%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL013-1 : 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 : n004.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 08:24:49 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 106 ( 103 unt; 0 def)
% Number of atoms : 109 ( 108 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 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; 4 con; 0-2 aty)
% Number of variables : 126 ( 19 sgn 25 !; 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_314,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_314]) ).
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_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
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(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
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_315,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_316,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_315]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_316]) ).
fof(goals_14,axiom,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_24,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_317,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_31,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_317]) ).
cnf(c_318,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_43,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_318]) ).
cnf(c_319,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_320,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_319]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_320]) ).
cnf(c_321,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_46,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_321]) ).
cnf(c_322,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_49,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_322]) ).
cnf(c_323,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_31]) ).
cnf(c_61,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_323]) ).
cnf(c_324,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_61,c_9]) ).
cnf(c_63,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_324]) ).
cnf(c_67,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_61,c_15]) ).
cnf(c_68,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_69,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_68,c_67]) ).
cnf(c_70,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_69,c_44]) ).
cnf(c_325,plain,
converse(A) = join(converse(zero),converse(complement(complement(A)))),
inference(paramod,[status(thm)],[c_70,c_12]) ).
cnf(c_85,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(copy,[status(thm)],[c_325]) ).
cnf(c_326,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_24]) ).
cnf(c_327,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_326]) ).
cnf(c_328,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_327]) ).
cnf(c_103,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_328]) ).
cnf(c_109,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_103,c_43]) ).
cnf(c_113,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_109,c_85]) ).
cnf(c_115,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_109,c_70]) ).
cnf(c_119,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_115,c_49]) ).
cnf(c_329,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_109,c_69]) ).
cnf(c_330,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_109,c_329]) ).
cnf(c_125,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_109,c_330]) ).
cnf(c_331,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_115,c_1]) ).
cnf(c_129,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_332,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_125,c_3]) ).
cnf(c_130,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_332]) ).
cnf(c_333,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_113]) ).
cnf(c_156,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_333]) ).
cnf(c_334,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_156,c_129]) ).
cnf(c_161,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_334]) ).
cnf(c_335,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_130]) ).
cnf(c_198,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_335]) ).
cnf(c_336,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_46,c_130]) ).
cnf(c_199,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_46,c_336]) ).
cnf(c_337,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_198,c_1]) ).
cnf(c_202,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_337]) ).
cnf(c_219,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_199]) ).
cnf(c_224,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_219,c_202]) ).
cnf(c_239,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_224,c_119]) ).
cnf(c_338,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_239,c_10]) ).
cnf(c_339,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_202,c_338]) ).
cnf(c_340,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_239,c_339]) ).
cnf(c_341,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_115,c_340]) ).
cnf(c_282,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_341]) ).
cnf(c_342,plain,
zero = composition(A,composition(B,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_282,c_8]) ).
cnf(c_343,plain,
zero = composition(A,zero),
inference(paramod,[status(thm)],[c_282,c_342]) ).
cnf(c_291,plain,
composition(A,zero) = zero,
inference(copy,[status(thm)],[c_343]) ).
cnf(c_344,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_282,c_13]) ).
cnf(c_345,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_161,c_344]) ).
cnf(c_292,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_345]) ).
cnf(c_346,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_282,c_68]) ).
cnf(c_293,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_346]) ).
cnf(c_347,plain,
( composition(zero,sk1) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_291,c_20]) ).
cnf(c_295,plain,
composition(zero,sk1) != zero,
inference(copy,[status(thm)],[c_347]) ).
cnf(c_348,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_293,c_292]) ).
cnf(c_296,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_161,c_348]) ).
cnf(c_312,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_11,c_296]) ).
cnf(c_313,plain,
$false,
inference(resolve,[status(thm)],[c_312,c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 05:27:51 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 906724 was started by sandbox2 on n004,
% 0.16/0.43 % Sat Sep 26 05:27:51 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.50
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50
% 0.16/0.50 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.16/0.50 % Length of proof is 57.
% 0.16/0.50 % Level of proof is 16.
% 0.16/0.50 % Maximum clause weight is 14.000.
% 0.16/0.50 % Given clauses 65.
% 0.16/0.50
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------