%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL203-10 : 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 : n026.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 07:58:17 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.68s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 68 unt; 0 def)
% Number of atoms : 68 ( 67 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; 3 con; 0-4 aty)
% Number of variables : 141 ( 21 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(or(p,q)),or(not(p),not(q)))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_11,plain,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_12,plain,
theorem(or(not(not(or(p,q))),or(not(p),not(q)))) != true,
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_1077,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_1078,plain,
axiom(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_1077]) ).
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_1078]) ).
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_1079,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_1079]) ).
cnf(c_1080,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_1080]) ).
cnf(c_1081,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_1081]) ).
cnf(c_1082,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_1082]) ).
cnf(c_1083,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_1083]) ).
cnf(c_1084,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_1084]) ).
cnf(c_1085,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_19,c_10]) ).
cnf(c_26,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_1085]) ).
cnf(c_1086,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_29,plain,
ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_1086]) ).
cnf(c_1087,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_36,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_1087]) ).
cnf(c_1088,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_47,plain,
ifeq(theorem(or(A,A)),true,theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_1088]) ).
cnf(c_1089,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,or(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_21,c_23]) ).
cnf(c_54,plain,
theorem(or(not(or(A,B)),or(A,or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_1089]) ).
cnf(c_1090,plain,
ifeq(true,true,theorem(or(A,or(not(B),B))),true) = true,
inference(paramod,[status(thm)],[c_21,c_26]) ).
cnf(c_59,plain,
theorem(or(A,or(not(B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_1090]) ).
cnf(c_1091,plain,
ifeq(true,true,theorem(or(not(A),A)),true) = true,
inference(paramod,[status(thm)],[c_59,c_47]) ).
cnf(c_75,plain,
theorem(or(not(A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_1091]) ).
cnf(c_1092,plain,
ifeq(true,true,theorem(or(A,not(A))),true) = true,
inference(paramod,[status(thm)],[c_75,c_29]) ).
cnf(c_79,plain,
theorem(or(A,not(A))) = true,
inference(paramod,[status(thm)],[c_1,c_1092]) ).
cnf(c_1093,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,not(not(B))))),true) = true,
inference(paramod,[status(thm)],[c_79,c_23]) ).
cnf(c_85,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))) = true,
inference(paramod,[status(thm)],[c_1,c_1093]) ).
cnf(c_1094,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(A,or(C,B))),true),true) = true,
inference(paramod,[status(thm)],[c_54,c_10]) ).
cnf(c_298,plain,
ifeq(theorem(or(A,B)),true,theorem(or(A,or(C,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_1094]) ).
cnf(c_1095,plain,
ifeq(true,true,theorem(or(not(A),not(not(or(B,A))))),true) = true,
inference(paramod,[status(thm)],[c_85,c_36]) ).
cnf(c_764,plain,
theorem(or(not(A),not(not(or(B,A))))) = true,
inference(paramod,[status(thm)],[c_1,c_1095]) ).
cnf(c_1096,plain,
ifeq(true,true,theorem(or(not(not(or(A,B))),not(B))),true) = true,
inference(paramod,[status(thm)],[c_764,c_29]) ).
cnf(c_899,plain,
theorem(or(not(not(or(A,B))),not(B))) = true,
inference(paramod,[status(thm)],[c_1,c_1096]) ).
cnf(c_1097,plain,
ifeq(true,true,theorem(or(not(not(or(A,B))),or(C,not(B)))),true) = true,
inference(paramod,[status(thm)],[c_899,c_298]) ).
cnf(c_1075,plain,
theorem(or(not(not(or(A,B))),or(C,not(B)))) = true,
inference(paramod,[status(thm)],[c_1,c_1097]) ).
cnf(c_1076,plain,
$false,
inference(resolve,[status(thm)],[c_1075,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL203-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n026.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Fri Sep 25 22:02:55 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.54 % Process 3569168 was started by sandbox on n026,
% 0.09/0.54 % Fri Sep 25 22:02:55 2026
% 0.09/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.54
% 0.09/0.54 % From the command line: assign(max_seconds, 300).
% 0.13/0.68
% 0.13/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.68
% 0.13/0.68 % Proof 1 at 0.08 (+ 0.05) seconds.
% 0.13/0.68 % Length of proof is 37.
% 0.13/0.68 % Level of proof is 11.
% 0.13/0.68 % Maximum clause weight is 60.000.
% 0.13/0.68 % Given clauses 142.
% 0.13/0.68
% 0.13/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------