,F))
& subset(A,cartesian_product2(B,C)) )
=> A = D ),
inference(assume_negation,[status(cth)],[t110_zfmisc_1]) ).
fof(nnf_8,plain,
! [A,B,C,D] :
( ? [E,F] :
( ordered_pair(E,F) = D
& in(F,C)
& in(E,B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[t103_zfmisc_1]) ).
fof(sk_t103_zfmisc_1_sk,plain,
! [A,B,C,D] :
( ( ordered_pair(sK0(A,B,C,D),sK1(A,B,C,D)) = D
& in(sK1(A,B,C,D),C)
& in(sK0(A,B,C,D),B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0(A,B,C,D)),skolemize(F,sK1(A,B,C,D))],[nnf_8]) ).
fof(sk_t103_zfmisc_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ordered_pair(sK0(VAR_0,VAR_1,VAR_2,VAR_3),sK1(VAR_0,VAR_1,VAR_2,VAR_3)) = VAR_3
| ~ in(VAR_3,VAR_0)
| ~ subset(VAR_0,cartesian_product2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK1(VAR_0,VAR_1,VAR_2,VAR_3),VAR_2)
| ~ in(VAR_3,VAR_0)
| ~ subset(VAR_0,cartesian_product2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_0)
| ~ subset(VAR_0,cartesian_product2(VAR_1,VAR_2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_t103_zfmisc_1_sk]) ).
cnf(c_20,plain,
( ordered_pair(sK0(A,B,C,D),sK1(A,B,C,D)) = D
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_t103_zfmisc_1]) ).
fof(nnf_9,plain,
! [A,B] :
( B = A
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(sk_t2_tarski_sk,plain,
! [A,B] :
( B = A
| ( ( ~ in(sK2(A,B),B)
| ~ in(sK2(A,B),A) )
& ( in(sK2(A,B),B)
| in(sK2(A,B),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_9]) ).
fof(sk_t2_tarski,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ in(sK2(VAR_0,VAR_1),VAR_1)
| ~ in(sK2(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| in(sK2(VAR_0,VAR_1),VAR_1)
| in(sK2(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t2_tarski_sk]) ).
cnf(c_21,plain,
( B = A
| in(sK2(A,B),B)
| in(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
cnf(c_22,plain,
( B = A
| ~ in(sK2(A,B),B)
| ~ in(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
fof(nnf_10,plain,
? [A,B,C,D,E,F] :
( D != A
& ! [G,H] :
( ( ~ in(ordered_pair(G,H),D)
| in(ordered_pair(G,H),A) )
& ( in(ordered_pair(G,H),D)
| ~ in(ordered_pair(G,H),A) ) )
& subset(D,cartesian_product2(E,F))
& subset(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[t110_zfmisc_1_neg]) ).
fof(sk_t110_zfmisc_1_neg,plain,
( sK6 != sK3
& ! [G,H] :
( ( ~ in(ordered_pair(G,H),sK6)
| in(ordered_pair(G,H),sK3) )
& ( in(ordered_pair(G,H),sK6)
| ~ in(ordered_pair(G,H),sK3) ) )
& subset(sK6,cartesian_product2(sK7,sK8))
& subset(sK3,cartesian_product2(sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(D,sK6),skolemize(E,sK7),skolemize(F,sK8)],[nnf_10]) ).
cnf(c_23,negated_conjecture,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(split_conjunct,[status(thm)],[sk_t110_zfmisc_1_neg]) ).
cnf(c_24,negated_conjecture,
subset(sK6,cartesian_product2(sK7,sK8)),
inference(split_conjunct,[status(thm)],[sk_t110_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
( in(ordered_pair(A,B),sK6)
| ~ in(ordered_pair(A,B),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t110_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
( ~ in(ordered_pair(A,B),sK6)
| in(ordered_pair(A,B),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t110_zfmisc_1_neg]) ).
cnf(c_27,negated_conjecture,
sK6 != sK3,
inference(split_conjunct,[status(thm)],[sk_t110_zfmisc_1_neg]) ).
cnf(c_37,plain,
( ordered_pair(sK0(sK3,sK4,sK5,A),sK1(sK3,sK4,sK5,A)) = A
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_40,plain,
( ordered_pair(sK0(sK6,sK7,sK8,A),sK1(sK6,sK7,sK8,A)) = A
| ~ in(A,sK6) ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_69,plain,
( sK3 = A
| in(sK2(A,sK3),A)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(A,sK3)),sK1(sK3,sK4,sK5,sK2(A,sK3))) = sK2(A,sK3) ),
inference(resolve,[status(thm)],[c_37,c_21]) ).
cnf(c_351,plain,
( ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))) = sK2(sK6,sK3)
| sK3 = sK6
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(resolve,[status(thm)],[c_69,c_40]) ).
cnf(c_352,plain,
( ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))) = sK2(sK6,sK3)
| sK6 = sK3
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_137,negated_conjecture,
( ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))) = sK2(sK6,sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(resolve,[status(thm)],[c_27,c_352]) ).
cnf(c_272,plain,
( ~ in(sK2(sK6,sK3),sK6)
| in(ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(paramod,[status(thm)],[c_137,c_26]) ).
cnf(c_353,plain,
( sK3 = sK6
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3)
| in(ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(resolve,[status(thm)],[c_272,c_69]) ).
cnf(c_354,plain,
( sK6 = sK3
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3)
| in(ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_355,plain,
( sK6 = sK3
| in(ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(copy,[status(thm)],[c_354]) ).
cnf(c_286,negated_conjecture,
( in(ordered_pair(sK0(sK6,sK7,sK8,sK2(sK6,sK3)),sK1(sK6,sK7,sK8,sK2(sK6,sK3))),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(resolve,[status(thm)],[c_27,c_355]) ).
cnf(c_356,plain,
( in(sK2(sK6,sK3),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(paramod,[status(thm)],[c_137,c_286]) ).
cnf(c_295,plain,
( in(sK2(sK6,sK3),sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_357,plain,
( ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3)
| ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3) ),
inference(resolve,[status(thm)],[c_295,c_37]) ).
cnf(c_298,plain,
ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))) = sK2(sK6,sK3),
inference(copy,[status(thm)],[c_357]) ).
cnf(c_301,plain,
( in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK6)
| ~ in(sK2(sK6,sK3),sK3) ),
inference(paramod,[status(thm)],[c_298,c_25]) ).
cnf(c_302,plain,
( ~ in(sK2(sK6,sK3),sK6)
| in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK3) ),
inference(paramod,[status(thm)],[c_298,c_26]) ).
cnf(c_358,plain,
( sK3 = sK6
| in(sK2(sK6,sK3),sK6)
| in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK6) ),
inference(resolve,[status(thm)],[c_301,c_21]) ).
cnf(c_359,plain,
( sK6 = sK3
| in(sK2(sK6,sK3),sK6)
| in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK6) ),
inference(copy,[status(thm)],[c_358]) ).
cnf(c_307,negated_conjecture,
( in(sK2(sK6,sK3),sK6)
| in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK6) ),
inference(resolve,[status(thm)],[c_27,c_359]) ).
cnf(c_360,plain,
( in(sK2(sK6,sK3),sK6)
| in(sK2(sK6,sK3),sK6) ),
inference(paramod,[status(thm)],[c_298,c_307]) ).
cnf(c_326,plain,
in(sK2(sK6,sK3),sK6),
inference(copy,[status(thm)],[c_360]) ).
cnf(c_327,plain,
in(ordered_pair(sK0(sK3,sK4,sK5,sK2(sK6,sK3)),sK1(sK3,sK4,sK5,sK2(sK6,sK3))),sK3),
inference(resolve,[status(thm)],[c_326,c_302]) ).
cnf(c_361,plain,
( sK3 = sK6
| ~ in(sK2(sK6,sK3),sK3) ),
inference(resolve,[status(thm)],[c_326,c_22]) ).
cnf(c_362,plain,
( sK6 = sK3
| ~ in(sK2(sK6,sK3),sK3) ),
inference(copy,[status(thm)],[c_361]) ).
cnf(c_331,negated_conjecture,
~ in(sK2(sK6,sK3),sK3),
inference(resolve,[status(thm)],[c_27,c_362]) ).
cnf(c_363,plain,
in(sK2(sK6,sK3),sK3),
inference(paramod,[status(thm)],[c_298,c_327]) ).
cnf(c_350,plain,
$false,
inference(resolve,[status(thm)],[c_331,c_363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:29:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 695 was started by sandbox on n018,
% 0.18/0.45 % Sat Sep 26 08:29:51 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.26/0.55
% 0.26/0.55 % SZS status Theorem for theBenchmark
% 0.26/0.55
% 0.26/0.55 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.26/0.55 % Length of proof is 26.
% 0.26/0.55 % Level of proof is 13.
% 0.26/0.55 % Maximum clause weight is 61.000.
% 0.26/0.55 % Given clauses 172.
% 0.26/0.55
% 0.26/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------