%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT002-4 : 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 : n009.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 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 : 25 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_g_equals_h,axiom,
g != h,
file('theBenchmark.p',prove_g_equals_h) ).
cnf(c_4,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_5,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(clausify,[status(thm)],[ab_h_equals_ab_g]) ).
cnf(c_6,plain,
compose(compose(a,b),g) = compose(compose(a,b),h),
inference(copy,[status(thm)],[c_5]) ).
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_8,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_9,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_13,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_14,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_42,plain,
compose(a,compose(b,g)) = compose(compose(a,b),h),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_22,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(paramod,[status(thm)],[c_14,c_42]) ).
cnf(c_43,plain,
( A = B
| compose(b,A) != compose(b,B) ),
inference(xxres,[status(thm)],[c_8]) ).
cnf(c_23,plain,
compose(b,g) != compose(b,h),
inference(resolve,[status(thm)],[c_43,c_4]) ).
cnf(c_44,plain,
( B = A
| compose(a,A) != compose(a,B) ),
inference(xxres,[status(thm)],[c_9]) ).
cnf(c_45,plain,
compose(b,h) = compose(b,g),
inference(resolve,[status(thm)],[c_44,c_22]) ).
cnf(c_40,plain,
compose(b,g) = compose(b,h),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_41,plain,
$false,
inference(resolve,[status(thm)],[c_40,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 22:47:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1314153 was started by sandbox2 on n009,
% 0.12/0.36 % Sat Sep 26 22:47:59 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 11.
% 0.12/0.38 % Level of proof is 4.
% 0.12/0.38 % Maximum clause weight is 13.000.
% 0.12/0.38 % Given clauses 14.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------