%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 23 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 26 ~; 39 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 67 ( 10 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_16,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_17,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_23,plain,
( B = C
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(clausify,[status(thm)],[t10_zfmisc_1]) ).
cnf(c_24,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_27,plain,
( B = A
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t8_zfmisc_1]) ).
cnf(c_258,plain,
( B = A
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_24,c_27]) ).
cnf(c_28,plain,
( A = C
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_29,plain,
( C = B
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t9_zfmisc_1]) ).
cnf(c_259,plain,
( C = B
| unordered_pair(A,A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_24,c_29]) ).
cnf(c_30,plain,
( B = A
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(copy,[status(thm)],[c_259]) ).
fof(nnf_15,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_15]) ).
cnf(c_31,negated_conjecture,
ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t33_zfmisc_1_neg]) ).
cnf(c_260,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_261,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_24,c_260]) ).
cnf(c_262,negated_conjecture,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = ordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_16,c_261]) ).
cnf(c_263,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_17,c_262]) ).
cnf(c_264,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_24,c_263]) ).
cnf(c_32,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_16,c_264]) ).
cnf(c_33,negated_conjecture,
( sK1 != sK3
| sK0 != sK2 ),
inference(split_conjunct,[status(thm)],[sk_t33_zfmisc_1_neg]) ).
cnf(c_37,plain,
( B = D
| A = D
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(paramod,[status(thm)],[c_16,c_23]) ).
cnf(c_39,plain,
( B = C
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(paramod,[status(thm)],[c_16,c_28]) ).
cnf(c_40,plain,
( A = B
| unordered_pair(A,B) != unordered_pair(C,C) ),
inference(paramod,[status(thm)],[c_16,c_30]) ).
cnf(c_41,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_32,c_23]) ).
cnf(c_50,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK3) ),
inference(resolve,[status(thm)],[c_37,c_32]) ).
cnf(c_265,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_32]) ).
cnf(c_266,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK2,sK2) = unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_37,c_265]) ).
cnf(c_267,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_51,negated_conjecture,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK0,sK1) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_268,plain,
( sK0 = sK1
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_41,c_40]) ).
cnf(c_57,plain,
( sK1 = sK0
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_269,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_57,c_41]) ).
cnf(c_270,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_88,plain,
unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK2) = unordered_pair(sK2,sK3) ),
inference(paramod,[status(thm)],[c_88,c_50]) ).
cnf(c_90,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK3) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_95,plain,
sK0 = sK2,
inference(resolve,[status(thm)],[c_88,c_39]) ).
cnf(c_104,plain,
( unordered_pair(sK2,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK3) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_95,c_90]) ).
cnf(c_272,negated_conjecture,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_95,c_51]) ).
cnf(c_109,negated_conjecture,
( unordered_pair(sK2,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_95,c_272]) ).
cnf(c_273,negated_conjecture,
( sK1 != sK3
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_95,c_33]) ).
cnf(c_110,negated_conjecture,
sK1 != sK3,
inference(copy,[status(thm)],[c_273]) ).
cnf(c_112,negated_conjecture,
unordered_pair(A,sK1) != unordered_pair(sK3,sK3),
inference(resolve,[status(thm)],[c_39,c_110]) ).
cnf(c_274,plain,
( sK1 = sK3
| sK2 = sK3
| unordered_pair(sK2,sK3) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_104,c_37]) ).
cnf(c_275,plain,
( sK1 = sK3
| sK3 = sK2
| unordered_pair(sK2,sK3) = unordered_pair(sK2,sK2) ),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_189,negated_conjecture,
( sK3 = sK2
| unordered_pair(sK2,sK3) = unordered_pair(sK2,sK2) ),
inference(resolve,[status(thm)],[c_110,c_275]) ).
cnf(c_276,plain,
( sK2 = sK3
| sK3 = sK2 ),
inference(resolve,[status(thm)],[c_189,c_40]) ).
cnf(c_277,plain,
( sK3 = sK2
| sK3 = sK2 ),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_199,plain,
sK3 = sK2,
inference(copy,[status(thm)],[c_277]) ).
cnf(c_278,negated_conjecture,
unordered_pair(A,sK1) != unordered_pair(sK2,sK3),
inference(paramod,[status(thm)],[c_199,c_112]) ).
cnf(c_254,negated_conjecture,
unordered_pair(A,sK1) != unordered_pair(sK2,sK2),
inference(paramod,[status(thm)],[c_199,c_278]) ).
cnf(c_279,negated_conjecture,
( unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2)
| unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2) ),
inference(paramod,[status(thm)],[c_199,c_109]) ).
cnf(c_280,negated_conjecture,
unordered_pair(sK2,sK1) = unordered_pair(sK2,sK2),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_257,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_254,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.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 08:43:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2475243 was started by sandbox on n003,
% 0.10/0.37 % Sat Sep 26 08:43:09 2026
% 0.10/0.37 % 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).
% 0.10/0.44
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.10/0.44 % Length of proof is 36.
% 0.10/0.44 % Level of proof is 11.
% 0.10/0.44 % Maximum clause weight is 15.000.
% 0.10/0.44 % Given clauses 45.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------