%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU156+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 : n009.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 08:45:13 AM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 32 unt; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 87 ( 37 ~; 40 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 28 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_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(t10_zfmisc_1,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(t33_zfmisc_1,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t33_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
inference(assume_negation,[status(cth)],[t33_zfmisc_1]) ).
cnf(c_13,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_14,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_20,plain,
( B = C
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(clausify,[status(thm)],[t10_zfmisc_1]) ).
cnf(c_21,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_24,plain,
( B = A
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t8_zfmisc_1]) ).
cnf(c_181,plain,
( B = A
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_21,c_24]) ).
cnf(c_25,plain,
( A = C
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_26,plain,
( C = B
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t9_zfmisc_1]) ).
cnf(c_182,plain,
( C = B
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_21,c_26]) ).
cnf(c_27,plain,
( B = A
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_182]) ).
fof(nnf_12,plain,
? [A,B,C,D] :
( ( D != B
| C != A )
& ordered_pair(C,D) = ordered_pair(A,B) ),
inference(fof_nnf,[status(thm)],[t33_zfmisc_1_neg]) ).
fof(sk_t33_zfmisc_1_neg,plain,
( ( sK1 != sK3
| sK0 != sK2 )
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK0),skolemize(D,sK1)],[nnf_12]) ).
cnf(c_28,negated_conjecture,
ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t33_zfmisc_1_neg]) ).
cnf(c_183,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_14,c_28]) ).
cnf(c_184,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_21,c_183]) ).
cnf(c_185,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_13,c_184]) ).
cnf(c_186,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),
inference(paramod,[status(thm)],[c_14,c_185]) ).
cnf(c_187,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = unordered_pair(unordered_pair(sK2,sK3),unordered_pair(sK2,sK2)),
inference(paramod,[status(thm)],[c_21,c_186]) ).
cnf(c_29,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),
inference(paramod,[status(thm)],[c_13,c_187]) ).
cnf(c_30,negated_conjecture,
( sK1 != sK3
| sK0 != sK2 ),
inference(split_conjunct,[status(thm)],[sk_t33_zfmisc_1_neg]) ).
cnf(c_188,plain,
( A = B
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(factor,[status(thm)],[c_20]) ).
cnf(c_31,plain,
( C = A
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_34,plain,
( B = D
| A = D
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(paramod,[status(thm)],[c_13,c_20]) ).
cnf(c_189,plain,
( A = C
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_35,plain,
( C = B
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_36,plain,
( B = C
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(paramod,[status(thm)],[c_13,c_25]) ).
cnf(c_37,plain,
( A = B
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(paramod,[status(thm)],[c_13,c_27]) ).
cnf(c_38,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_29,c_20]) ).
cnf(c_190,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_191,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK2,sK2) = unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_34,c_190]) ).
cnf(c_192,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_45,negated_conjecture,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_48,plain,
( sK0 = sK2
| unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_38,c_36]) ).
cnf(c_193,plain,
( sK2 = sK0
| sK0 = sK2 ),
inference(resolve,[status(thm)],[c_48,c_31]) ).
cnf(c_194,plain,
( sK0 = sK2
| sK0 = sK2 ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_71,plain,
sK0 = sK2,
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,negated_conjecture,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_71,c_45]) ).
cnf(c_77,negated_conjecture,
( unordered_pair(sK2,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_71,c_195]) ).
cnf(c_196,negated_conjecture,
( sK1 != sK3
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_71,c_30]) ).
cnf(c_80,negated_conjecture,
sK1 != sK3,
inference(copy,[status(thm)],[c_196]) ).
cnf(c_197,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK0),unordered_pair(sK0,sK1)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),
inference(paramod,[status(thm)],[c_71,c_29]) ).
cnf(c_198,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK1)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),
inference(paramod,[status(thm)],[c_71,c_197]) ).
cnf(c_81,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK1)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),
inference(paramod,[status(thm)],[c_71,c_198]) ).
cnf(c_199,negated_conjecture,
unordered_pair(A,sK3) != unordered_pair(sK1,sK1),
inference(resolve,[status(thm)],[c_35,c_80]) ).
cnf(c_84,negated_conjecture,
unordered_pair(sK1,sK1) != unordered_pair(A,sK3),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_200,plain,
unordered_pair(A,unordered_pair(B,sK3)) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,sK1)),
inference(resolve,[status(thm)],[c_35,c_84]) ).
cnf(c_113,plain,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,sK1)) != unordered_pair(A,unordered_pair(B,sK3)),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,plain,
( sK2 = sK1
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK3) ),
inference(resolve,[status(thm)],[c_77,c_37]) ).
cnf(c_126,plain,
( sK1 = sK2
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK3) ),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
( B = D
| A = D
| unordered_pair(C,D) != unordered_pair(A,B) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_203,plain,
( sK3 = sK1
| sK2 = sK1
| sK1 = sK2 ),
inference(resolve,[status(thm)],[c_126,c_202]) ).
cnf(c_204,plain,
( sK3 = sK1
| sK1 = sK2
| sK1 = sK2 ),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_205,plain,
( sK1 = sK3
| sK1 = sK2
| sK1 = sK2 ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_206,plain,
( sK1 = sK3
| sK1 = sK2 ),
inference(copy,[status(thm)],[c_205]) ).
cnf(c_141,negated_conjecture,
sK1 = sK2,
inference(resolve,[status(thm)],[c_80,c_206]) ).
cnf(c_207,plain,
unordered_pair(unordered_pair(sK2,sK1),unordered_pair(sK1,sK1)) != unordered_pair(A,unordered_pair(B,sK3)),
inference(paramod,[status(thm)],[c_141,c_113]) ).
cnf(c_208,plain,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK1,sK1)) != unordered_pair(A,unordered_pair(B,sK3)),
inference(paramod,[status(thm)],[c_141,c_207]) ).
cnf(c_209,plain,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK1)) != unordered_pair(A,unordered_pair(B,sK3)),
inference(paramod,[status(thm)],[c_141,c_208]) ).
cnf(c_210,plain,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)) != unordered_pair(A,unordered_pair(B,sK3)),
inference(paramod,[status(thm)],[c_141,c_209]) ).
cnf(c_156,plain,
unordered_pair(A,unordered_pair(B,sK3)) != unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)),
inference(copy,[status(thm)],[c_210]) ).
cnf(c_211,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),
inference(paramod,[status(thm)],[c_141,c_81]) ).
cnf(c_212,negated_conjecture,
unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)),
inference(copy,[status(thm)],[c_211]) ).
cnf(c_180,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_156,c_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:41:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3876706 was started by sandbox on n009,
% 0.07/0.35 % Sat Sep 26 08:41:44 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.41
% 0.12/0.41 % SZS status Theorem for theBenchmark
% 0.12/0.41
% 0.12/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.41 % Length of proof is 36.
% 0.12/0.41 % Level of proof is 10.
% 0.12/0.41 % Maximum clause weight is 29.000.
% 0.12/0.41 % Given clauses 32.
% 0.12/0.41
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------