%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.12s 25.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 96 ( 13 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 34 |; 22 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 94 ( 0 sgn 62 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
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(t109_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
file('theBenchmark.p',t109_zfmisc_1) ).
fof(t109_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
inference(assume_negation,[status(cth)],[t109_zfmisc_1]) ).
cnf(c_12,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_14,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_15,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_16,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_17,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_12,c_16]) ).
fof(nnf_9,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(sK1(A,B,C,D),sK2(A,B,C,D)) = D
& in(sK2(A,B,C,D),C)
& in(sK1(A,B,C,D),B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(E,sK1(A,B,C,D)),skolemize(F,sK2(A,B,C,D))],[nnf_9]) ).
fof(sk_t103_zfmisc_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ordered_pair(sK1(VAR_0,VAR_1,VAR_2,VAR_3),sK2(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(sK2(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(sK1(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_25,plain,
( ordered_pair(sK1(A,B,C,D),sK2(A,B,C,D)) = D
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_t103_zfmisc_1]) ).
cnf(c_26,plain,
( unordered_pair(singleton(sK1(A,B,C,D)),unordered_pair(sK1(A,B,C,D),sK2(A,B,C,D))) = D
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(paramod,[status(thm)],[c_17,c_25]) ).
fof(nnf_10,plain,
? [A,B,C,D] :
( ~ subset(A,D)
& ! [E,F] :
( in(ordered_pair(E,F),D)
| ~ in(ordered_pair(E,F),A) )
& subset(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[t109_zfmisc_1_neg]) ).
fof(sk_t109_zfmisc_1_neg,plain,
( ~ subset(sK3,sK6)
& ! [E,F] :
( in(ordered_pair(E,F),sK6)
| ~ in(ordered_pair(E,F),sK3) )
& subset(sK3,cartesian_product2(sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(D,sK6)],[nnf_10]) ).
cnf(c_27,negated_conjecture,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(split_conjunct,[status(thm)],[sk_t109_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
( in(ordered_pair(A,B),sK6)
| ~ in(ordered_pair(A,B),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t109_zfmisc_1_neg]) ).
cnf(c_482,negated_conjecture,
( in(ordered_pair(A,B),sK6)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK3) ),
inference(paramod,[status(thm)],[c_17,c_28]) ).
cnf(c_29,negated_conjecture,
( in(unordered_pair(singleton(A),unordered_pair(A,B)),sK6)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK3) ),
inference(paramod,[status(thm)],[c_17,c_482]) ).
cnf(c_30,negated_conjecture,
~ subset(sK3,sK6),
inference(split_conjunct,[status(thm)],[sk_t109_zfmisc_1_neg]) ).
cnf(c_45,plain,
in(sK0(sK3,sK6),sK3),
inference(resolve,[status(thm)],[c_30,c_14]) ).
cnf(c_46,negated_conjecture,
~ in(sK0(sK3,sK6),sK6),
inference(resolve,[status(thm)],[c_15,c_30]) ).
cnf(c_483,negated_conjecture,
( unordered_pair(singleton(sK1(sK3,sK4,sK5,A)),unordered_pair(sK1(sK3,sK4,sK5,A),sK2(sK3,sK4,sK5,A))) = A
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_50,negated_conjecture,
unordered_pair(singleton(sK1(sK3,sK4,sK5,sK0(sK3,sK6))),unordered_pair(sK1(sK3,sK4,sK5,sK0(sK3,sK6)),sK2(sK3,sK4,sK5,sK0(sK3,sK6)))) = sK0(sK3,sK6),
inference(resolve,[status(thm)],[c_483,c_45]) ).
cnf(c_484,plain,
( in(unordered_pair(singleton(sK1(sK3,sK4,sK5,sK0(sK3,sK6))),unordered_pair(sK1(sK3,sK4,sK5,sK0(sK3,sK6)),sK2(sK3,sK4,sK5,sK0(sK3,sK6)))),sK6)
| ~ in(sK0(sK3,sK6),sK3) ),
inference(paramod,[status(thm)],[c_50,c_29]) ).
cnf(c_485,plain,
( in(sK0(sK3,sK6),sK6)
| ~ in(sK0(sK3,sK6),sK3) ),
inference(paramod,[status(thm)],[c_50,c_484]) ).
cnf(c_486,plain,
in(sK0(sK3,sK6),sK6),
inference(resolve,[status(thm)],[c_45,c_485]) ).
cnf(c_481,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/25.38 % Computer : n012.cluster.edu
% 0.08/25.38 % Model : x86_64 x86_64
% 0.08/25.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/25.38 % Memory : 8046.5625MB
% 0.08/25.38 % OS : Linux 6.8.0-71-generic
% 0.08/25.38 % CPULimit : 300
% 0.08/25.38 % WCLimit : 300
% 0.08/25.38 % DateTime : Sat Sep 26 08:28:02 UTC 2026
% 0.08/25.38 % CPUTime :
% 0.08/25.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/25.38 % Process 139929 was started by sandbox2 on n012,
% 0.08/25.38 % Sat Sep 26 08:28:02 2026
% 0.08/25.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/25.38
% 0.08/25.38 % From the command line: assign(max_seconds, 300).
% 0.12/25.48
% 0.12/25.48 % Assigning unary symbol singleton kb_weight 0 and highest precedence (17).
% 0.12/25.48
% 0.12/25.48 % SZS status Theorem for theBenchmark
% 0.12/25.48
% 0.12/25.48 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/25.48 % Length of proof is 20.
% 0.12/25.48 % Level of proof is 5.
% 0.12/25.48 % Maximum clause weight is 58.000.
% 0.12/25.48 % Given clauses 107.
% 0.12/25.48
% 0.12/25.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------