%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL250-10 : 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 : n010.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 07:58:28 AM UTC 2026
% Result : Unsatisfiable 50.15s 7.61s
% Output : CNFRefutation 50.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 19 sgn 21 !; 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(prove_this,axiom,
theorem(implies(implies(q,r),implies(and(p,q),r))) != true,
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
theorem(implies(implies(q,r),implies(and(p,q),r))) != true,
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_10853,plain,
theorem(implies(or(not(q),r),implies(and(p,q),r))) != true,
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_10854,plain,
theorem(implies(or(not(q),r),implies(not(or(not(p),not(q))),r))) != true,
inference(paramod,[status(thm)],[c_11,c_10853]) ).
cnf(c_10855,plain,
theorem(implies(or(not(q),r),or(not(not(or(not(p),not(q)))),r))) != true,
inference(paramod,[status(thm)],[c_7,c_10854]) ).
cnf(c_13,plain,
theorem(or(not(or(not(q),r)),or(not(not(or(not(p),not(q)))),r))) != true,
inference(paramod,[status(thm)],[c_7,c_10855]) ).
cnf(c_10856,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_10857,plain,
axiom(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_10856]) ).
cnf(c_14,plain,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_7,c_10857]) ).
cnf(c_15,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(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_17,plain,
axiom(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_18,plain,
axiom(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_10858,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_14,c_8]) ).
cnf(c_19,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_10858]) ).
cnf(c_10859,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_20,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_10859]) ).
cnf(c_10860,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_21,plain,
theorem(or(not(or(A,B)),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_10860]) ).
cnf(c_10861,plain,
ifeq(true,true,theorem(or(not(A),or(B,A))),true) = true,
inference(paramod,[status(thm)],[c_17,c_8]) ).
cnf(c_22,plain,
theorem(or(not(A),or(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_10861]) ).
cnf(c_10862,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_23,plain,
theorem(or(not(or(A,A)),A)) = true,
inference(paramod,[status(thm)],[c_1,c_10862]) ).
cnf(c_10863,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_19,c_10]) ).
cnf(c_24,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_10863]) ).
cnf(c_10864,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_22,c_10]) ).
cnf(c_28,plain,
ifeq(theorem(or(not(or(not(A),or(B,A))),C)),true,theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_10864]) ).
cnf(c_10865,plain,
ifeq(true,true,ifeq(theorem(or(A,A)),true,theorem(A),true),true) = true,
inference(paramod,[status(thm)],[c_23,c_10]) ).
cnf(c_35,plain,
ifeq(theorem(or(A,A)),true,theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_10865]) ).
cnf(c_10866,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true),true) = true,
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_38,plain,
ifeq(theorem(or(A,B)),true,theorem(or(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_10866]) ).
cnf(c_10867,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_20,c_10]) ).
cnf(c_41,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_10867]) ).
cnf(c_10868,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,or(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_22,c_24]) ).
cnf(c_64,plain,
theorem(or(not(or(A,B)),or(A,or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_10868]) ).
cnf(c_10869,plain,
ifeq(true,true,theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_21,c_24]) ).
cnf(c_66,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_10869]) ).
cnf(c_10870,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(A,or(C,B))),true),true) = true,
inference(paramod,[status(thm)],[c_64,c_10]) ).
cnf(c_80,plain,
ifeq(theorem(or(A,B)),true,theorem(or(A,or(C,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_10870]) ).
cnf(c_10871,plain,
ifeq(true,true,theorem(or(A,or(not(B),B))),true) = true,
inference(paramod,[status(thm)],[c_20,c_28]) ).
cnf(c_139,plain,
theorem(or(A,or(not(B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_10871]) ).
cnf(c_10872,plain,
ifeq(true,true,theorem(or(not(A),A)),true) = true,
inference(paramod,[status(thm)],[c_139,c_35]) ).
cnf(c_145,plain,
theorem(or(not(A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_10872]) ).
cnf(c_10873,plain,
ifeq(true,true,theorem(or(A,not(A))),true) = true,
inference(paramod,[status(thm)],[c_145,c_38]) ).
cnf(c_151,plain,
theorem(or(A,not(A))) = true,
inference(paramod,[status(thm)],[c_1,c_10873]) ).
cnf(c_10874,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(A,not(not(B))))),true) = true,
inference(paramod,[status(thm)],[c_151,c_24]) ).
cnf(c_156,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))) = true,
inference(paramod,[status(thm)],[c_1,c_10874]) ).
cnf(c_10875,plain,
ifeq(true,true,theorem(or(A,or(not(or(A,B)),B))),true) = true,
inference(paramod,[status(thm)],[c_145,c_41]) ).
cnf(c_410,plain,
theorem(or(A,or(not(or(A,B)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_10875]) ).
cnf(c_10876,plain,
ifeq(true,true,theorem(or(or(not(or(A,B)),B),A)),true) = true,
inference(paramod,[status(thm)],[c_410,c_38]) ).
cnf(c_418,plain,
theorem(or(or(not(or(A,B)),B),A)) = true,
inference(paramod,[status(thm)],[c_1,c_10876]) ).
cnf(c_10877,plain,
ifeq(true,true,theorem(or(or(not(or(A,B)),B),or(C,A))),true) = true,
inference(paramod,[status(thm)],[c_418,c_80]) ).
cnf(c_431,plain,
theorem(or(or(not(or(A,B)),B),or(C,A))) = true,
inference(paramod,[status(thm)],[c_1,c_10877]) ).
cnf(c_10878,plain,
ifeq(true,true,ifeq(theorem(or(A,or(B,C))),true,theorem(or(A,or(C,B))),true),true) = true,
inference(paramod,[status(thm)],[c_66,c_10]) ).
cnf(c_1173,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(A,or(C,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_10878]) ).
cnf(c_10879,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(not(not(B)),A))),true) = true,
inference(paramod,[status(thm)],[c_156,c_1173]) ).
cnf(c_3226,plain,
theorem(or(not(or(A,B)),or(not(not(B)),A))) = true,
inference(paramod,[status(thm)],[c_1,c_10879]) ).
cnf(c_10880,plain,
ifeq(true,true,ifeq(theorem(or(A,B)),true,theorem(or(not(not(B)),A)),true),true) = true,
inference(paramod,[status(thm)],[c_3226,c_10]) ).
cnf(c_5088,plain,
ifeq(theorem(or(A,B)),true,theorem(or(not(not(B)),A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_10880]) ).
cnf(c_10881,plain,
ifeq(true,true,theorem(or(not(not(or(A,B))),or(not(or(B,C)),C))),true) = true,
inference(paramod,[status(thm)],[c_431,c_5088]) ).
cnf(c_6258,plain,
theorem(or(not(not(or(A,B))),or(not(or(B,C)),C))) = true,
inference(paramod,[status(thm)],[c_1,c_10881]) ).
cnf(c_10882,plain,
ifeq(true,true,theorem(or(not(or(A,B)),or(not(not(or(C,A))),B))),true) = true,
inference(paramod,[status(thm)],[c_6258,c_41]) ).
cnf(c_10851,plain,
theorem(or(not(or(A,B)),or(not(not(or(C,A))),B))) = true,
inference(paramod,[status(thm)],[c_1,c_10882]) ).
cnf(c_10852,plain,
$false,
inference(resolve,[status(thm)],[c_10851,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL250-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n010.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 22:07:46 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 1808311 was started by sandbox2 on n010,
% 0.19/0.44 % Fri Sep 25 22:07:46 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 50.15/7.61
% 50.15/7.61 % given #500 (W,wt=48): 1217 theorem(or(not(not(or(A,not(A)))),B)) = true. [para(209(a,1),1193(a,1,1)),rewrite([1(10)])].
% 50.15/7.61
% 50.15/7.61 % SZS status Unsatisfiable for theBenchmark
% 50.15/7.61
% 50.15/7.61 % Proof 1 at 5.08 (+ 2.02) seconds.
% 50.15/7.61 % Length of proof is 44.
% 50.15/7.61 % Level of proof is 12.
% 50.15/7.61 % Maximum clause weight is 62.000.
% 50.15/7.61 % Given clauses 692.
% 50.15/7.61
% 50.15/7.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------