%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL045-2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 20.79s 13.81s
% Output : CNFRefutation 20.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 9 RR)
% Number of literals : 78 ( 77 equ; 4 neg)
% Maximal clause size : 1 ( 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 : 121 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
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/sandbox2/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(modular_law_1_15,axiom,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',modular_law_1_15) ).
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/sandbox2/benchmark/Axioms/REL001-1.ax',modular_law_2_16) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(goals_17,negated_conjecture,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
cnf(c_0_16,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_17,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_18,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]) ).
cnf(c_0_21,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_22,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_23,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_24,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_30,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_28]) ).
cnf(c_0_31,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_32,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_33,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_34,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_22]) ).
cnf(c_0_35,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_36,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_35]) ).
cnf(c_0_39,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_24]) ).
cnf(c_0_40,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_32]) ).
cnf(c_0_41,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_42,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_35]) ).
cnf(c_0_43,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_47,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_48,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_49,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_28]),c_0_24]) ).
cnf(c_0_50,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_51,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_47,c_0_17]) ).
cnf(c_0_52,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_53,axiom,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
modular_law_1_15 ).
cnf(c_0_54,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_55,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_57,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_58,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_59,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_25]),c_0_24]) ).
cnf(c_0_60,plain,
join(meet(composition(X1,X2),X3),meet(X3,composition(X1,meet(X2,composition(converse(X1),X3))))) = meet(X3,composition(X1,meet(X2,composition(converse(X1),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_40]),c_0_40]) ).
cnf(c_0_61,plain,
join(meet(composition(X1,X2),X3),meet(X3,composition(meet(X1,composition(X3,converse(X2))),X2))) = meet(X3,composition(meet(X1,composition(X3,converse(X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_40]),c_0_40]) ).
cnf(c_0_62,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_63,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_45]),c_0_48]) ).
cnf(c_0_64,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_56,c_0_50]) ).
cnf(c_0_65,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_66,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_24]) ).
cnf(c_0_67,negated_conjecture,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
goals_17 ).
cnf(c_0_68,plain,
join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_58]),c_0_59]),c_0_58]) ).
cnf(c_0_69,plain,
join(meet(X1,composition(X2,X3)),meet(X1,composition(X2,meet(X3,composition(converse(X2),X1))))) = meet(X1,composition(X2,meet(X3,composition(converse(X2),X1)))),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_70,plain,
meet(X1,composition(X1,top)) = X1,
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_61,c_0_62]),c_0_63]),c_0_64]),c_0_63]),c_0_65]),c_0_62]),c_0_66]),c_0_64]),c_0_63]),c_0_65]),c_0_62]) ).
cnf(c_0_71,negated_conjecture,
join(sk1,composition(sk1,composition(converse(sk1),sk1))) != composition(sk1,composition(converse(sk1),sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_65]),c_0_65]) ).
cnf(c_0_72,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_17]) ).
cnf(c_0_73,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_40]) ).
cnf(c_0_74,plain,
meet(X1,composition(X1,composition(converse(X1),X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_63]),c_0_66]),c_0_63]) ).
cnf(c_0_75,negated_conjecture,
composition(sk1,join(one,composition(converse(sk1),sk1))) != composition(sk1,composition(converse(sk1),sk1)),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
composition(X1,join(one,composition(converse(X1),X1))) = composition(X1,composition(converse(X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_24]),c_0_72]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL045-2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:44:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 20.79/13.81 % Version : CSE_E---1.7
% 20.79/13.81 % Problem : theBenchmark.p
% 20.79/13.81 % SZS status Unsatisfiable for theBenchmark.p
% 20.79/13.81 % SZS output start CNFRefutation
% See solution above
% 20.79/13.88 % Total time : 10.383s
%------------------------------------------------------------------------------