%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT003-3 : 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 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 14 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 20 ( 0 sgn 6 !; 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(ha_equals_ga,axiom,
compose(h,a) = compose(g,a),
file('theBenchmark.p',ha_equals_ga) ).
cnf(c_8,plain,
compose(h,a) = compose(g,a),
inference(clausify,[status(thm)],[ha_equals_ga]) ).
cnf(c_9,plain,
compose(g,a) = compose(h,a),
inference(copy,[status(thm)],[c_8]) ).
fof(epimorphism,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(VAR_2,compose(a,b)) != VAR_1
| compose(VAR_0,compose(a,b)) != VAR_1 ),
file('theBenchmark.p',epimorphism) ).
cnf(c_11,plain,
( A = C
| compose(C,compose(a,b)) != B
| compose(A,compose(a,b)) != B ),
inference(clausify,[status(thm)],[epimorphism]) ).
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_21,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_22,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_55,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_56,plain,
( A = B
| compose(A,compose(a,b)) != compose(compose(B,a),b) ),
inference(resolve,[status(thm)],[c_11,c_55]) ).
cnf(c_57,plain,
h != g,
inference(copy,[status(thm)],[c_7]) ).
cnf(c_58,plain,
compose(h,compose(a,b)) != compose(compose(g,a),b),
inference(resolve,[status(thm)],[c_56,c_57]) ).
cnf(c_59,plain,
compose(h,compose(a,b)) != compose(compose(h,a),b),
inference(paramod,[status(thm)],[c_9,c_58]) ).
cnf(c_60,plain,
compose(h,compose(a,b)) != compose(h,compose(a,b)),
inference(paramod,[status(thm)],[c_22,c_59]) ).
cnf(c_54,plain,
$false,
inference(copy,[status(thm)],[c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 % Computer : n016.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sat Sep 26 22:53:02 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.47 % Process 1914010 was started by sandbox on n016,
% 0.19/0.47 % Sat Sep 26 22:53:02 2026
% 0.19/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.49
% 0.19/0.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.49 % Length of proof is 7.
% 0.19/0.49 % Level of proof is 2.
% 0.19/0.49 % Maximum clause weight is 17.000.
% 0.19/0.49 % Given clauses 13.
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------