%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MSC006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:04:16 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 18 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 37 ( 5 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p_transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( p(VAR_0,VAR_2)
| ~ p(VAR_1,VAR_2)
| ~ p(VAR_0,VAR_1) ),
file('theBenchmark.p',p_transitivity) ).
cnf(c_1,plain,
( p(A,C)
| ~ p(B,C)
| ~ p(A,B) ),
inference(clausify,[status(thm)],[p_transitivity]) ).
fof(q_transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( q(VAR_0,VAR_2)
| ~ q(VAR_1,VAR_2)
| ~ q(VAR_0,VAR_1) ),
file('theBenchmark.p',q_transitivity) ).
cnf(c_2,plain,
( q(A,C)
| ~ q(B,C)
| ~ q(A,B) ),
inference(clausify,[status(thm)],[q_transitivity]) ).
fof(q_symmetry,axiom,
! [VAR_0,VAR_1] :
( q(VAR_1,VAR_0)
| ~ q(VAR_0,VAR_1) ),
file('theBenchmark.p',q_symmetry) ).
cnf(c_3,plain,
( q(B,A)
| ~ q(A,B) ),
inference(clausify,[status(thm)],[q_symmetry]) ).
fof(all_related,axiom,
! [VAR_0,VAR_1] :
( q(VAR_0,VAR_1)
| p(VAR_0,VAR_1) ),
file('theBenchmark.p',all_related) ).
cnf(c_4,plain,
( q(A,B)
| p(A,B) ),
inference(clausify,[status(thm)],[all_related]) ).
fof(p_is_not_total,axiom,
~ p(a,b),
file('theBenchmark.p',p_is_not_total) ).
cnf(c_5,plain,
~ p(a,b),
inference(clausify,[status(thm)],[p_is_not_total]) ).
fof(prove_q_is_total,axiom,
~ q(c,d),
file('theBenchmark.p',prove_q_is_total) ).
cnf(c_6,plain,
~ q(c,d),
inference(clausify,[status(thm)],[prove_q_is_total]) ).
cnf(c_7,plain,
( p(C,B)
| ~ p(C,A)
| q(A,B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_9,plain,
q(a,b),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_10,plain,
~ q(d,c),
inference(resolve,[status(thm)],[c_3,c_6]) ).
cnf(c_11,plain,
( q(C,A)
| p(C,B)
| q(A,B) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_12,plain,
q(b,a),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_15,plain,
( q(A,a)
| ~ q(A,b) ),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_20,plain,
( q(a,A)
| q(A,b) ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_23,plain,
( q(A,a)
| q(a,A) ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_38,plain,
( q(A,a)
| q(A,a) ),
inference(resolve,[status(thm)],[c_23,c_3]) ).
cnf(c_31,plain,
q(A,a),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_39,plain,
( q(a,A)
| q(a,A) ),
inference(resolve,[status(thm)],[c_23,c_3]) ).
cnf(c_32,plain,
q(a,A),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_40,plain,
( q(B,A)
| ~ q(a,A) ),
inference(resolve,[status(thm)],[c_31,c_2]) ).
cnf(c_36,plain,
q(A,B),
inference(resolve,[status(thm)],[c_32,c_40]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MSC006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 00:15:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.40 % Process 4061863 was started by sandbox2 on n019,
% 0.12/0.40 % Sat Sep 26 00:15:06 2026
% 0.12/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.42 % Length of proof is 18.
% 0.12/0.42 % Level of proof is 7.
% 0.12/0.42 % Maximum clause weight is 9.000.
% 0.12/0.42 % Given clauses 21.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------