%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 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 08:45:38 AM UTC 2026
% Result : Theorem 0.05s 15.56s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 25 ~; 16 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 14 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('theBenchmark.p',d1_mcart_1) ).
fof(d2_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('theBenchmark.p',d2_mcart_1) ).
fof(t7_mcart_1,conjecture,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
fof(t7_mcart_1_neg,negated_conjecture,
~ ! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(assume_negation,[status(cth)],[t7_mcart_1]) ).
fof(nnf_18,plain,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
| pair_first(ordered_pair(A,B)) != A ),
inference(fof_nnf,[status(thm)],[t7_mcart_1_neg]) ).
fof(sk_t7_mcart_1_neg,plain,
( pair_second(ordered_pair(sK0,sK1)) != sK1
| pair_first(ordered_pair(sK0,sK1)) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_18]) ).
cnf(c_23,negated_conjecture,
( pair_second(ordered_pair(sK0,sK1)) != sK1
| pair_first(ordered_pair(sK0,sK1)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t7_mcart_1_neg]) ).
cnf(c_26,plain,
( F = D
| ordered_pair(E,F) != C
| pair_second(C) != D
| ordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_mcart_1]) ).
cnf(c_29,plain,
( E = D
| ordered_pair(E,F) != C
| pair_first(C) != D
| ordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d1_mcart_1]) ).
cnf(c_38,plain,
( B = D
| pair_second(C) != D
| ordered_pair(A,B) != C ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_39,plain,
( A = D
| pair_first(C) != D
| ordered_pair(A,B) != C ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_48,plain,
( B = C
| pair_second(ordered_pair(A,B)) != C ),
inference(xxres,[status(thm)],[c_38]) ).
cnf(c_65,plain,
A = pair_second(ordered_pair(B,A)),
inference(xxres,[status(thm)],[c_48]) ).
cnf(c_54,plain,
pair_second(ordered_pair(A,B)) = B,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_66,negated_conjecture,
( sK1 != sK1
| pair_first(ordered_pair(sK0,sK1)) != sK0 ),
inference(paramod,[status(thm)],[c_54,c_23]) ).
cnf(c_57,negated_conjecture,
pair_first(ordered_pair(sK0,sK1)) != sK0,
inference(copy,[status(thm)],[c_66]) ).
cnf(c_67,plain,
( A = pair_first(C)
| ordered_pair(A,B) != C ),
inference(xxres,[status(thm)],[c_39]) ).
cnf(c_68,negated_conjecture,
sK0 != pair_first(ordered_pair(sK0,sK1)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_69,negated_conjecture,
ordered_pair(sK0,A) != ordered_pair(sK0,sK1),
inference(resolve,[status(thm)],[c_67,c_68]) ).
cnf(c_70,negated_conjecture,
ordered_pair(sK0,sK1) != ordered_pair(sK0,A),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_64,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/15.54 % Computer : n012.cluster.edu
% 0.05/15.54 % Model : x86_64 x86_64
% 0.05/15.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/15.54 % Memory : 8046.5625MB
% 0.05/15.54 % OS : Linux 6.8.0-71-generic
% 0.05/15.54 % CPULimit : 300
% 0.05/15.54 % WCLimit : 300
% 0.05/15.54 % DateTime : Sat Sep 26 09:01:53 UTC 2026
% 0.05/15.54 % CPUTime :
% 0.05/15.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/15.54 % Process 212359 was started by sandbox2 on n012,
% 0.05/15.54 % Sat Sep 26 09:01:53 2026
% 0.05/15.54 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/15.55
% 0.05/15.55 % From the command line: assign(max_seconds, 300).
% 0.05/15.56
% 0.05/15.56 % SZS status Theorem for theBenchmark
% 0.05/15.56
% 0.05/15.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.05/15.56 % Length of proof is 12.
% 0.05/15.56 % Level of proof is 6.
% 0.05/15.56 % Maximum clause weight is 17.000.
% 0.05/15.56 % Given clauses 26.
% 0.05/15.56
% 0.05/15.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------