%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MSC008-1.002 : 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 : n015.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 : Unsatisfiable 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 29 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 98 ( 29 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p_1_is_not_p_2,axiom,
~ eq(p_1,p_2),
file('theBenchmark.p',p_1_is_not_p_2) ).
cnf(c_1,plain,
~ eq(p_1,p_2),
inference(clausify,[status(thm)],[p_1_is_not_p_2]) ).
fof(symmetry,axiom,
! [VAR_0,VAR_1] :
( eq(VAR_1,VAR_0)
| ~ eq(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry) ).
cnf(c_3,plain,
( eq(B,A)
| ~ eq(A,B) ),
inference(clausify,[status(thm)],[symmetry]) ).
fof(latin_element_is_unique,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(VAR_2,VAR_3)
| ~ latin(VAR_0,VAR_1,VAR_3)
| ~ latin(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',latin_element_is_unique) ).
cnf(c_4,plain,
( eq(C,D)
| ~ latin(A,B,D)
| ~ latin(A,B,C) ),
inference(clausify,[status(thm)],[latin_element_is_unique]) ).
fof(greek_element_is_unique,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(VAR_2,VAR_3)
| ~ greek(VAR_0,VAR_1,VAR_3)
| ~ greek(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',greek_element_is_unique) ).
cnf(c_7,plain,
( eq(C,D)
| ~ greek(A,B,D)
| ~ greek(A,B,C) ),
inference(clausify,[status(thm)],[greek_element_is_unique]) ).
fof(latin_column_required,axiom,
! [VAR_0,VAR_1] :
( latin(VAR_0,p_2,VAR_1)
| latin(VAR_0,p_1,VAR_1) ),
file('theBenchmark.p',latin_column_required) ).
cnf(c_11,plain,
( latin(A,p_2,B)
| latin(A,p_1,B) ),
inference(clausify,[status(thm)],[latin_column_required]) ).
fof(latin_row_required,axiom,
! [VAR_0,VAR_1] :
( latin(p_2,VAR_0,VAR_1)
| latin(p_1,VAR_0,VAR_1) ),
file('theBenchmark.p',latin_row_required) ).
cnf(c_12,plain,
( latin(p_2,A,B)
| latin(p_1,A,B) ),
inference(clausify,[status(thm)],[latin_row_required]) ).
fof(greek_column_required,axiom,
! [VAR_0,VAR_1] :
( greek(VAR_0,p_2,VAR_1)
| greek(VAR_0,p_1,VAR_1) ),
file('theBenchmark.p',greek_column_required) ).
cnf(c_14,plain,
( greek(A,p_2,B)
| greek(A,p_1,B) ),
inference(clausify,[status(thm)],[greek_column_required]) ).
fof(greek_row_required,axiom,
! [VAR_0,VAR_1] :
( greek(p_2,VAR_0,VAR_1)
| greek(p_1,VAR_0,VAR_1) ),
file('theBenchmark.p',greek_row_required) ).
cnf(c_15,plain,
( greek(p_2,A,B)
| greek(p_1,A,B) ),
inference(clausify,[status(thm)],[greek_row_required]) ).
fof(no_two_same1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( eq(VAR_1,VAR_5)
| ~ latin(VAR_4,VAR_5,VAR_3)
| ~ greek(VAR_4,VAR_5,VAR_2)
| ~ latin(VAR_0,VAR_1,VAR_3)
| ~ greek(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',no_two_same1) ).
cnf(c_16,plain,
( eq(B,F)
| ~ latin(E,F,D)
| ~ greek(E,F,C)
| ~ latin(A,B,D)
| ~ greek(A,B,C) ),
inference(clausify,[status(thm)],[no_two_same1]) ).
cnf(c_18,plain,
~ eq(p_2,p_1),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_276,plain,
( greek(p_1,A,E)
| eq(A,D)
| ~ latin(C,D,B)
| ~ greek(C,D,E)
| ~ latin(p_2,A,B) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_277,plain,
( latin(p_1,E,D)
| greek(p_1,E,C)
| eq(E,B)
| ~ latin(A,B,D)
| ~ greek(A,B,C) ),
inference(resolve,[status(thm)],[c_276,c_12]) ).
cnf(c_278,plain,
( greek(A,p_1,D)
| latin(p_1,C,B)
| greek(p_1,C,D)
| eq(C,p_2)
| ~ latin(A,p_2,B) ),
inference(resolve,[status(thm)],[c_277,c_14]) ).
cnf(c_109,plain,
( latin(D,p_1,C)
| greek(D,p_1,B)
| latin(p_1,A,C)
| greek(p_1,A,B)
| eq(A,p_2) ),
inference(resolve,[status(thm)],[c_278,c_11]) ).
cnf(c_279,plain,
( latin(p_1,p_1,B)
| latin(p_1,p_1,B)
| greek(p_1,p_1,A)
| eq(p_1,p_2) ),
inference(factor,[status(thm)],[c_109]) ).
cnf(c_280,plain,
( latin(p_1,p_1,B)
| greek(p_1,p_1,A)
| eq(p_1,p_2) ),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_144,plain,
( latin(p_1,p_1,B)
| greek(p_1,p_1,A) ),
inference(resolve,[status(thm)],[c_1,c_280]) ).
cnf(c_281,plain,
( greek(p_1,p_1,C)
| eq(B,A)
| ~ latin(p_1,p_1,A) ),
inference(resolve,[status(thm)],[c_4,c_144]) ).
cnf(c_220,plain,
( greek(p_1,p_1,D)
| greek(p_1,p_1,C)
| eq(A,B) ),
inference(resolve,[status(thm)],[c_281,c_144]) ).
cnf(c_229,plain,
( greek(p_1,p_1,C)
| eq(A,B) ),
inference(factor,[status(thm)],[c_220]) ).
cnf(c_282,plain,
( eq(C,D)
| eq(B,A)
| ~ greek(p_1,p_1,A) ),
inference(resolve,[status(thm)],[c_7,c_229]) ).
cnf(c_258,plain,
( eq(E,F)
| eq(C,D)
| eq(A,B) ),
inference(resolve,[status(thm)],[c_282,c_229]) ).
cnf(c_273,plain,
( eq(C,D)
| eq(A,B) ),
inference(factor,[status(thm)],[c_258]) ).
cnf(c_274,plain,
eq(A,B),
inference(factor,[status(thm)],[c_273]) ).
cnf(c_275,plain,
$false,
inference(resolve,[status(thm)],[c_274,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MSC008-1.002 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 00:18:19 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 2620434 was started by sandbox2 on n015,
% 0.09/5.38 % Sat Sep 26 00:18:19 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.45
% 0.15/5.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.45
% 0.15/5.45 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.15/5.45 % Length of proof is 18.
% 0.15/5.45 % Level of proof is 8.
% 0.15/5.45 % Maximum clause weight is 24.000.
% 0.15/5.45 % Given clauses 20.
% 0.15/5.45
% 0.15/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------