%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:04:27 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 21 ~; 29 |; 7 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 45 ( 2 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_to_right,axiom,
! [A,B] :
( ( p(B)
& less(A,B)
& p(A) )
=> goal ),
file('theBenchmark.p',left_to_right) ).
fof(right_to_left,axiom,
! [A] :
( ? [B] :
( p(B)
& less(A,B) )
| p(A) ),
file('theBenchmark.p',right_to_left) ).
fof(transitive_less,axiom,
! [A,B,C] :
( ( less(B,C)
& less(A,B) )
=> less(A,C) ),
file('theBenchmark.p',transitive_less) ).
fof(serial_less,axiom,
! [A] :
? [B] : less(A,B),
file('theBenchmark.p',serial_less) ).
fof(goal_to_be_proved,conjecture,
goal,
file('theBenchmark.p',goal_to_be_proved) ).
fof(goal_to_be_proved_neg,negated_conjecture,
~ goal,
inference(assume_negation,[status(cth)],[goal_to_be_proved]) ).
cnf(c_6,plain,
( goal
| ~ p(B)
| ~ less(A,B)
| ~ p(A) ),
inference(clausify,[status(thm)],[left_to_right]) ).
fof(nnf_2,plain,
! [A] :
( ? [B] :
( p(B)
& less(A,B) )
| p(A) ),
inference(fof_nnf,[status(thm)],[right_to_left]) ).
fof(sk_right_to_left_sk,plain,
! [A] :
( ( p(sK0(A))
& less(A,sK0(A)) )
| p(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_2]) ).
fof(sk_right_to_left,plain,
( ! [VAR_0] :
( p(sK0(VAR_0))
| p(VAR_0) )
& ! [VAR_0] :
( less(VAR_0,sK0(VAR_0))
| p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_right_to_left_sk]) ).
cnf(c_7,plain,
( less(A,sK0(A))
| p(A) ),
inference(split_conjunct,[status(thm)],[sk_right_to_left]) ).
cnf(c_8,plain,
( p(sK0(A))
| p(A) ),
inference(split_conjunct,[status(thm)],[sk_right_to_left]) ).
cnf(c_9,plain,
( less(A,C)
| ~ less(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitive_less]) ).
fof(nnf_4,plain,
! [A] :
? [B] : less(A,B),
inference(fof_nnf,[status(thm)],[serial_less]) ).
fof(sk_serial_less,plain,
! [A] : less(A,sK1(A)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(B,sK1(A))],[nnf_4]) ).
cnf(c_10,plain,
less(A,sK1(A)),
inference(split_conjunct,[status(thm)],[sk_serial_less]) ).
cnf(c_11,negated_conjecture,
~ goal,
inference(clausify,[status(thm)],[goal_to_be_proved_neg]) ).
cnf(c_13,negated_conjecture,
( ~ p(B)
| ~ less(A,B)
| ~ p(A) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_15,plain,
( p(B)
| less(A,sK0(B))
| ~ less(A,B) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_16,plain,
( less(A,sK1(B))
| ~ less(A,B) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_19,plain,
( p(A)
| ~ p(B)
| ~ less(sK0(A),B) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_20,plain,
( ~ p(sK1(A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_23,plain,
( p(sK1(A))
| less(A,sK0(sK1(A))) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_24,plain,
less(A,sK1(sK1(A))),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_25,plain,
( p(A)
| ~ p(sK1(sK0(A))) ),
inference(resolve,[status(thm)],[c_20,c_8]) ).
cnf(c_26,plain,
( p(B)
| p(A)
| ~ less(sK0(A),sK0(B)) ),
inference(resolve,[status(thm)],[c_19,c_8]) ).
cnf(c_46,plain,
( p(sK1(sK0(A)))
| p(A)
| p(sK1(sK0(A))) ),
inference(resolve,[status(thm)],[c_23,c_26]) ).
cnf(c_32,plain,
( p(A)
| p(sK1(sK0(A))) ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_39,plain,
( ~ p(sK1(sK1(A)))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_24,c_13]) ).
cnf(c_47,plain,
( p(A)
| p(A) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_44,plain,
p(A),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_48,plain,
~ p(sK1(sK1(A))),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_45,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 00:15:31 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1488622 was started by sandbox2 on n014,
% 0.17/0.43 % Sat Sep 26 00:15:31 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 24.
% 0.17/0.45 % Level of proof is 7.
% 0.17/0.45 % Maximum clause weight is 26.000.
% 0.17/0.45 % Given clauses 23.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------