%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU159+3 : 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 : 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 : Sun Sep 27 08:45:14 AM UTC 2026
% Result : Theorem 9.32s 3.13s
% Output : CNFRefutation 9.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 122 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 123 ( 47 ~; 56 |; 14 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 4 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t38_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t38_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
inference(assume_negation,[status(cth)],[t38_zfmisc_1]) ).
cnf(c_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_11,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_12,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_4,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_4]) ).
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_17,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_18,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_19,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_8,plain,
? [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| ~ subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| subset(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t38_zfmisc_1_neg]) ).
fof(sk_t38_zfmisc_1_neg_sk,plain,
( ( ~ in(sK2,sK3)
| ~ in(sK1,sK3)
| ~ subset(unordered_pair(sK1,sK2),sK3) )
& ( ( in(sK2,sK3)
& in(sK1,sK3) )
| subset(unordered_pair(sK1,sK2),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_8]) ).
fof(sk_t38_zfmisc_1_neg,plain,
( ( ~ in(sK2,sK3)
| ~ in(sK1,sK3)
| ~ subset(unordered_pair(sK1,sK2),sK3) )
& ( in(sK2,sK3)
| subset(unordered_pair(sK1,sK2),sK3) )
& ( in(sK1,sK3)
| subset(unordered_pair(sK1,sK2),sK3) ) ),
inference(cnf_transformation,[status(thm)],[sk_t38_zfmisc_1_neg_sk]) ).
cnf(c_23,negated_conjecture,
( in(sK1,sK3)
| subset(unordered_pair(sK1,sK2),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t38_zfmisc_1_neg]) ).
cnf(c_24,negated_conjecture,
( in(sK2,sK3)
| subset(unordered_pair(sK1,sK2),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t38_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
( ~ in(sK2,sK3)
| ~ in(sK1,sK3)
| ~ subset(unordered_pair(sK1,sK2),sK3) ),
inference(split_conjunct,[status(thm)],[sk_t38_zfmisc_1_neg]) ).
cnf(c_31,plain,
( A = B
| A = C
| ~ in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_33,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_58,plain,
( in(A,sK3)
| ~ in(A,unordered_pair(sK1,sK2))
| in(sK1,sK3) ),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_63,plain,
( ~ in(sK1,unordered_pair(sK1,sK2))
| in(sK1,sK3) ),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_65,plain,
( in(A,sK3)
| ~ in(A,unordered_pair(sK1,sK2))
| in(sK2,sK3) ),
inference(resolve,[status(thm)],[c_24,c_17]) ).
cnf(c_70,plain,
( ~ in(sK2,unordered_pair(sK1,sK2))
| in(sK2,sK3) ),
inference(factor,[status(thm)],[c_65]) ).
cnf(c_109,plain,
( subset(unordered_pair(A,B),C)
| sK0(unordered_pair(A,B),C) = A
| sK0(unordered_pair(A,B),C) = B ),
inference(resolve,[status(thm)],[c_31,c_18]) ).
cnf(c_150,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_152,plain,
in(sK2,sK3),
inference(resolve,[status(thm)],[c_150,c_70]) ).
cnf(c_157,negated_conjecture,
( ~ in(sK1,sK3)
| ~ subset(unordered_pair(sK1,sK2),sK3) ),
inference(resolve,[status(thm)],[c_152,c_25]) ).
cnf(c_193,plain,
in(A,unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_10,c_150]) ).
cnf(c_197,plain,
in(sK1,sK3),
inference(resolve,[status(thm)],[c_193,c_63]) ).
cnf(c_198,negated_conjecture,
~ subset(unordered_pair(sK1,sK2),sK3),
inference(resolve,[status(thm)],[c_197,c_157]) ).
cnf(c_307,negated_conjecture,
~ in(sK0(unordered_pair(sK1,sK2),sK3),sK3),
inference(resolve,[status(thm)],[c_19,c_198]) ).
cnf(c_3319,plain,
( ~ in(sK2,sK3)
| subset(unordered_pair(sK1,sK2),sK3)
| sK0(unordered_pair(sK1,sK2),sK3) = sK1 ),
inference(paramod,[status(thm)],[c_109,c_307]) ).
cnf(c_3320,negated_conjecture,
( ~ in(sK2,sK3)
| sK0(unordered_pair(sK1,sK2),sK3) = sK1 ),
inference(resolve,[status(thm)],[c_198,c_3319]) ).
cnf(c_3230,negated_conjecture,
sK0(unordered_pair(sK1,sK2),sK3) = sK1,
inference(resolve,[status(thm)],[c_152,c_3320]) ).
cnf(c_3321,plain,
( ~ in(sK1,sK3)
| subset(unordered_pair(sK1,sK2),sK3)
| sK0(unordered_pair(sK1,sK2),sK3) = sK2 ),
inference(paramod,[status(thm)],[c_109,c_307]) ).
cnf(c_3322,plain,
( ~ in(sK1,sK3)
| subset(unordered_pair(sK1,sK2),sK3)
| sK1 = sK2 ),
inference(paramod,[status(thm)],[c_3230,c_3321]) ).
cnf(c_3323,plain,
( ~ in(sK1,sK3)
| subset(unordered_pair(sK1,sK2),sK3)
| sK2 = sK1 ),
inference(copy,[status(thm)],[c_3322]) ).
cnf(c_3324,negated_conjecture,
( ~ in(sK1,sK3)
| sK2 = sK1 ),
inference(resolve,[status(thm)],[c_198,c_3323]) ).
cnf(c_3231,negated_conjecture,
sK2 = sK1,
inference(resolve,[status(thm)],[c_197,c_3324]) ).
cnf(c_3271,negated_conjecture,
~ in(sK0(unordered_pair(sK1,sK1),sK3),sK3),
inference(paramod,[status(thm)],[c_3231,c_307]) ).
cnf(c_3273,negated_conjecture,
sK0(unordered_pair(sK1,sK1),sK3) = sK1,
inference(paramod,[status(thm)],[c_3231,c_3230]) ).
cnf(c_3325,negated_conjecture,
~ in(sK1,sK3),
inference(paramod,[status(thm)],[c_3273,c_3271]) ).
cnf(c_3318,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_197,c_3325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU159+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % Computer : n005.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Sat Sep 26 08:42:17 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.46 % Process 1724923 was started by sandbox on n005,
% 0.11/0.46 % Sat Sep 26 08:42:17 2026
% 0.11/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.46
% 0.11/0.46 % From the command line: assign(max_seconds, 300).
% 9.32/3.13
% 9.32/3.13 % SZS status Theorem for theBenchmark
% 9.32/3.13
% 9.32/3.13 % Proof 1 at 0.83 (+ 0.35) seconds.
% 9.32/3.13 % Length of proof is 32.
% 9.32/3.13 % Level of proof is 11.
% 9.32/3.13 % Maximum clause weight is 25.000.
% 9.32/3.13 % Given clauses 252.
% 9.32/3.13
% 9.32/3.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------