%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL211-10 : 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 : n004.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 07:58:19 AM UTC 2026
% Result : Unsatisfiable 16.90s 2.54s
% Output : CNFRefutation 16.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 69 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 135 ( 9 sgn 19 !; 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(prove_this,axiom,
theorem(implies(not(q),implies(or(p,q),p))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_11,plain,
theorem(implies(not(q),implies(or(p,q),p))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_4206,plain,
theorem(implies(not(q),or(not(or(p,q)),p))) != true,
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_12,plain,
theorem(or(not(not(q)),or(not(or(p,q)),p))) != true,
inference(paramod,[status(thm)],[c_7,c_4206]) ).
cnf(c_4207,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_4208,plain,
axiom(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_4207]) ).
cnf(c_13,plain,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_4208]) ).
cnf(c_14,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_15,plain,
axiom(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_16,plain,
axiom(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_17,plain,
axiom(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_4209,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_13,c_8]) ).
cnf(c_18,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_4209]) ).
cnf(c_4210,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_19,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_4210]) ).
cnf(c_4211,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_20,plain,
theorem(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_4211]) ).
cnf(c_4212,plain,
ifeq(true,true,theorem(or(not(A),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_21,plain,
theorem(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_4212]) ).
cnf(c_4213,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true,
inference(paramod,[status(thm)],[c_17,c_8]) ).
cnf(c_22,plain,
theorem(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_1,c_4213]) ).
cnf(c_4214,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_18,c_10]) ).
cnf(c_23,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_4214]) ).
cnf(c_4215,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_21,c_10]) ).
cnf(c_27,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_4215]) ).
cnf(c_4216,plain,
ifeq(true,true,ifeq(theorem(or(A,A)),true,theorem(A),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_34,plain,
ifeq(theorem(or(A,A)),true,theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_4216]) ).
cnf(c_4217,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true),true) = true,
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_37,plain,
ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_4217]) ).
cnf(c_4218,plain,
ifeq(theorem(or(not(or(not(or(A,B)),or(B,A))),C)),true,ifeq(true,true,theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_38,plain,
ifeq(theorem(or(not(or(not(or(A,B)),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_4218]) ).
cnf(c_4219,plain,
ifeq(true,true,theorem(or(A,or(not(B),B))),true) = true,
inference(paramod,[status(thm)],[c_19,c_27]) ).
cnf(c_138,plain,
theorem(or(A,or(not(B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4219]) ).
cnf(c_4220,plain,
ifeq(true,true,theorem(or(not(A),A)),true) = true,
inference(paramod,[status(thm)],[c_138,c_34]) ).
cnf(c_144,plain,
theorem(or(not(A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_4220]) ).
cnf(c_4221,plain,
ifeq(true,true,theorem(or(A,not(A))),true) = true,
inference(paramod,[status(thm)],[c_144,c_37]) ).
cnf(c_150,plain,
theorem(or(A,not(A))) = true,
inference(paramod,[status(thm)],[c_1,c_4221]) ).
cnf(c_4222,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,not(not(B))))),true) = true,
inference(paramod,[status(thm)],[c_150,c_23]) ).
cnf(c_155,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))) = true,
inference(paramod,[status(thm)],[c_1,c_4222]) ).
cnf(c_4223,plain,
ifeq(true,true,theorem(or(A,or(not(or(B,A)),B))),true) = true,
inference(paramod,[status(thm)],[c_19,c_38]) ).
cnf(c_285,plain,
theorem(or(A,or(not(or(B,A)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4223]) ).
cnf(c_4224,plain,
ifeq(true,true,theorem(or(or(not(or(A,B)),A),B)),true) = true,
inference(paramod,[status(thm)],[c_285,c_37]) ).
cnf(c_314,plain,
theorem(or(or(not(or(A,B)),A),B)) = true,
inference(paramod,[status(thm)],[c_1,c_4224]) ).
cnf(c_4225,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(A,not(not(B)))),true),true) = true,
inference(paramod,[status(thm)],[c_155,c_10]) ).
cnf(c_702,plain,
ifeq(theorem(or(A,B)),true,theorem(or(A,not(not(B)))),true) = true,
inference(paramod,[status(thm)],[c_1,c_4225]) ).
cnf(c_4226,plain,
ifeq(true,true,theorem(or(or(not(or(A,B)),A),not(not(B)))),true) = true,
inference(paramod,[status(thm)],[c_314,c_702]) ).
cnf(c_1081,plain,
theorem(or(or(not(or(A,B)),A),not(not(B)))) = true,
inference(paramod,[status(thm)],[c_1,c_4226]) ).
cnf(c_4227,plain,
ifeq(true,true,theorem(or(not(not(A)),or(not(or(B,A)),B))),true) = true,
inference(paramod,[status(thm)],[c_1081,c_37]) ).
cnf(c_4204,plain,
theorem(or(not(not(A)),or(not(or(B,A)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_4227]) ).
cnf(c_4205,plain,
$false,
inference(resolve,[status(thm)],[c_4204,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL211-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:01:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 72459 was started by sandbox2 on n004,
% 0.08/0.36 % Fri Sep 25 22:01:06 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 16.90/2.54
% 16.90/2.54 % SZS status Unsatisfiable for theBenchmark
% 16.90/2.54
% 16.90/2.54 % Proof 1 at 1.36 (+ 0.53) seconds.
% 16.90/2.54 % Length of proof is 37.
% 16.90/2.54 % Level of proof is 11.
% 16.90/2.54 % Maximum clause weight is 61.000.
% 16.90/2.54 % Given clauses 318.
% 16.90/2.54
% 16.90/2.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------