%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 76 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 33 ~; 26 |; 14 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 40 !; 5 ?)
% 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(t111_zfmisc_1,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
file('theBenchmark.p',t111_zfmisc_1) ).
fof(t111_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
inference(assume_negation,[status(cth)],[t111_zfmisc_1]) ).
cnf(c_11,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_13,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_14,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_15,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
fof(nnf_9,plain,
? [A,B] :
( ~ subset(A,B)
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
& ! [X0] :
( ? [X1,E] : ordered_pair(X1,E) = X0
| ~ in(X0,A) ) ),
inference(fof_nnf,[status(thm)],[t111_zfmisc_1_neg]) ).
fof(sk_t111_zfmisc_1_neg,plain,
( ~ subset(sK1,sK4)
& ! [C,D] :
( in(ordered_pair(C,D),sK4)
| ~ in(ordered_pair(C,D),sK1) )
& ! [X0] :
( ordered_pair(sK2(X0),sK3(X0)) = X0
| ~ in(X0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(A,sK1),skolemize(B,sK4),skolemize(X1,sK2(X0)),skolemize(E,sK3(X0))],[nnf_9]) ).
cnf(c_21,negated_conjecture,
( ordered_pair(sK2(A),sK3(A)) = A
| ~ in(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t111_zfmisc_1_neg]) ).
cnf(c_57,negated_conjecture,
( unordered_pair(unordered_pair(sK2(A),sK3(A)),singleton(sK2(A))) = A
| ~ in(A,sK1) ),
inference(paramod,[status(thm)],[c_15,c_21]) ).
cnf(c_22,negated_conjecture,
( unordered_pair(singleton(sK2(A)),unordered_pair(sK2(A),sK3(A))) = A
| ~ in(A,sK1) ),
inference(paramod,[status(thm)],[c_11,c_57]) ).
cnf(c_23,negated_conjecture,
( in(ordered_pair(A,B),sK4)
| ~ in(ordered_pair(A,B),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t111_zfmisc_1_neg]) ).
cnf(c_58,negated_conjecture,
( in(ordered_pair(A,B),sK4)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_15,c_23]) ).
cnf(c_24,negated_conjecture,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK4)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1) ),
inference(paramod,[status(thm)],[c_15,c_58]) ).
cnf(c_25,negated_conjecture,
~ subset(sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_t111_zfmisc_1_neg]) ).
cnf(c_31,plain,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK4)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK1) ),
inference(paramod,[status(thm)],[c_11,c_24]) ).
cnf(c_32,plain,
in(sK0(sK1,sK4),sK1),
inference(resolve,[status(thm)],[c_25,c_13]) ).
cnf(c_33,negated_conjecture,
~ in(sK0(sK1,sK4),sK4),
inference(resolve,[status(thm)],[c_14,c_25]) ).
cnf(c_36,plain,
unordered_pair(singleton(sK2(sK0(sK1,sK4))),unordered_pair(sK2(sK0(sK1,sK4)),sK3(sK0(sK1,sK4)))) = sK0(sK1,sK4),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_59,plain,
( in(unordered_pair(unordered_pair(sK2(sK0(sK1,sK4)),sK3(sK0(sK1,sK4))),singleton(sK2(sK0(sK1,sK4)))),sK4)
| ~ in(sK0(sK1,sK4),sK1) ),
inference(paramod,[status(thm)],[c_36,c_31]) ).
cnf(c_60,plain,
( in(unordered_pair(singleton(sK2(sK0(sK1,sK4))),unordered_pair(sK2(sK0(sK1,sK4)),sK3(sK0(sK1,sK4)))),sK4)
| ~ in(sK0(sK1,sK4),sK1) ),
inference(paramod,[status(thm)],[c_11,c_59]) ).
cnf(c_61,plain,
( in(sK0(sK1,sK4),sK4)
| ~ in(sK0(sK1,sK4),sK1) ),
inference(paramod,[status(thm)],[c_36,c_60]) ).
cnf(c_62,plain,
in(sK0(sK1,sK4),sK4),
inference(resolve,[status(thm)],[c_32,c_61]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:33:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1381885 was started by sandbox on n001,
% 0.10/0.38 % Sat Sep 26 08:33:27 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 18.
% 0.10/0.40 % Level of proof is 4.
% 0.10/0.40 % Maximum clause weight is 49.000.
% 0.10/0.40 % Given clauses 28.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------