%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL231-10 : 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 : n008.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 07:58:24 AM UTC 2026
% Result : Unsatisfiable 40.19s 21.20s
% Output : CNFRefutation 40.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 120 ( 11 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(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_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(implies(implies(p,q),implies(p,r)),implies(p,implies(q,r)))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_11,plain,
theorem(implies(implies(implies(p,q),implies(p,r)),implies(p,implies(q,r)))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_13965,plain,
theorem(implies(implies(or(not(p),q),implies(p,r)),implies(p,implies(q,r)))) != true,
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_13966,plain,
theorem(implies(implies(or(not(p),q),or(not(p),r)),implies(p,implies(q,r)))) != true,
inference(paramod,[status(thm)],[c_7,c_13965]) ).
cnf(c_13967,plain,
theorem(implies(or(not(or(not(p),q)),or(not(p),r)),implies(p,implies(q,r)))) != true,
inference(paramod,[status(thm)],[c_7,c_13966]) ).
cnf(c_13968,plain,
theorem(implies(or(not(or(not(p),q)),or(not(p),r)),implies(p,or(not(q),r)))) != true,
inference(paramod,[status(thm)],[c_7,c_13967]) ).
cnf(c_13969,plain,
theorem(implies(or(not(or(not(p),q)),or(not(p),r)),or(not(p),or(not(q),r)))) != true,
inference(paramod,[status(thm)],[c_7,c_13968]) ).
cnf(c_12,plain,
theorem(or(not(or(not(or(not(p),q)),or(not(p),r))),or(not(p),or(not(q),r)))) != true,
inference(paramod,[status(thm)],[c_7,c_13969]) ).
cnf(c_13970,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_13971,plain,
axiom(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_13970]) ).
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_13971]) ).
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_16,plain,
axiom(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_13972,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_13972]) ).
cnf(c_13973,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_13973]) ).
cnf(c_13974,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_13974]) ).
cnf(c_13975,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_13975]) ).
cnf(c_13976,plain,
ifeq(theorem(or(not(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),D)),true,ifeq(true,true,theorem(D),true),true) = true,
inference(paramod,[status(thm)],[c_18,c_10]) ).
cnf(c_24,plain,
ifeq(theorem(or(not(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),D)),true,theorem(D),true) = true,
inference(paramod,[status(thm)],[c_1,c_13976]) ).
cnf(c_13977,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_13977]) ).
cnf(c_13978,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,or(C,D)))),or(A,or(C,or(B,D))))),true) = true,
inference(paramod,[status(thm)],[c_19,c_23]) ).
cnf(c_52,plain,
theorem(or(not(or(A,or(B,or(C,D)))),or(A,or(C,or(B,D))))) = true,
inference(paramod,[status(thm)],[c_1,c_13978]) ).
cnf(c_13979,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_19,c_24]) ).
cnf(c_56,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_13979]) ).
cnf(c_13980,plain,
ifeq(true,true,ifeq(theorem(or(A,or(B,or(C,D)))),true,theorem(or(A,or(C,or(B,D)))),true),true) = true,
inference(paramod,[status(thm)],[c_52,c_10]) ).
cnf(c_223,plain,
ifeq(theorem(or(A,or(B,or(C,D)))),true,theorem(or(A,or(C,or(B,D)))),true) = true,
inference(paramod,[status(thm)],[c_1,c_13980]) ).
cnf(c_13981,plain,
ifeq(true,true,theorem(or(not(or(not(or(A,B)),C)),or(not(B),C))),true) = true,
inference(paramod,[status(thm)],[c_56,c_36]) ).
cnf(c_424,plain,
theorem(or(not(or(not(or(A,B)),C)),or(not(B),C))) = true,
inference(paramod,[status(thm)],[c_1,c_13981]) ).
cnf(c_13982,plain,
ifeq(true,true,theorem(or(not(or(not(or(A,B)),or(C,D))),or(C,or(not(B),D)))),true) = true,
inference(paramod,[status(thm)],[c_424,c_223]) ).
cnf(c_13963,plain,
theorem(or(not(or(not(or(A,B)),or(C,D))),or(C,or(not(B),D)))) = true,
inference(paramod,[status(thm)],[c_1,c_13982]) ).
cnf(c_13964,plain,
$false,
inference(resolve,[status(thm)],[c_13963,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL231-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/15.42 % Computer : n008.cluster.edu
% 0.16/15.42 % Model : x86_64 x86_64
% 0.16/15.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/15.42 % Memory : 8046.5625MB
% 0.16/15.42 % OS : Linux 6.8.0-71-generic
% 0.16/15.43 % CPULimit : 300
% 0.16/15.43 % WCLimit : 300
% 0.16/15.43 % DateTime : Fri Sep 25 22:05:40 UTC 2026
% 0.16/15.43 % CPUTime :
% 0.16/15.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/15.43 % Process 2027316 was started by sandbox2 on n008,
% 0.16/15.43 % Fri Sep 25 22:05:40 2026
% 0.16/15.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/15.43
% 0.16/15.43 % From the command line: assign(max_seconds, 300).
% 40.19/21.20
% 40.19/21.20 % given #500 (T,wt=53): 1271 theorem(or(or(A,B),or(not(or(B,B)),C))) = true. [para(199(a,1),1248(a,1,1)),rewrite([1(10)])].
% 40.19/21.20
% 40.19/21.20 % SZS status Unsatisfiable for theBenchmark
% 40.19/21.20
% 40.19/21.20 % Proof 1 at 4.56 (+ 1.18) seconds.
% 40.19/21.20 % Length of proof is 25.
% 40.19/21.20 % Level of proof is 7.
% 40.19/21.20 % Maximum clause weight is 80.000.
% 40.19/21.20 % Given clauses 806.
% 40.19/21.20
% 40.19/21.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------