%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 06:55:54 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_g_equals_h,axiom,
g != h,
file('theBenchmark.p',prove_g_equals_h) ).
cnf(c_7,plain,
g != h,
inference(clausify,[status(thm)],[prove_g_equals_h]) ).
fof(ab_h_equals_ab_g,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('theBenchmark.p',ab_h_equals_ab_g) ).
cnf(c_8,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(clausify,[status(thm)],[ab_h_equals_ab_g]) ).
cnf(c_9,plain,
compose(compose(a,b),g) = compose(compose(a,b),h),
inference(copy,[status(thm)],[c_8]) ).
fof(cancellation_for_compose2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(b,VAR_2) != VAR_1
| compose(b,VAR_0) != VAR_1 ),
file('theBenchmark.p',cancellation_for_compose2) ).
cnf(c_11,plain,
( A = C
| compose(b,C) != B
| compose(b,A) != B ),
inference(clausify,[status(thm)],[cancellation_for_compose2]) ).
fof(cancellation_for_compose1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(a,VAR_2) != VAR_1
| compose(a,VAR_0) != VAR_1 ),
file('theBenchmark.p',cancellation_for_compose1) ).
cnf(c_12,plain,
( A = C
| compose(a,C) != B
| compose(a,A) != B ),
inference(clausify,[status(thm)],[cancellation_for_compose1]) ).
fof(associativity_of_compose,axiom,
! [VAR_0,VAR_1,VAR_2] : compose(VAR_0,compose(VAR_1,VAR_2)) = compose(compose(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_compose) ).
cnf(c_22,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_23,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_112,plain,
( A = B
| compose(b,A) != compose(b,B) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_34,plain,
compose(b,g) != compose(b,h),
inference(resolve,[status(thm)],[c_112,c_7]) ).
cnf(c_113,plain,
compose(a,compose(b,g)) = compose(compose(a,b),h),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_84,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(copy,[status(thm)],[c_113]) ).
cnf(c_114,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_115,plain,
( A = compose(B,C)
| compose(a,A) != compose(compose(a,B),C) ),
inference(resolve,[status(thm)],[c_12,c_114]) ).
cnf(c_116,plain,
compose(a,compose(b,g)) != compose(compose(a,b),h),
inference(resolve,[status(thm)],[c_115,c_34]) ).
cnf(c_117,plain,
compose(compose(a,b),h) != compose(a,compose(b,g)),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_111,plain,
$false,
inference(resolve,[status(thm)],[c_84,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n016.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 22:52:46 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 1913602 was started by sandbox on n016,
% 0.20/0.46 % Sat Sep 26 22:52:46 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.48
% 0.20/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.48 % Length of proof is 10.
% 0.20/0.48 % Level of proof is 3.
% 0.20/0.48 % Maximum clause weight is 30.000.
% 0.20/0.48 % Given clauses 23.
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------