%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL050-2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:04:32 PM UTC 2026
% Result : Unsatisfiable 2.37s 2.04s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 91 ( 88 unt; 0 nHn; 10 RR)
% Number of literals : 94 ( 93 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 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 : 125 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(goals_14,negated_conjecture,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
cnf(c_0_14,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_15,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_16,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_18,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_20,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_21,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_22,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_23,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_24,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_26,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_28,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_21]),c_0_25]) ).
cnf(c_0_29,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_31,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_32,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_34,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_27]),c_0_29]),c_0_20]) ).
cnf(c_0_36,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_39,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_40,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_27]) ).
cnf(c_0_41,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_42,plain,
join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_43,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_44,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_45,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_46,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_20]) ).
cnf(c_0_47,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_48,plain,
join(X1,complement(join(complement(X2),X1))) = join(X2,complement(join(complement(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_37]),c_0_20]) ).
cnf(c_0_49,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
join(X1,complement(join(complement(X2),X1))) = join(X2,complement(join(X2,complement(X1)))),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_52,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_53,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_17]) ).
cnf(c_0_54,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_55,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_56,plain,
join(X1,complement(join(X2,complement(join(X2,X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_37]) ).
cnf(c_0_57,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_58,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_25]),c_0_20]) ).
cnf(c_0_60,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_37]),c_0_31]),c_0_20]),c_0_55]),c_0_37]) ).
cnf(c_0_61,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_63,plain,
join(X1,join(X2,join(X1,X3))) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_47]),c_0_31]),c_0_31]) ).
cnf(c_0_64,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_65,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_29]),c_0_62]) ).
cnf(c_0_66,plain,
join(X1,join(X2,composition(top,X1))) = join(X2,composition(top,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
join(converse(X1),join(converse(complement(X1)),X2)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_61]),c_0_45]) ).
cnf(c_0_68,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_65]),c_0_17]),c_0_17]) ).
cnf(c_0_69,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_61,c_0_17]) ).
cnf(c_0_70,plain,
join(composition(top,converse(X1)),converse(complement(X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_20]) ).
cnf(c_0_71,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_72,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_45,c_0_64]) ).
cnf(c_0_73,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_68,c_0_37]) ).
cnf(c_0_74,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_69]),c_0_29]),c_0_62]) ).
cnf(c_0_75,plain,
join(composition(X1,top),complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_70]),c_0_58]),c_0_14]),c_0_17]),c_0_58]),c_0_17]) ).
cnf(c_0_76,plain,
composition(top,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,plain,
complement(converse(complement(converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_73]),c_0_37]),c_0_20]),c_0_74]) ).
cnf(c_0_78,plain,
join(X1,composition(complement(X1),top)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_37]),c_0_20]) ).
cnf(c_0_79,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_76]),c_0_58]),c_0_64]) ).
cnf(c_0_80,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_37,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top)) ),
goals_14 ).
cnf(c_0_82,plain,
complement(join(complement(X1),complement(composition(X1,top)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_78]),c_0_29]),c_0_37]),c_0_36]) ).
cnf(c_0_83,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_79]),c_0_58]) ).
cnf(c_0_84,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top)) ),
inference(rw,[status(thm)],[c_0_81,c_0_20]) ).
cnf(c_0_86,plain,
join(X1,composition(X1,top)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_82]),c_0_37]),c_0_20]),c_0_37]) ).
cnf(c_0_87,plain,
composition(complement(composition(converse(X1),top)),top) = complement(composition(converse(X1),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_14]),c_0_58]),c_0_84]),c_0_14]),c_0_58]) ).
cnf(c_0_88,negated_conjecture,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_86])]) ).
cnf(c_0_89,plain,
composition(complement(composition(X1,top)),top) = complement(composition(X1,top)),
inference(spm,[status(thm)],[c_0_87,c_0_17]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL050-2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n016.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:45:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.37/2.04 % Version : CSE_E---1.7
% 2.37/2.04 % Problem : theBenchmark.p
% 2.37/2.04 % SZS status Unsatisfiable for theBenchmark.p
% 2.37/2.04 % SZS output start CNFRefutation
% See solution above
% 2.37/2.05 % Total time : 1.367s
%------------------------------------------------------------------------------