%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:58:21 AM UTC 2026
% Result : Unsatisfiable 36.51s 5.61s
% Output : CNFRefutation 36.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 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 : 9 ( 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 : 82 ( 10 sgn 16 !; 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(axiom_1_5,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(or(not(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(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(clausify,[status(thm)],[axiom_1_5]) ).
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_2,axiom,
! [VAR_0,VAR_1] : ifeq(theorem(VAR_0),true,ifeq(axiom(or(not(VAR_0),VAR_1)),true,theorem(VAR_1),true),true) = true,
file('theBenchmark.p',rule_2) ).
cnf(c_8,plain,
ifeq(theorem(A),true,ifeq(axiom(or(not(A),B)),true,theorem(B),true),true) = true,
inference(clausify,[status(thm)],[rule_2]) ).
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(or(not(or(p,q)),q)),or(not(p),q))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_10,plain,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_4294,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_4294]) ).
cnf(c_4295,plain,
ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_19,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_4295]) ).
cnf(c_4296,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_4296]) ).
cnf(c_4297,plain,
ifeq(theorem(or(not(or(A,B)),C)),true,ifeq(true,true,theorem(or(not(or(B,A)),C)),true),true) = true,
inference(paramod,[status(thm)],[c_4,c_9]) ).
cnf(c_23,plain,
ifeq(theorem(or(not(or(A,B)),C)),true,theorem(or(not(or(B,A)),C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_4297]) ).
cnf(c_4298,plain,
ifeq(true,true,theorem(or(A,or(not(or(B,A)),B))),true) = true,
inference(paramod,[status(thm)],[c_13,c_19]) ).
cnf(c_124,plain,
theorem(or(A,or(not(or(B,A)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4298]) ).
cnf(c_4299,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(not(or(C,not(or(B,A)))),C))),true) = true,
inference(paramod,[status(thm)],[c_124,c_23]) ).
cnf(c_236,plain,
theorem(or(not(or(A,B)),or(not(or(C,not(or(B,A)))),C))) = true,
inference(paramod,[status(thm)],[c_1,c_4299]) ).
cnf(c_4300,plain,
ifeq(true,true,theorem(or(not(A),or(not(or(B,not(or(A,C)))),B))),true) = true,
inference(paramod,[status(thm)],[c_236,c_22]) ).
cnf(c_3091,plain,
theorem(or(not(A),or(not(or(B,not(or(A,C)))),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4300]) ).
cnf(c_4301,plain,
ifeq(true,true,theorem(or(not(or(A,not(or(B,C)))),or(not(B),A))),true) = true,
inference(paramod,[status(thm)],[c_3091,c_19]) ).
cnf(c_4280,plain,
theorem(or(not(or(A,not(or(B,C)))),or(not(B),A))) = true,
inference(paramod,[status(thm)],[c_1,c_4301]) ).
cnf(c_4302,plain,
ifeq(true,true,theorem(or(not(or(not(or(A,B)),C)),or(not(A),C))),true) = true,
inference(paramod,[status(thm)],[c_4280,c_23]) ).
cnf(c_4292,plain,
theorem(or(not(or(not(or(A,B)),C)),or(not(A),C))) = true,
inference(paramod,[status(thm)],[c_1,c_4302]) ).
cnf(c_4293,plain,
$false,
inference(resolve,[status(thm)],[c_4292,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:00:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2028561 was started by sandbox2 on n007,
% 0.09/0.37 % Fri Sep 25 22:00:10 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 36.51/5.61
% 36.51/5.61 % given #500 (W,wt=58): 366 theorem(or(A,or(or(not(B),or(B,C)),D))) = true. [para(302(a,1),17(a,1,1)),rewrite([1(10)])].
% 36.51/5.61
% 36.51/5.61 % SZS status Unsatisfiable for theBenchmark
% 36.51/5.61
% 36.51/5.61 % Proof 1 at 3.61 (+ 1.28) seconds.
% 36.51/5.61 % Length of proof is 18.
% 36.51/5.61 % Level of proof is 7.
% 36.51/5.61 % Maximum clause weight is 62.000.
% 36.51/5.61 % Given clauses 944.
% 36.51/5.61
% 36.51/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------