%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL006-1 : TPTP v9.3.1. Released v4.0.0.
% 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 08:24:45 AM UTC 2026
% Result : Unsatisfiable 2.02s 0.73s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of formulae : 121 ( 121 unt; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 15 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_1129,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_1129]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_1130,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_19,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1130]) ).
fof(goals_14,axiom,
meet(converse(sk1),sk2) = zero,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
meet(converse(sk1),sk2) = zero,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_1131,plain,
complement(join(complement(converse(sk1)),complement(sk2))) = zero,
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_1132,plain,
complement(join(complement(sk2),complement(converse(sk1)))) = zero,
inference(paramod,[status(thm)],[c_1,c_1131]) ).
cnf(c_21,plain,
complement(join(complement(sk2),complement(converse(sk1)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_1132]) ).
fof(goals_15,axiom,
meet(sk1,converse(sk2)) != zero,
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
meet(sk1,converse(sk2)) != zero,
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_1133,plain,
complement(join(complement(sk1),complement(converse(sk2)))) != zero,
inference(paramod,[status(thm)],[c_6,c_22]) ).
cnf(c_23,plain,
complement(join(complement(sk1),complement(converse(sk2)))) != complement(top),
inference(paramod,[status(thm)],[c_19,c_1133]) ).
cnf(c_1134,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_1134]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1135,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_28,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_1135]) ).
cnf(c_1136,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_34,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1136]) ).
cnf(c_46,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1137,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_47,plain,
join(complement(top),complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1137]) ).
cnf(c_1138,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1138]) ).
cnf(c_51,plain,
join(complement(top),complement(join(complement(sk2),complement(complement(converse(sk1)))))) = sk2,
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_1139,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_56,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_1139]) ).
cnf(c_1140,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_58,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1140]) ).
cnf(c_1141,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_58,c_9]) ).
cnf(c_60,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1141]) ).
cnf(c_64,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_58,c_15]) ).
cnf(c_65,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_66,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_65,c_64]) ).
cnf(c_67,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_66,c_47]) ).
cnf(c_97,plain,
join(A,converse(complement(converse(A)))) = converse(top),
inference(paramod,[status(thm)],[c_11,c_49]) ).
cnf(c_1142,plain,
join(A,converse(top)) = join(converse(B),join(A,converse(complement(B)))),
inference(paramod,[status(thm)],[c_49,c_25]) ).
cnf(c_100,plain,
join(converse(A),join(B,converse(complement(A)))) = join(B,converse(top)),
inference(copy,[status(thm)],[c_1142]) ).
cnf(c_1143,plain,
A = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_102,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),A))) = B,
inference(copy,[status(thm)],[c_1143]) ).
cnf(c_1144,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_1145,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1144]) ).
cnf(c_109,plain,
join(complement(top),complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1145]) ).
cnf(c_117,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_109,c_46]) ).
cnf(c_124,plain,
join(complement(top),A) = A,
inference(paramod,[status(thm)],[c_117,c_67]) ).
cnf(c_1146,plain,
join(complement(top),complement(join(complement(sk2),converse(sk1)))) = sk2,
inference(paramod,[status(thm)],[c_117,c_51]) ).
cnf(c_125,plain,
complement(join(complement(sk2),converse(sk1))) = sk2,
inference(paramod,[status(thm)],[c_124,c_1146]) ).
cnf(c_1147,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_117,c_5]) ).
cnf(c_130,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_117,c_1147]) ).
cnf(c_1148,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_117,c_66]) ).
cnf(c_1149,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_117,c_1148]) ).
cnf(c_133,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_117,c_1149]) ).
cnf(c_1150,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_133,c_3]) ).
cnf(c_135,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1150]) ).
cnf(c_1151,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_133,c_28]) ).
cnf(c_1152,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_130,c_1151]) ).
cnf(c_1153,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_117,c_1152]) ).
cnf(c_152,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_1153]) ).
cnf(c_1154,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_133,c_28]) ).
cnf(c_1155,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_1154]) ).
cnf(c_1156,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_152,c_1155]) ).
cnf(c_153,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_1156]) ).
cnf(c_1157,plain,
complement(sk2) = join(complement(sk2),converse(sk1)),
inference(paramod,[status(thm)],[c_125,c_117]) ).
cnf(c_168,plain,
join(complement(sk2),converse(sk1)) = complement(sk2),
inference(copy,[status(thm)],[c_1157]) ).
cnf(c_1158,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_135]) ).
cnf(c_226,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1158]) ).
cnf(c_1159,plain,
join(A,converse(top)) = join(A,converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_97,c_135]) ).
cnf(c_230,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_97,c_1159]) ).
cnf(c_234,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_226,c_56]) ).
cnf(c_237,plain,
join(converse(A),join(B,converse(complement(A)))) = converse(top),
inference(paramod,[status(thm)],[c_230,c_100]) ).
cnf(c_1160,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_226,c_1]) ).
cnf(c_238,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1160]) ).
cnf(c_1161,plain,
top = converse(top),
inference(paramod,[status(thm)],[c_238,c_97]) ).
cnf(c_244,plain,
converse(top) = top,
inference(copy,[status(thm)],[c_1161]) ).
cnf(c_245,plain,
join(converse(A),join(B,converse(complement(A)))) = top,
inference(paramod,[status(thm)],[c_244,c_237]) ).
cnf(c_281,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_117,c_234]) ).
cnf(c_312,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_153]) ).
cnf(c_433,plain,
join(converse(complement(A)),join(B,converse(A))) = top,
inference(paramod,[status(thm)],[c_117,c_245]) ).
cnf(c_1162,plain,
join(converse(complement(sk1)),complement(sk2)) = top,
inference(paramod,[status(thm)],[c_168,c_433]) ).
cnf(c_588,plain,
join(complement(sk2),converse(complement(sk1))) = top,
inference(paramod,[status(thm)],[c_1,c_1162]) ).
cnf(c_1163,plain,
join(complement(join(complement(converse(complement(sk1))),complement(sk2))),complement(top)) = sk2,
inference(paramod,[status(thm)],[c_588,c_102]) ).
cnf(c_1164,plain,
join(complement(join(complement(sk2),complement(converse(complement(sk1))))),complement(top)) = sk2,
inference(paramod,[status(thm)],[c_1,c_1163]) ).
cnf(c_1165,plain,
join(complement(top),complement(join(complement(sk2),complement(converse(complement(sk1)))))) = sk2,
inference(paramod,[status(thm)],[c_1,c_1164]) ).
cnf(c_913,plain,
complement(join(complement(sk2),complement(converse(complement(sk1))))) = sk2,
inference(paramod,[status(thm)],[c_124,c_1165]) ).
cnf(c_1166,plain,
join(converse(complement(sk1)),sk2) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_913,c_312]) ).
cnf(c_1094,plain,
join(sk2,converse(complement(sk1))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_1,c_1166]) ).
cnf(c_1167,plain,
converse(converse(complement(sk1))) = join(converse(sk2),converse(converse(complement(sk1)))),
inference(paramod,[status(thm)],[c_1094,c_12]) ).
cnf(c_1168,plain,
complement(sk1) = join(converse(sk2),converse(converse(complement(sk1)))),
inference(paramod,[status(thm)],[c_11,c_1167]) ).
cnf(c_1169,plain,
complement(sk1) = join(converse(sk2),complement(sk1)),
inference(paramod,[status(thm)],[c_11,c_1168]) ).
cnf(c_1170,plain,
complement(sk1) = join(complement(sk1),converse(sk2)),
inference(paramod,[status(thm)],[c_1,c_1169]) ).
cnf(c_1097,plain,
join(complement(sk1),converse(sk2)) = complement(sk1),
inference(copy,[status(thm)],[c_1170]) ).
cnf(c_1171,plain,
join(complement(converse(sk2)),complement(sk1)) = top,
inference(paramod,[status(thm)],[c_1097,c_281]) ).
cnf(c_1123,plain,
join(complement(sk1),complement(converse(sk2))) = top,
inference(paramod,[status(thm)],[c_1,c_1171]) ).
cnf(c_1172,plain,
complement(top) != complement(top),
inference(paramod,[status(thm)],[c_1123,c_23]) ).
cnf(c_1128,plain,
$false,
inference(copy,[status(thm)],[c_1172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL006-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n010.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sat Sep 26 05:26:29 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 2567725 was started by sandbox2 on n010,
% 0.20/0.45 % Sat Sep 26 05:26:29 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 2.02/0.73
% 2.02/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.02/0.73
% 2.02/0.73 % Proof 1 at 0.19 (+ 0.07) seconds.
% 2.02/0.73 % Length of proof is 64.
% 2.02/0.73 % Level of proof is 18.
% 2.02/0.73 % Maximum clause weight is 18.000.
% 2.02/0.73 % Given clauses 167.
% 2.02/0.73
% 2.02/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
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