%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:58:13 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 36 ( 6 sgn 11 !; 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_3,axiom,
! [VAR_0,VAR_1] : axiom(or(not(VAR_0),or(VAR_1,VAR_0))) = true,
file('theBenchmark.p',axiom_1_3) ).
cnf(c_3,plain,
axiom(or(not(A),or(B,A))) = true,
inference(clausify,[status(thm)],[axiom_1_3]) ).
fof(axiom_1_4,axiom,
! [VAR_0,VAR_1] : axiom(or(not(or(VAR_0,VAR_1)),or(VAR_1,VAR_0))) = true,
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(or(not(or(A,B)),or(B,A))) = true,
inference(clausify,[status(thm)],[axiom_1_4]) ).
fof(rule_1,axiom,
! [VAR_0] : ifeq(axiom(VAR_0),true,theorem(VAR_0),true) = true,
file('theBenchmark.p',rule_1) ).
cnf(c_7,plain,
ifeq(axiom(A),true,theorem(A),true) = true,
inference(clausify,[status(thm)],[rule_1]) ).
fof(rule_3,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(theorem(or(not(VAR_0),VAR_1)),true,ifeq(axiom(or(not(VAR_2),VAR_0)),true,theorem(or(not(VAR_2),VAR_1)),true),true) = true,
file('theBenchmark.p',rule_3) ).
cnf(c_9,plain,
ifeq(theorem(or(not(A),B)),true,ifeq(axiom(or(not(C),A)),true,theorem(or(not(C),B)),true),true) = true,
inference(clausify,[status(thm)],[rule_3]) ).
fof(prove_this,axiom,
theorem(or(not(not(p)),or(not(p),q))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_10,plain,
theorem(or(not(not(p)),or(not(p),q))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_110,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_13,plain,
theorem(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_110]) ).
cnf(c_111,plain,
ifeq(theorem(or(not(or(A,B)),C)),true,ifeq(true,true,theorem(or(not(B),C)),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_22,plain,
ifeq(theorem(or(not(or(A,B)),C)),true,theorem(or(not(B),C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_111]) ).
cnf(c_112,plain,
ifeq(true,true,theorem(or(not(A),or(A,B))),true) = true,
inference(paramod,[status(thm)],[c_13,c_22]) ).
cnf(c_108,plain,
theorem(or(not(A),or(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_112]) ).
cnf(c_109,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.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 22:00:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2942477 was started by sandbox on n018,
% 0.10/0.37 % Fri Sep 25 22:00:50 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 10.
% 0.14/0.38 % Level of proof is 3.
% 0.14/0.38 % Maximum clause weight is 53.000.
% 0.14/0.38 % Given clauses 31.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------