%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL005-3 : 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 : n029.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 05:04:11 PM UTC 2026
% Result : Unsatisfiable 1.95s 1.93s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of clauses : 93 ( 93 unt; 0 nHn; 6 RR)
% Number of literals : 93 ( 92 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 141 ( 10 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(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(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/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/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(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(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_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
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(goals_17,negated_conjecture,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(c_0_12,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_13,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_14,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_16,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_13]) ).
cnf(c_0_17,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_18,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
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_16]) ).
cnf(c_0_22,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_24,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_26,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_21]),c_0_24]) ).
cnf(c_0_27,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_28,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_29,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_30,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]) ).
cnf(c_0_31,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_32,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_31]) ).
cnf(c_0_35,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_20]) ).
cnf(c_0_36,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_28]) ).
cnf(c_0_37,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_38,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_31]) ).
cnf(c_0_39,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_43,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_41]),c_0_42]) ).
cnf(c_0_44,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_46,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_47,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_48,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_32]),c_0_20]) ).
cnf(c_0_49,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_28,c_0_44]) ).
cnf(c_0_50,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_51,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_52,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_53,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
cnf(c_0_54,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_49,c_0_20]) ).
cnf(c_0_55,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_56,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_51]) ).
cnf(c_0_57,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_52,c_0_13]) ).
cnf(c_0_58,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_53]) ).
cnf(c_0_59,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_60,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_32]),c_0_17]) ).
cnf(c_0_61,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_56]),c_0_20]),c_0_18]),c_0_34]) ).
cnf(c_0_62,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_57,c_0_18]) ).
cnf(c_0_63,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_60]),c_0_34]),c_0_61]) ).
cnf(c_0_65,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_17]) ).
cnf(c_0_66,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_67,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_62,c_0_50]) ).
cnf(c_0_68,plain,
meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_63]),c_0_54]),c_0_42]),c_0_43]),c_0_36]) ).
cnf(c_0_69,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_44,c_0_49]) ).
cnf(c_0_70,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_48]),c_0_36]) ).
cnf(c_0_71,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_48]) ).
cnf(c_0_72,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_63,c_0_66]) ).
cnf(c_0_73,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_62,c_0_67]) ).
cnf(c_0_74,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_68]),c_0_69]),c_0_44]),c_0_36]),c_0_70]) ).
cnf(c_0_75,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_71,c_0_59]) ).
cnf(c_0_76,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_53]),c_0_36]) ).
cnf(c_0_77,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_34]),c_0_61]) ).
cnf(c_0_78,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_79,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_80,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_77]),c_0_13]),c_0_13]) ).
cnf(c_0_81,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_73]),c_0_79]),c_0_36]) ).
cnf(c_0_82,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_80]),c_0_36]),c_0_81]) ).
cnf(c_0_83,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_13,c_0_82]) ).
cnf(c_0_84,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_44,c_0_83]) ).
cnf(c_0_85,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_52,c_0_13]) ).
cnf(c_0_86,plain,
complement(converse(join(complement(X1),X2))) = converse(meet(complement(X2),X1)),
inference(spm,[status(thm)],[c_0_84,c_0_54]) ).
cnf(c_0_87,plain,
converse(join(X1,complement(converse(X2)))) = join(converse(X1),complement(X2)),
inference(spm,[status(thm)],[c_0_85,c_0_84]) ).
cnf(c_0_88,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_69,c_0_44]) ).
cnf(c_0_89,plain,
converse(meet(converse(X1),X2)) = meet(converse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_84]),c_0_88]),c_0_44]),c_0_44]) ).
cnf(c_0_90,negated_conjecture,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
goals_17 ).
cnf(c_0_91,plain,
meet(converse(X1),converse(X2)) = converse(meet(X2,X1)),
inference(spm,[status(thm)],[c_0_89,c_0_13]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL005-3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:39:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.95/1.93 % Version : CSE_E---1.7
% 1.95/1.93 % Problem : theBenchmark.p
% 1.95/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 1.95/1.93 % SZS output start CNFRefutation
% See solution above
% 1.95/1.94 % Total time : 1.371s
%------------------------------------------------------------------------------