%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT004-3 : 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 : n014.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 0.19s 5.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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 : 28 ( 18 ~; 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 : 25 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_h_equals_g,axiom,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
cnf(c_7,plain,
h != g,
inference(clausify,[status(thm)],[prove_h_equals_g]) ).
cnf(c_8,plain,
g != h,
inference(copy,[status(thm)],[c_7]) ).
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_9,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(clausify,[status(thm)],[h_ab_equals_g_ab]) ).
cnf(c_10,plain,
compose(g,compose(a,b)) = compose(h,compose(a,b)),
inference(copy,[status(thm)],[c_9]) ).
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_12,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_13,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_23,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(clausify,[status(thm)],[associativity_of_compose]) ).
cnf(c_24,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_34,plain,
( A = B
| compose(A,b) != compose(B,b) ),
inference(xxres,[status(thm)],[c_12]) ).
cnf(c_95,plain,
( A = B
| compose(A,a) != compose(B,a) ),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_38,plain,
compose(g,a) != compose(h,a),
inference(resolve,[status(thm)],[c_95,c_8]) ).
cnf(c_96,plain,
compose(compose(g,a),b) != compose(compose(h,a),b),
inference(resolve,[status(thm)],[c_34,c_38]) ).
cnf(c_97,plain,
compose(g,compose(a,b)) != compose(compose(h,a),b),
inference(paramod,[status(thm)],[c_24,c_96]) ).
cnf(c_98,plain,
compose(h,compose(a,b)) != compose(compose(h,a),b),
inference(paramod,[status(thm)],[c_10,c_97]) ).
cnf(c_99,plain,
compose(h,compose(a,b)) != compose(h,compose(a,b)),
inference(paramod,[status(thm)],[c_24,c_98]) ).
cnf(c_94,plain,
$false,
inference(copy,[status(thm)],[c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n014.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.44 % CPULimit : 300
% 0.19/5.44 % WCLimit : 300
% 0.19/5.44 % DateTime : Sat Sep 26 22:48:22 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.45 % Process 99566 was started by sandbox2 on n014,
% 0.19/5.45 % Sat Sep 26 22:48:22 2026
% 0.19/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.45
% 0.19/5.45 % From the command line: assign(max_seconds, 300).
% 0.19/5.46
% 0.19/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.19/5.46
% 0.19/5.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/5.46 % Length of proof is 11.
% 0.19/5.46 % Level of proof is 3.
% 0.19/5.46 % Maximum clause weight is 36.000.
% 0.19/5.46 % Given clauses 24.
% 0.19/5.46
% 0.19/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------