%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL043-2 : 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 : n013.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 05:04:30 PM UTC 2026
% Result : Unsatisfiable 18.36s 11.58s
% Output : CNFRefutation 18.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 17 RR)
% Number of literals : 87 ( 86 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 121 ( 15 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(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
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(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(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(modular_law_2_16,axiom,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-1.ax',modular_law_2_16) ).
cnf(goals_17,negated_conjecture,
join(composition(sk1,converse(sk2)),sk3) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(goals_18,negated_conjecture,
join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(c_0_15,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_16,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_17,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_19,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
cnf(c_0_20,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_21,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_22,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_25,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_26,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
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_23,c_0_24]),c_0_22]),c_0_24]) ).
cnf(c_0_29,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,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_21]) ).
cnf(c_0_34,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_35,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,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_27]),c_0_28]),c_0_29]),c_0_21]) ).
cnf(c_0_37,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_38,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_40,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_27]) ).
cnf(c_0_41,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_42,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_43,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_45,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
cnf(c_0_46,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_21]) ).
cnf(c_0_47,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_48,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_49,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_50,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_48,c_0_27]) ).
cnf(c_0_52,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_21]) ).
cnf(c_0_53,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_54,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_55,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_56,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_34,c_0_47]) ).
cnf(c_0_57,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
composition(top,zero) = zero,
inference(rw,[status(thm)],[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_23,c_0_54]),c_0_29]),c_0_55]),c_0_29]),c_0_46]),c_0_47]),c_0_29]) ).
cnf(c_0_59,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_60,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_33]),c_0_31]) ).
cnf(c_0_61,plain,
join(X1,join(complement(join(X2,complement(X1))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_57]) ).
cnf(c_0_62,axiom,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
modular_law_2_16 ).
cnf(c_0_63,negated_conjecture,
join(composition(sk1,converse(sk2)),sk3) = sk3,
goals_17 ).
cnf(c_0_64,plain,
composition(join(X1,one),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_58]),c_0_46]),c_0_47]),c_0_58]) ).
cnf(c_0_65,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_66,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_38]),c_0_16]) ).
cnf(c_0_67,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_60,c_0_21]) ).
cnf(c_0_68,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_33]),c_0_41]) ).
cnf(c_0_69,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_70,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)))),
inference(rw,[status(thm)],[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_62,c_0_26]),c_0_26]),c_0_26]),c_0_21]),c_0_26]),c_0_26]),c_0_21]) ).
cnf(c_0_71,negated_conjecture,
join(sk3,composition(sk1,converse(sk2))) = sk3,
inference(rw,[status(thm)],[c_0_63,c_0_21]) ).
cnf(c_0_72,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_38]),c_0_64]) ).
cnf(c_0_73,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,plain,
join(complement(zero),X1) = top,
inference(spm,[status(thm)],[c_0_67,c_0_36]) ).
cnf(c_0_75,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_68,c_0_41]) ).
cnf(c_0_76,plain,
join(X1,join(X2,complement(join(X2,X1)))) = top,
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_77,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_57,c_0_41]) ).
cnf(c_0_78,plain,
join(complement(join(complement(composition(complement(X1),X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(X1,complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(X1,complement(composition(X3,converse(X2))))),X2)))),
inference(spm,[status(thm)],[c_0_70,c_0_41]) ).
cnf(c_0_79,negated_conjecture,
join(sk3,complement(composition(sk1,converse(sk2)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_21]) ).
cnf(c_0_80,plain,
composition(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_72]),c_0_73]),c_0_73]) ).
cnf(c_0_81,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_23,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1),
goals_18 ).
cnf(c_0_83,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_29]),c_0_31]),c_0_65]),c_0_31]),c_0_21]),c_0_77]) ).
cnf(c_0_84,negated_conjecture,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_78,c_0_79]),c_0_29]),c_0_80]),c_0_81]),c_0_43]),c_0_29]),c_0_65]),c_0_29]),c_0_80]),c_0_81]),c_0_43]),c_0_29]),c_0_21]) ).
cnf(c_0_85,negated_conjecture,
join(complement(sk1),composition(complement(sk3),sk2)) != complement(sk1),
inference(rw,[status(thm)],[c_0_82,c_0_21]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_65]),c_0_41]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : REL043-2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.11/0.30 % Computer : n013.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue May 5 01:45:11 EDT 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.31 % start to proof: theBenchmark
% 18.36/11.58 % Version : CSE_E---1.7
% 18.36/11.58 % Problem : theBenchmark.p
% 18.36/11.58 % SZS status Unsatisfiable for theBenchmark.p
% 18.36/11.58 % SZS output start CNFRefutation
% See solution above
% 18.46/11.66 % Total time : 8.385s
%------------------------------------------------------------------------------