%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET558-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:36:28 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 19 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_compatible_functions_alternate_defn1_3,axiom,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
file('theBenchmark.p',prove_compatible_functions_alternate_defn1_3) ).
cnf(c_36,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(clausify,[status(thm)],[prove_compatible_functions_alternate_defn1_3]) ).
fof(prove_compatible_functions_alternate_defn1_2,axiom,
compatible(xh,xf1,xf2),
file('theBenchmark.p',prove_compatible_functions_alternate_defn1_2) ).
cnf(c_37,plain,
compatible(xh,xf1,xf2),
inference(clausify,[status(thm)],[prove_compatible_functions_alternate_defn1_2]) ).
fof(prove_compatible_functions_alternate_defn1_1,axiom,
operation(xf1),
file('theBenchmark.p',prove_compatible_functions_alternate_defn1_1) ).
cnf(c_38,plain,
operation(xf1),
inference(clausify,[status(thm)],[prove_compatible_functions_alternate_defn1_1]) ).
fof(compatible2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( domain_of(domain_of(VAR_1)) = domain_of(VAR_0)
| ~ compatible(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',compatible2) ).
cnf(c_62,plain,
( domain_of(domain_of(B)) = domain_of(A)
| ~ compatible(A,B,C) ),
inference(clausify,[status(thm)],[compatible2]) ).
fof(operation2,axiom,
! [VAR_0] :
( cross_product(domain_of(domain_of(VAR_0)),domain_of(domain_of(VAR_0))) = domain_of(VAR_0)
| ~ operation(VAR_0) ),
file('theBenchmark.p',operation2) ).
cnf(c_64,plain,
( cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) = domain_of(A)
| ~ operation(A) ),
inference(clausify,[status(thm)],[operation2]) ).
cnf(c_254,plain,
domain_of(domain_of(xf1)) = domain_of(xh),
inference(resolve,[status(thm)],[c_62,c_37]) ).
cnf(c_256,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1),
inference(resolve,[status(thm)],[c_64,c_38]) ).
cnf(c_257,plain,
cross_product(domain_of(xh),domain_of(domain_of(xf1))) = domain_of(xf1),
inference(paramod,[status(thm)],[c_254,c_256]) ).
cnf(c_258,plain,
cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1),
inference(paramod,[status(thm)],[c_254,c_257]) ).
cnf(c_255,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET558-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:59:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3509027 was started by sandbox on n015,
% 0.11/0.37 % Sat Sep 26 07:59:13 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.43
% 0.11/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.43
% 0.11/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.43 % Length of proof is 7.
% 0.11/0.43 % Level of proof is 2.
% 0.11/0.43 % Maximum clause weight is 12.000.
% 0.11/0.43 % Given clauses 13.
% 0.11/0.43
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------