%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:58:46 AM UTC 2026
% Result : Unsatisfiable 174.47s 23.63s
% Output : CNFRefutation 174.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 6
% Syntax : Number of formulae : 121 ( 121 unt; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 348 ( 86 sgn 11 !; 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(condensed_detachment,axiom,
! [VAR_0,VAR_1] : ifeq(is_a_theorem(implies(VAR_0,VAR_1)),true,ifeq(is_a_theorem(VAR_0),true,is_a_theorem(VAR_1),true),true) = true,
file('theBenchmark.p',condensed_detachment) ).
cnf(c_2,plain,
ifeq(is_a_theorem(implies(A,B)),true,ifeq(is_a_theorem(A),true,is_a_theorem(B),true),true) = true,
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(cn_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))) = true,
file('theBenchmark.p',cn_1) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) = true,
inference(clausify,[status(thm)],[cn_1]) ).
fof(cn_2,axiom,
! [VAR_0] : is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0)) = true,
file('theBenchmark.p',cn_2) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(not(A),A),A)) = true,
inference(clausify,[status(thm)],[cn_2]) ).
fof(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))) = true,
file('theBenchmark.p',cn_3) ).
cnf(c_5,plain,
is_a_theorem(implies(A,implies(not(A),B))) = true,
inference(clausify,[status(thm)],[cn_3]) ).
fof(prove_cn_47,axiom,
is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) != true,
file('theBenchmark.p',prove_cn_47) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) != true,
inference(clausify,[status(thm)],[prove_cn_47]) ).
cnf(c_13977,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_7,plain,
ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_13977]) ).
cnf(c_13978,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),D)),true,ifeq(true,true,is_a_theorem(D),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_8,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),D)),true,is_a_theorem(D),true) = true,
inference(paramod,[status(thm)],[c_1,c_13978]) ).
cnf(c_13979,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(A),A)),true,is_a_theorem(A),true),true) = true,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_10,plain,
ifeq(is_a_theorem(implies(not(A),A)),true,is_a_theorem(A),true) = true,
inference(paramod,[status(thm)],[c_1,c_13979]) ).
cnf(c_13980,plain,
ifeq(is_a_theorem(implies(implies(implies(not(A),A),A),B)),true,ifeq(true,true,is_a_theorem(B),true),true) = true,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_11,plain,
ifeq(is_a_theorem(implies(implies(implies(not(A),A),A),B)),true,is_a_theorem(B),true) = true,
inference(paramod,[status(thm)],[c_1,c_13980]) ).
cnf(c_13981,plain,
ifeq(true,true,ifeq(is_a_theorem(A),true,is_a_theorem(implies(not(A),B)),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_13,plain,
ifeq(is_a_theorem(A),true,is_a_theorem(implies(not(A),B)),true) = true,
inference(paramod,[status(thm)],[c_1,c_13981]) ).
cnf(c_13982,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),true) = true,
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_16,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))) = true,
inference(paramod,[status(thm)],[c_1,c_13982]) ).
cnf(c_13983,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),true) = true,
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))) = true,
inference(paramod,[status(thm)],[c_1,c_13983]) ).
cnf(c_13984,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_19,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))) = true,
inference(paramod,[status(thm)],[c_1,c_13984]) ).
cnf(c_13985,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(not(A),A),B)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_29,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(not(A),A),B)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_13985]) ).
cnf(c_13986,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))),true) = true,
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_30,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))) = true,
inference(paramod,[status(thm)],[c_1,c_13986]) ).
cnf(c_13987,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(A,C)),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_32,plain,
ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(A,C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_13987]) ).
cnf(c_13988,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D)),true,ifeq(true,true,is_a_theorem(D),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_33,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D)),true,is_a_theorem(D),true) = true,
inference(paramod,[status(thm)],[c_1,c_13988]) ).
cnf(c_13989,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))),true) = true,
inference(paramod,[status(thm)],[c_19,c_7]) ).
cnf(c_34,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))) = true,
inference(paramod,[status(thm)],[c_1,c_13989]) ).
cnf(c_13990,plain,
ifeq(true,true,is_a_theorem(implies(A,A)),true) = true,
inference(paramod,[status(thm)],[c_4,c_32]) ).
cnf(c_53,plain,
is_a_theorem(implies(A,A)) = true,
inference(paramod,[status(thm)],[c_1,c_13990]) ).
cnf(c_13991,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(A,A)),B)),true) = true,
inference(paramod,[status(thm)],[c_53,c_13]) ).
cnf(c_59,plain,
is_a_theorem(implies(not(implies(A,A)),B)) = true,
inference(paramod,[status(thm)],[c_1,c_13991]) ).
cnf(c_13992,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))),true) = true,
inference(paramod,[status(thm)],[c_59,c_7]) ).
cnf(c_63,plain,
is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_13992]) ).
cnf(c_13993,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(not(implies(B,B)),C))),true) = true,
inference(paramod,[status(thm)],[c_63,c_32]) ).
cnf(c_70,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))) = true,
inference(paramod,[status(thm)],[c_1,c_13993]) ).
cnf(c_13994,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))),true) = true,
inference(paramod,[status(thm)],[c_70,c_7]) ).
cnf(c_72,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))) = true,
inference(paramod,[status(thm)],[c_1,c_13994]) ).
cnf(c_13995,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)),true,is_a_theorem(implies(implies(C,A),D)),true),true) = true,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_116,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)),true,is_a_theorem(implies(implies(C,A),D)),true) = true,
inference(paramod,[status(thm)],[c_1,c_13995]) ).
cnf(c_13996,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D)),E)),true,ifeq(true,true,is_a_theorem(E),true),true) = true,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_117,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D)),E)),true,is_a_theorem(E),true) = true,
inference(paramod,[status(thm)],[c_1,c_13996]) ).
cnf(c_13997,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,B))),true) = true,
inference(paramod,[status(thm)],[c_72,c_11]) ).
cnf(c_181,plain,
is_a_theorem(implies(A,implies(B,B))) = true,
inference(paramod,[status(thm)],[c_1,c_13997]) ).
cnf(c_13998,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),true) = true,
inference(paramod,[status(thm)],[c_181,c_7]) ).
cnf(c_185,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))) = true,
inference(paramod,[status(thm)],[c_1,c_13998]) ).
cnf(c_13999,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(not(B),B),B))),true) = true,
inference(paramod,[status(thm)],[c_185,c_29]) ).
cnf(c_199,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_13999]) ).
cnf(c_14000,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))),true) = true,
inference(paramod,[status(thm)],[c_199,c_7]) ).
cnf(c_215,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))) = true,
inference(paramod,[status(thm)],[c_1,c_14000]) ).
cnf(c_14001,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(A),A),B),C)),true,is_a_theorem(implies(implies(A,B),C)),true),true) = true,
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_226,plain,
ifeq(is_a_theorem(implies(implies(implies(not(A),A),B),C)),true,is_a_theorem(implies(implies(A,B),C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_14001]) ).
cnf(c_14002,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_16,c_33]) ).
cnf(c_298,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_14002]) ).
cnf(c_14003,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),true) = true,
inference(paramod,[status(thm)],[c_298,c_7]) ).
cnf(c_304,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))) = true,
inference(paramod,[status(thm)],[c_1,c_14003]) ).
cnf(c_14004,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(A),B),C),implies(implies(C,D),implies(A,D)))),true) = true,
inference(paramod,[status(thm)],[c_34,c_8]) ).
cnf(c_354,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(implies(C,D),implies(A,D)))) = true,
inference(paramod,[status(thm)],[c_1,c_14004]) ).
cnf(c_14005,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,implies(B,C)),D)),true,is_a_theorem(implies(implies(B,not(A)),D)),true),true) = true,
inference(paramod,[status(thm)],[c_304,c_2]) ).
cnf(c_586,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,C)),D)),true,is_a_theorem(implies(implies(B,not(A)),D)),true) = true,
inference(paramod,[status(thm)],[c_1,c_14005]) ).
cnf(c_14006,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(implies(C,D),implies(A,D))),true),true) = true,
inference(paramod,[status(thm)],[c_354,c_2]) ).
cnf(c_622,plain,
ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(implies(C,D),implies(A,D))),true) = true,
inference(paramod,[status(thm)],[c_1,c_14006]) ).
cnf(c_14007,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),true) = true,
inference(paramod,[status(thm)],[c_215,c_116]) ).
cnf(c_1410,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_14007]) ).
cnf(c_14008,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),true) = true,
inference(paramod,[status(thm)],[c_1410,c_586]) ).
cnf(c_1579,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))) = true,
inference(paramod,[status(thm)],[c_1,c_14008]) ).
cnf(c_14009,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(B,A),A)))),true) = true,
inference(paramod,[status(thm)],[c_1410,c_116]) ).
cnf(c_1580,plain,
is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(B,A),A)))) = true,
inference(paramod,[status(thm)],[c_1,c_14009]) ).
cnf(c_14010,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(C,D))),true) = true,
inference(paramod,[status(thm)],[c_1579,c_622]) ).
cnf(c_1595,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(C,D))) = true,
inference(paramod,[status(thm)],[c_1,c_14010]) ).
cnf(c_14011,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,A))),true) = true,
inference(paramod,[status(thm)],[c_1595,c_11]) ).
cnf(c_1756,plain,
is_a_theorem(implies(A,implies(B,A))) = true,
inference(paramod,[status(thm)],[c_1,c_14011]) ).
cnf(c_14012,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),true) = true,
inference(paramod,[status(thm)],[c_1756,c_7]) ).
cnf(c_1769,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))) = true,
inference(paramod,[status(thm)],[c_1,c_14012]) ).
cnf(c_14013,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(B,C)),true),true) = true,
inference(paramod,[status(thm)],[c_1769,c_2]) ).
cnf(c_1817,plain,
ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(B,C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_14013]) ).
cnf(c_14014,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))),true) = true,
inference(paramod,[status(thm)],[c_1769,c_7]) ).
cnf(c_1819,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))) = true,
inference(paramod,[status(thm)],[c_1,c_14014]) ).
cnf(c_14015,plain,
ifeq(true,true,is_a_theorem(implies(not(A),implies(B,implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_1579,c_1817]) ).
cnf(c_1856,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_14015]) ).
cnf(c_14016,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(not(B),D))),true) = true,
inference(paramod,[status(thm)],[c_1856,c_7]) ).
cnf(c_1873,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(not(B),D))) = true,
inference(paramod,[status(thm)],[c_1,c_14016]) ).
cnf(c_14017,plain,
ifeq(true,true,is_a_theorem(implies(not(A),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_1873,c_11]) ).
cnf(c_2585,plain,
is_a_theorem(implies(not(A),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_14017]) ).
cnf(c_14018,plain,
ifeq(is_a_theorem(implies(implies(not(A),implies(A,B)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_2585,c_2]) ).
cnf(c_2600,plain,
ifeq(is_a_theorem(implies(implies(not(A),implies(A,B)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_14018]) ).
cnf(c_14019,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,D),implies(B,D)))),true) = true,
inference(paramod,[status(thm)],[c_1819,c_8]) ).
cnf(c_7071,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,D),implies(B,D)))) = true,
inference(paramod,[status(thm)],[c_1,c_14019]) ).
cnf(c_14020,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(implies(C,D),implies(B,D))),true),true) = true,
inference(paramod,[status(thm)],[c_7071,c_2]) ).
cnf(c_7125,plain,
ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(implies(C,D),implies(B,D))),true) = true,
inference(paramod,[status(thm)],[c_1,c_14020]) ).
cnf(c_14021,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),true) = true,
inference(paramod,[status(thm)],[c_1580,c_2600]) ).
cnf(c_7436,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_14021]) ).
cnf(c_14022,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),A),A)),true) = true,
inference(paramod,[status(thm)],[c_7436,c_10]) ).
cnf(c_7452,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_14022]) ).
cnf(c_14023,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_7452,c_116]) ).
cnf(c_7489,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_14023]) ).
cnf(c_14024,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),true) = true,
inference(paramod,[status(thm)],[c_7489,c_116]) ).
cnf(c_7505,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_14024]) ).
cnf(c_14025,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_7505,c_7125]) ).
cnf(c_7569,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))) = true,
inference(paramod,[status(thm)],[c_1,c_14025]) ).
cnf(c_14026,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_7569,c_117]) ).
cnf(c_10085,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_14026]) ).
cnf(c_14027,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(C,A),implies(C,B))),true),true) = true,
inference(paramod,[status(thm)],[c_10085,c_2]) ).
cnf(c_10129,plain,
ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(C,A),implies(C,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_14027]) ).
cnf(c_14028,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_7452,c_10129]) ).
cnf(c_10735,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_14028]) ).
cnf(c_14029,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,A))),true) = true,
inference(paramod,[status(thm)],[c_10735,c_586]) ).
cnf(c_13930,plain,
is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,A))) = true,
inference(paramod,[status(thm)],[c_1,c_14029]) ).
cnf(c_14030,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))),true) = true,
inference(paramod,[status(thm)],[c_13930,c_226]) ).
cnf(c_13975,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))) = true,
inference(paramod,[status(thm)],[c_1,c_14030]) ).
cnf(c_13976,plain,
$false,
inference(resolve,[status(thm)],[c_13975,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 22:25:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3956848 was started by sandbox on n020,
% 0.12/0.38 % Fri Sep 25 22:25:04 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 174.47/23.63
% 174.47/23.63 % given #500 (T,wt=37): 7489 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) = true. [para(7452(a,1),116(a,1,1)),rewrite([1(9)])].
% 174.47/23.63
% 174.47/23.63 % SZS status Unsatisfiable for theBenchmark
% 174.47/23.63
% 174.47/23.63 % Proof 1 at 5.44 (+ 1.69) seconds.
% 174.47/23.63 % Length of proof is 61.
% 174.47/23.63 % Level of proof is 33.
% 174.47/23.63 % Maximum clause weight is 65.000.
% 174.47/23.63 % Given clauses 712.
% 174.47/23.63
% 174.47/23.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------