%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:58:26 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 86 ( 9 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(implies(or(VAR_0,VAR_0),VAR_0)) = true,
file('theBenchmark.p',axiom_1_2) ).
cnf(c_2,plain,
axiom(implies(or(A,A),A)) = true,
inference(clausify,[status(thm)],[axiom_1_2]) ).
fof(axiom_1_3,axiom,
! [VAR_0,VAR_1] : axiom(implies(VAR_0,or(VAR_1,VAR_0))) = true,
file('theBenchmark.p',axiom_1_3) ).
cnf(c_3,plain,
axiom(implies(A,or(B,A))) = true,
inference(clausify,[status(thm)],[axiom_1_3]) ).
fof(axiom_1_4,axiom,
! [VAR_0,VAR_1] : axiom(implies(or(VAR_0,VAR_1),or(VAR_1,VAR_0))) = true,
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(implies(or(A,B),or(B,A))) = true,
inference(clausify,[status(thm)],[axiom_1_4]) ).
fof(axiom_1_5,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(implies(or(VAR_0,or(VAR_1,VAR_2)),or(VAR_1,or(VAR_0,VAR_2)))) = true,
file('theBenchmark.p',axiom_1_5) ).
cnf(c_5,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true,
inference(clausify,[status(thm)],[axiom_1_5]) ).
fof(implies_definition,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = or(not(VAR_0),VAR_1),
file('theBenchmark.p',implies_definition) ).
cnf(c_7,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
fof(rule_1,axiom,
! [VAR_0] : ifeq(axiom(VAR_0),true,theorem(VAR_0),true) = true,
file('theBenchmark.p',rule_1) ).
cnf(c_8,plain,
ifeq(axiom(A),true,theorem(A),true) = true,
inference(clausify,[status(thm)],[rule_1]) ).
fof(rule_2,axiom,
! [VAR_0,VAR_1] : ifeq(theorem(implies(VAR_0,VAR_1)),true,ifeq(theorem(VAR_0),true,theorem(VAR_1),true),true) = true,
file('theBenchmark.p',rule_2) ).
cnf(c_9,plain,
ifeq(theorem(implies(A,B)),true,ifeq(theorem(A),true,theorem(B),true),true) = true,
inference(clausify,[status(thm)],[rule_2]) ).
cnf(c_10,plain,
ifeq(theorem(or(not(A),B)),true,ifeq(theorem(A),true,theorem(B),true),true) = true,
inference(paramod,[status(thm)],[c_7,c_9]) ).
fof(and_defn,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_defn) ).
cnf(c_11,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_defn]) ).
fof(prove_this,axiom,
theorem(not(and(p,not(p)))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
theorem(not(and(p,not(p)))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_13,plain,
theorem(not(not(or(not(p),not(not(p)))))) != true,
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_15,plain,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_16,plain,
axiom(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_17,plain,
axiom(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_18,plain,
axiom(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_154,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_20,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_154]) ).
cnf(c_155,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_21,plain,
theorem(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_155]) ).
cnf(c_156,plain,
ifeq(true,true,theorem(or(not(A),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_17,c_8]) ).
cnf(c_22,plain,
theorem(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_156]) ).
cnf(c_157,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_23,plain,
theorem(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_1,c_157]) ).
cnf(c_158,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,ifeq(true,true,theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_28,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_158]) ).
cnf(c_159,plain,
ifeq(true,true,ifeq(theorem(or(A,A)),true,theorem(A),true),true) = true,
inference(paramod,[status(thm)],[c_23,c_10]) ).
cnf(c_30,plain,
ifeq(theorem(or(A,A)),true,theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_159]) ).
cnf(c_160,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true),true) = true,
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_33,plain,
ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_160]) ).
cnf(c_161,plain,
ifeq(true,true,theorem(or(A,or(not(B),B))),true) = true,
inference(paramod,[status(thm)],[c_20,c_28]) ).
cnf(c_91,plain,
theorem(or(A,or(not(B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_161]) ).
cnf(c_162,plain,
ifeq(true,true,theorem(or(not(A),A)),true) = true,
inference(paramod,[status(thm)],[c_91,c_30]) ).
cnf(c_97,plain,
theorem(or(not(A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_162]) ).
cnf(c_163,plain,
ifeq(true,true,theorem(or(A,not(A))),true) = true,
inference(paramod,[status(thm)],[c_97,c_33]) ).
cnf(c_102,plain,
theorem(or(A,not(A))) = true,
inference(paramod,[status(thm)],[c_1,c_163]) ).
cnf(c_164,plain,
ifeq(true,true,ifeq(theorem(A),true,theorem(not(not(A))),true),true) = true,
inference(paramod,[status(thm)],[c_102,c_10]) ).
cnf(c_104,plain,
ifeq(theorem(A),true,theorem(not(not(A))),true) = true,
inference(paramod,[status(thm)],[c_1,c_164]) ).
cnf(c_165,plain,
ifeq(true,true,theorem(not(not(or(A,not(A))))),true) = true,
inference(paramod,[status(thm)],[c_102,c_104]) ).
cnf(c_152,plain,
theorem(not(not(or(A,not(A))))) = true,
inference(paramod,[status(thm)],[c_1,c_165]) ).
cnf(c_153,plain,
$false,
inference(resolve,[status(thm)],[c_152,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 22:07:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2959305 was started by sandbox2 on n018,
% 0.18/0.44 % Fri Sep 25 22:07:35 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.49 % Length of proof is 29.
% 0.18/0.49 % Level of proof is 9.
% 0.18/0.49 % Maximum clause weight is 17.000.
% 0.18/0.49 % Given clauses 48.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------