%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL265-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:58:31 AM UTC 2026
% Result : Unsatisfiable 70.23s 10.32s
% Output : CNFRefutation 70.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 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 : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-4 aty)
% Number of variables : 157 ( 9 sgn 23 !; 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(axiom_1_6,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(implies(implies(VAR_0,VAR_1),implies(or(VAR_2,VAR_0),or(VAR_2,VAR_1)))) = true,
file('theBenchmark.p',axiom_1_6) ).
cnf(c_6,plain,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true,
inference(clausify,[status(thm)],[axiom_1_6]) ).
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(equivalent_defn,axiom,
! [VAR_0,VAR_1] : equivalent(VAR_0,VAR_1) = and(implies(VAR_0,VAR_1),implies(VAR_1,VAR_0)),
file('theBenchmark.p',equivalent_defn) ).
cnf(c_12,plain,
equivalent(A,B) = and(implies(A,B),implies(B,A)),
inference(clausify,[status(thm)],[equivalent_defn]) ).
cnf(c_4385,plain,
equivalent(A,B) = and(or(not(A),B),implies(B,A)),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_4386,plain,
equivalent(A,B) = and(or(not(A),B),or(not(B),A)),
inference(paramod,[status(thm)],[c_7,c_4385]) ).
cnf(c_13,plain,
equivalent(A,B) = not(or(not(or(not(A),B)),not(or(not(B),A)))),
inference(paramod,[status(thm)],[c_11,c_4386]) ).
fof(prove_this,axiom,
theorem(equivalent(p,not(not(p)))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_14,plain,
theorem(equivalent(p,not(not(p)))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_15,plain,
theorem(not(or(not(or(not(p),not(not(p)))),not(or(not(not(not(p))),p))))) != true,
inference(paramod,[status(thm)],[c_13,c_14]) ).
cnf(c_4387,plain,
axiom(implies(or(not(A),B),implies(or(C,A),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_4388,plain,
axiom(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_4387]) ).
cnf(c_16,plain,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_4388]) ).
cnf(c_17,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_18,plain,
axiom(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_19,plain,
axiom(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_20,plain,
axiom(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_4389,plain,
ifeq(true,true,theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_21,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_4389]) ).
cnf(c_4390,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_17,c_8]) ).
cnf(c_22,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_4390]) ).
cnf(c_4391,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_23,plain,
theorem(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_4391]) ).
cnf(c_4392,plain,
ifeq(true,true,theorem(or(not(A),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_24,plain,
theorem(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_4392]) ).
cnf(c_4393,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true,
inference(paramod,[status(thm)],[c_20,c_8]) ).
cnf(c_25,plain,
theorem(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_1,c_4393]) ).
cnf(c_4394,plain,
ifeq(true,true,ifeq(theorem(or(not(A),B)),true,theorem(or(not(or(C,A)),or(C,B))),true),true) = true,
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_26,plain,
ifeq(theorem(or(not(A),B)),true,theorem(or(not(or(C,A)),or(C,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_4394]) ).
cnf(c_4395,plain,
ifeq(true,true,ifeq(theorem(or(A,A)),true,theorem(A),true),true) = true,
inference(paramod,[status(thm)],[c_25,c_10]) ).
cnf(c_29,plain,
ifeq(theorem(or(A,A)),true,theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_4395]) ).
cnf(c_4396,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_24,c_10]) ).
cnf(c_33,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_4396]) ).
cnf(c_4397,plain,
ifeq(true,true,ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_43,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_4397]) ).
cnf(c_4398,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true),true) = true,
inference(paramod,[status(thm)],[c_23,c_10]) ).
cnf(c_46,plain,
ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_4398]) ).
cnf(c_4399,plain,
ifeq(true,true,theorem(or(A,or(not(B),B))),true) = true,
inference(paramod,[status(thm)],[c_22,c_33]) ).
cnf(c_126,plain,
theorem(or(A,or(not(B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4399]) ).
cnf(c_4400,plain,
ifeq(true,true,theorem(or(not(A),A)),true) = true,
inference(paramod,[status(thm)],[c_126,c_29]) ).
cnf(c_130,plain,
theorem(or(not(A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_4400]) ).
cnf(c_4401,plain,
ifeq(true,true,theorem(or(A,not(A))),true) = true,
inference(paramod,[status(thm)],[c_130,c_46]) ).
cnf(c_137,plain,
theorem(or(A,not(A))) = true,
inference(paramod,[status(thm)],[c_1,c_4401]) ).
cnf(c_4402,plain,
ifeq(theorem(or(not(or(A,not(A))),B)),true,ifeq(true,true,theorem(B),true),true) = true,
inference(paramod,[status(thm)],[c_137,c_10]) ).
cnf(c_141,plain,
ifeq(theorem(or(not(or(A,not(A))),B)),true,theorem(B),true) = true,
inference(paramod,[status(thm)],[c_1,c_4402]) ).
cnf(c_4403,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,not(not(B))))),true) = true,
inference(paramod,[status(thm)],[c_137,c_26]) ).
cnf(c_143,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))) = true,
inference(paramod,[status(thm)],[c_1,c_4403]) ).
cnf(c_4404,plain,
ifeq(true,true,theorem(or(A,or(not(or(A,B)),B))),true) = true,
inference(paramod,[status(thm)],[c_130,c_43]) ).
cnf(c_195,plain,
theorem(or(A,or(not(or(A,B)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4404]) ).
cnf(c_4405,plain,
ifeq(true,true,theorem(or(not(or(not(or(A,not(A))),B)),B)),true) = true,
inference(paramod,[status(thm)],[c_195,c_141]) ).
cnf(c_408,plain,
theorem(or(not(or(not(or(A,not(A))),B)),B)) = true,
inference(paramod,[status(thm)],[c_1,c_4405]) ).
cnf(c_4406,plain,
ifeq(true,true,theorem(or(A,not(or(not(or(B,not(B))),A)))),true) = true,
inference(paramod,[status(thm)],[c_408,c_46]) ).
cnf(c_428,plain,
theorem(or(A,not(or(not(or(B,not(B))),A)))) = true,
inference(paramod,[status(thm)],[c_1,c_4406]) ).
cnf(c_4407,plain,
ifeq(true,true,ifeq(theorem(A),true,theorem(not(or(not(or(B,not(B))),not(A)))),true),true) = true,
inference(paramod,[status(thm)],[c_428,c_10]) ).
cnf(c_449,plain,
ifeq(theorem(A),true,theorem(not(or(not(or(B,not(B))),not(A)))),true) = true,
inference(paramod,[status(thm)],[c_1,c_4407]) ).
cnf(c_4408,plain,
ifeq(true,true,theorem(or(A,not(not(not(A))))),true) = true,
inference(paramod,[status(thm)],[c_143,c_141]) ).
cnf(c_2246,plain,
theorem(or(A,not(not(not(A))))) = true,
inference(paramod,[status(thm)],[c_1,c_4408]) ).
cnf(c_4409,plain,
ifeq(true,true,theorem(or(not(not(not(A))),A)),true) = true,
inference(paramod,[status(thm)],[c_2246,c_46]) ).
cnf(c_2309,plain,
theorem(or(not(not(not(A))),A)) = true,
inference(paramod,[status(thm)],[c_1,c_4409]) ).
cnf(c_4410,plain,
ifeq(true,true,theorem(not(or(not(or(A,not(A))),not(or(not(not(not(B))),B))))),true) = true,
inference(paramod,[status(thm)],[c_2309,c_449]) ).
cnf(c_4383,plain,
theorem(not(or(not(or(A,not(A))),not(or(not(not(not(B))),B))))) = true,
inference(paramod,[status(thm)],[c_1,c_4410]) ).
cnf(c_4384,plain,
$false,
inference(resolve,[status(thm)],[c_4383,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL265-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:14:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 183150 was started by sandbox on n001,
% 0.09/0.36 % Fri Sep 25 22:14:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 70.23/10.32
% 70.23/10.32 % SZS status Unsatisfiable for theBenchmark
% 70.23/10.32
% 70.23/10.32 % Proof 1 at 1.34 (+ 0.49) seconds.
% 70.23/10.32 % Length of proof is 43.
% 70.23/10.32 % Level of proof is 12.
% 70.23/10.32 % Maximum clause weight is 25.000.
% 70.23/10.32 % Given clauses 339.
% 70.23/10.32
% 70.23/10.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------