%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT001-3 : 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 : n008.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 06:55:53 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 9 |; 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 : 26 ( 0 sgn 6 !; 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(bh_equals_bg,axiom,
compose(b,h) = compose(b,g),
file('theBenchmark.p',bh_equals_bg) ).
cnf(c_9,plain,
compose(b,h) = compose(b,g),
inference(clausify,[status(thm)],[bh_equals_bg]) ).
cnf(c_10,plain,
compose(b,g) = compose(b,h),
inference(copy,[status(thm)],[c_9]) ).
fof(monomorphism,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(compose(a,b),VAR_2) != VAR_1
| compose(compose(a,b),VAR_0) != VAR_1 ),
file('theBenchmark.p',monomorphism) ).
cnf(c_12,plain,
( A = C
| compose(compose(a,b),C) != B
| compose(compose(a,b),A) != B ),
inference(clausify,[status(thm)],[monomorphism]) ).
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_65,plain,
( A = C
| compose(compose(a,b),C) != B
| compose(a,compose(b,A)) != B ),
inference(paramod,[status(thm)],[c_23,c_12]) ).
cnf(c_31,plain,
( A = C
| compose(a,compose(b,C)) != B
| compose(a,compose(b,A)) != B ),
inference(paramod,[status(thm)],[c_23,c_65]) ).
cnf(c_66,plain,
compose(A,compose(B,C)) = compose(compose(A,B),C),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_67,plain,
( A = B
| compose(a,compose(b,A)) != compose(compose(a,b),B) ),
inference(resolve,[status(thm)],[c_31,c_66]) ).
cnf(c_68,plain,
compose(a,compose(b,g)) != compose(compose(a,b),h),
inference(resolve,[status(thm)],[c_67,c_8]) ).
cnf(c_69,plain,
compose(a,compose(b,h)) != compose(compose(a,b),h),
inference(paramod,[status(thm)],[c_10,c_68]) ).
cnf(c_70,plain,
compose(a,compose(b,h)) != compose(a,compose(b,h)),
inference(paramod,[status(thm)],[c_23,c_69]) ).
cnf(c_64,plain,
$false,
inference(copy,[status(thm)],[c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n008.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 22:48:17 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 552380 was started by sandbox2 on n008,
% 0.09/5.37 % Sat Sep 26 22:48:17 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.38
% 0.09/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.38
% 0.09/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.38 % Length of proof is 9.
% 0.09/5.38 % Level of proof is 3.
% 0.09/5.38 % Maximum clause weight is 17.000.
% 0.09/5.38 % Given clauses 18.
% 0.09/5.38
% 0.09/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------