%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP781-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:31:26 AM UTC 2026
% Result : Unsatisfiable 25.14s 3.66s
% Output : CNFRefutation 25.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 30 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : m(VAR_0,m(VAR_1,VAR_2)) = m(m(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity) ).
cnf(c_1,plain,
m(A,m(B,C)) = m(m(A,B),C),
inference(clausify,[status(thm)],[associativity]) ).
cnf(c_2,plain,
m(m(A,B),C) = m(A,m(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| m(VAR_0,VAR_1) != m(VAR_2,VAR_1) ),
file('theBenchmark.p',cancellation) ).
cnf(c_3,plain,
( A = C
| m(A,B) != m(C,B) ),
inference(clausify,[status(thm)],[cancellation]) ).
fof(cancellation_001,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| m(VAR_0,VAR_1) != m(VAR_0,VAR_2) ),
file('theBenchmark.p',cancellation_001) ).
cnf(c_4,plain,
( B = C
| m(A,B) != m(A,C) ),
inference(clausify,[status(thm)],[cancellation_001]) ).
fof(commutator,axiom,
! [VAR_0,VAR_1] : m(VAR_0,m(VAR_1,c(VAR_1,VAR_0))) = m(VAR_1,VAR_0),
file('theBenchmark.p',commutator) ).
cnf(c_5,plain,
m(A,m(B,c(B,A))) = m(B,A),
inference(clausify,[status(thm)],[commutator]) ).
fof(assumption,axiom,
! [VAR_0,VAR_1,VAR_2] : m(VAR_0,m(VAR_1,m(VAR_2,m(VAR_1,VAR_0)))) = m(VAR_1,m(VAR_0,m(VAR_2,m(VAR_0,VAR_1)))),
file('theBenchmark.p',assumption) ).
cnf(c_6,plain,
m(A,m(B,m(C,m(B,A)))) = m(B,m(A,m(C,m(A,B)))),
inference(clausify,[status(thm)],[assumption]) ).
fof(distributivity,axiom,
c(m(x,y),z) != m(c(x,z),c(y,z)),
file('theBenchmark.p',distributivity) ).
cnf(c_7,plain,
c(m(x,y),z) != m(c(x,z),c(y,z)),
inference(clausify,[status(thm)],[distributivity]) ).
cnf(c_6620,plain,
( C = D
| m(A,m(B,C)) != m(m(A,B),D) ),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_9,plain,
( C = D
| m(A,m(B,C)) != m(A,m(B,D)) ),
inference(paramod,[status(thm)],[c_2,c_6620]) ).
cnf(c_10,plain,
m(A,c(A,A)) = A,
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_6621,plain,
m(m(A,B),C) = m(B,m(m(A,c(A,B)),C)),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_6622,plain,
m(A,m(B,C)) = m(B,m(m(A,c(A,B)),C)),
inference(paramod,[status(thm)],[c_2,c_6621]) ).
cnf(c_6623,plain,
m(A,m(B,C)) = m(B,m(A,m(c(A,B),C))),
inference(paramod,[status(thm)],[c_2,c_6622]) ).
cnf(c_11,plain,
m(A,m(B,m(c(B,A),C))) = m(B,m(A,C)),
inference(copy,[status(thm)],[c_6623]) ).
cnf(c_6624,plain,
m(c(m(x,y),z),A) != m(m(c(x,z),c(y,z)),A),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_25,plain,
m(c(m(x,y),z),A) != m(c(x,z),m(c(y,z),A)),
inference(paramod,[status(thm)],[c_2,c_6624]) ).
cnf(c_39,plain,
( m(C,m(A,B)) = D
| m(A,m(B,m(C,m(B,A)))) != m(B,m(A,D)) ),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_103,plain,
m(c(A,A),B) = B,
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_108,plain,
( m(A,m(c(A,B),C)) = D
| m(A,m(B,C)) != m(B,D) ),
inference(paramod,[status(thm)],[c_11,c_4]) ).
cnf(c_6625,plain,
( C = m(c(B,A),D)
| m(A,m(B,C)) != m(B,m(A,D)) ),
inference(paramod,[status(thm)],[c_11,c_9]) ).
cnf(c_118,plain,
( m(c(B,A),D) = C
| m(A,m(B,C)) != m(B,m(A,D)) ),
inference(copy,[status(thm)],[c_6625]) ).
cnf(c_6626,plain,
( c(C,C) = B
| A != m(B,A) ),
inference(paramod,[status(thm)],[c_103,c_3]) ).
cnf(c_201,plain,
( c(C,C) = A
| m(A,B) != B ),
inference(copy,[status(thm)],[c_6626]) ).
cnf(c_219,plain,
c(A,A) = c(B,B),
inference(resolve,[status(thm)],[c_201,c_103]) ).
cnf(c_226,plain,
m(A,c(B,B)) = A,
inference(paramod,[status(thm)],[c_219,c_10]) ).
cnf(c_6627,plain,
( c(C,C) = B
| A != m(A,B) ),
inference(paramod,[status(thm)],[c_226,c_4]) ).
cnf(c_275,plain,
( c(C,C) = B
| m(A,B) != A ),
inference(copy,[status(thm)],[c_6627]) ).
cnf(c_867,plain,
m(c(A,B),m(B,A)) = m(A,B),
inference(resolve,[status(thm)],[c_39,c_11]) ).
cnf(c_6628,plain,
( c(A,B) = C
| m(A,B) != m(C,m(B,A)) ),
inference(paramod,[status(thm)],[c_867,c_3]) ).
cnf(c_902,plain,
( c(C,B) = A
| m(A,m(B,C)) != m(C,B) ),
inference(copy,[status(thm)],[c_6628]) ).
cnf(c_2288,plain,
m(A,m(c(A,B),c(B,A))) = A,
inference(resolve,[status(thm)],[c_108,c_5]) ).
cnf(c_5084,plain,
c(A,A) = m(c(B,C),c(C,B)),
inference(resolve,[status(thm)],[c_275,c_2288]) ).
cnf(c_6629,plain,
m(c(m(x,y),z),c(z,y)) != m(c(x,z),c(A,A)),
inference(paramod,[status(thm)],[c_5084,c_25]) ).
cnf(c_5305,plain,
m(c(m(x,y),z),c(z,y)) != c(x,z),
inference(paramod,[status(thm)],[c_226,c_6629]) ).
cnf(c_6630,plain,
c(x,z) != m(c(m(x,y),z),c(z,y)),
inference(copy,[status(thm)],[c_5305]) ).
cnf(c_6631,plain,
m(m(c(m(x,y),z),c(z,y)),m(z,x)) != m(x,z),
inference(resolve,[status(thm)],[c_902,c_6630]) ).
cnf(c_5524,plain,
m(c(m(x,y),z),m(c(z,y),m(z,x))) != m(x,z),
inference(paramod,[status(thm)],[c_2,c_6631]) ).
cnf(c_6632,plain,
m(z,m(m(x,y),m(x,z))) != m(m(x,y),m(z,m(c(z,y),m(z,x)))),
inference(resolve,[status(thm)],[c_118,c_5524]) ).
cnf(c_6633,plain,
m(z,m(x,m(y,m(x,z)))) != m(m(x,y),m(z,m(c(z,y),m(z,x)))),
inference(paramod,[status(thm)],[c_2,c_6632]) ).
cnf(c_6634,plain,
m(z,m(x,m(y,m(x,z)))) != m(x,m(y,m(z,m(c(z,y),m(z,x))))),
inference(paramod,[status(thm)],[c_2,c_6633]) ).
cnf(c_6635,plain,
m(z,m(x,m(y,m(x,z)))) != m(x,m(z,m(y,m(z,x)))),
inference(paramod,[status(thm)],[c_11,c_6634]) ).
cnf(c_6618,plain,
m(x,m(z,m(y,m(z,x)))) != m(z,m(x,m(y,m(x,z)))),
inference(copy,[status(thm)],[c_6635]) ).
cnf(c_6619,plain,
$false,
inference(resolve,[status(thm)],[c_6618,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP781-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n007.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 15:44:53 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.43 % Process 1400781 was started by sandbox2 on n007,
% 0.14/0.43 % Fri Sep 25 15:44:53 2026
% 0.14/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.43
% 0.14/0.43 % From the command line: assign(max_seconds, 300).
% 25.14/3.66
% 25.14/3.66 % SZS status Unsatisfiable for theBenchmark
% 25.14/3.66
% 25.14/3.66 % Proof 1 at 2.73 (+ 0.47) seconds.
% 25.14/3.66 % Length of proof is 27.
% 25.14/3.66 % Level of proof is 12.
% 25.14/3.66 % Maximum clause weight is 74.000.
% 25.14/3.66 % Given clauses 415.
% 25.14/3.66
% 25.14/3.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------