%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE074+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:44:15 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(goals,conjecture,
! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) != domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))) != domain(multiplication(multiplication(sK0,sK1),domain(sK2))),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_25,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_36,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_47,negated_conjecture,
domain(multiplication(sK0,domain(multiplication(sK1,sK2)))) != domain(multiplication(multiplication(sK0,sK1),domain(sK2))),
inference(paramod,[status(thm)],[c_25,c_21]) ).
cnf(c_48,negated_conjecture,
domain(multiplication(sK0,multiplication(sK1,sK2))) != domain(multiplication(multiplication(sK0,sK1),domain(sK2))),
inference(paramod,[status(thm)],[c_25,c_47]) ).
cnf(c_49,negated_conjecture,
domain(multiplication(sK0,multiplication(sK1,sK2))) != domain(multiplication(sK0,multiplication(sK1,domain(sK2)))),
inference(paramod,[status(thm)],[c_36,c_48]) ).
cnf(c_41,negated_conjecture,
domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) != domain(multiplication(sK0,multiplication(sK1,sK2))),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_50,plain,
domain(multiplication(A,domain(multiplication(B,C)))) = domain(multiplication(A,multiplication(B,domain(C)))),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_51,plain,
domain(multiplication(A,multiplication(B,C))) = domain(multiplication(A,multiplication(B,domain(C)))),
inference(paramod,[status(thm)],[c_25,c_50]) ).
cnf(c_45,plain,
domain(multiplication(A,multiplication(B,domain(C)))) = domain(multiplication(A,multiplication(B,C))),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE074+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:22:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3924508 was started by sandbox2 on n002,
% 0.10/0.36 % Fri Sep 25 19:22:35 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 10.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 16.000.
% 0.10/0.38 % Given clauses 3.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------