%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT004-4 : 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 06:55:55 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% 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 : 27 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 26 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_h_equals_g,axiom,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
cnf(c_4,plain,
h != g,
inference(clausify,[status(thm)],[prove_h_equals_g]) ).
cnf(c_5,plain,
g != h,
inference(copy,[status(thm)],[c_4]) ).
fof(h_ab_equals_g_ab,axiom,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('theBenchmark.p',h_ab_equals_g_ab) ).
cnf(c_6,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(clausify,[status(thm)],[h_ab_equals_g_ab]) ).
cnf(c_7,plain,
compose(g,compose(a,b)) = compose(h,compose(a,b)),
inference(copy,[status(thm)],[c_6]) ).
fof(cancellation_for_product2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(VAR_2,b) != VAR_1
| compose(VAR_0,b) != VAR_1 ),
file('theBenchmark.p',cancellation_for_product2) ).
cnf(c_9,plain,
( A = C
| compose(C,b) != B
| compose(A,b) != B ),
inference(clausify,[status(thm)],[cancellation_for_product2]) ).
fof(cancellation_for_product1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(VAR_2,a) != VAR_1
| compose(VAR_0,a) != VAR_1 ),
file('theBenchmark.p',cancellation_for_product1) ).
cnf(c_10,plain,
( A = C
| compose(C,a) != B
| compose(A,a) != B ),
inference(clausify,[status(thm)],[cancellation_for_product1]) ).
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_14,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_15,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_50,plain,
( A = B
| compose(A,a) != compose(B,a) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_24,plain,
compose(g,a) != compose(h,a),
inference(resolve,[status(thm)],[c_50,c_5]) ).
cnf(c_51,plain,
( A = compose(B,C)
| compose(A,b) != compose(B,compose(C,b)) ),
inference(resolve,[status(thm)],[c_9,c_15]) ).
cnf(c_52,plain,
compose(compose(g,a),b) != compose(h,compose(a,b)),
inference(resolve,[status(thm)],[c_51,c_24]) ).
cnf(c_53,plain,
compose(g,compose(a,b)) != compose(h,compose(a,b)),
inference(paramod,[status(thm)],[c_15,c_52]) ).
cnf(c_54,plain,
compose(h,compose(a,b)) != compose(h,compose(a,b)),
inference(paramod,[status(thm)],[c_7,c_53]) ).
cnf(c_49,plain,
$false,
inference(copy,[status(thm)],[c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:53:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1914777 was started by sandbox on n016,
% 0.09/0.37 % Sat Sep 26 22:53:17 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 10.
% 0.09/0.39 % Level of proof is 3.
% 0.09/0.39 % Maximum clause weight is 13.000.
% 0.09/0.39 % Given clauses 16.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------