%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL010-2 : 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 : n027.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 05:04:14 PM UTC 2026
% Result : Unsatisfiable 4.51s 3.49s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 15 RR)
% Number of literals : 75 ( 74 equ; 2 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 96 ( 6 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(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(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(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(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/sandbox/benchmark/Axioms/REL001-1.ax',modular_law_1_15) ).
cnf(goals_17,negated_conjecture,
meet(composition(sk1,sk2),sk3) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(goals_18,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero,
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(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_21,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_22,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_24,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_28,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_29,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]),c_0_27]) ).
cnf(c_0_30,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_31,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_32,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]) ).
cnf(c_0_33,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_34,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_35,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_37,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_35]) ).
cnf(c_0_40,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_41,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_42,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_39]),c_0_23]) ).
cnf(c_0_43,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_34]) ).
cnf(c_0_44,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_45,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_35]) ).
cnf(c_0_46,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_48,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_51,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_46]) ).
cnf(c_0_52,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_27]),c_0_23]) ).
cnf(c_0_53,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_23]) ).
cnf(c_0_54,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_50]) ).
cnf(c_0_56,plain,
composition(top,join(one,converse(X1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41]),c_0_46]),c_0_53]) ).
cnf(c_0_57,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_55]) ).
cnf(c_0_58,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_59,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_60,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_61,plain,
composition(top,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_37]) ).
cnf(c_0_62,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_57]) ).
cnf(c_0_63,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,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_60,c_0_43]),c_0_43]) ).
cnf(c_0_65,negated_conjecture,
meet(composition(sk1,sk2),sk3) = zero,
goals_17 ).
cnf(c_0_66,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(spm,[status(thm)],[c_0_26,c_0_61]),c_0_39]),c_0_46]),c_0_39]),c_0_62]),c_0_39]) ).
cnf(c_0_67,plain,
complement(zero) = top,
inference(rw,[status(thm)],[c_0_63,c_0_57]) ).
cnf(c_0_68,plain,
join(meet(composition(converse(X1),X2),X3),meet(X3,composition(converse(X1),meet(X2,composition(X1,X3))))) = meet(X3,composition(converse(X1),meet(X2,composition(X1,X3)))),
inference(spm,[status(thm)],[c_0_64,c_0_16]) ).
cnf(c_0_69,negated_conjecture,
meet(sk3,composition(sk1,sk2)) = zero,
inference(rw,[status(thm)],[c_0_65,c_0_43]) ).
cnf(c_0_70,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_66]),c_0_62]),c_0_41]),c_0_66]) ).
cnf(c_0_71,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_67]),c_0_37]),c_0_39]) ).
cnf(c_0_72,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_57]),c_0_23]),c_0_21]),c_0_39]) ).
cnf(c_0_73,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero,
goals_18 ).
cnf(c_0_74,negated_conjecture,
$false,
inference(sr,[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_68,c_0_69]),c_0_70]),c_0_71]),c_0_72]),c_0_70]),c_0_71]),c_0_43]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL010-2 : 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 : n027.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 01:40:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.51/3.49 % Version : CSE_E---1.7
% 4.51/3.49 % Problem : theBenchmark.p
% 4.51/3.49 % SZS status Unsatisfiable for theBenchmark.p
% 4.51/3.49 % SZS output start CNFRefutation
% See solution above
% 4.62/3.50 % Total time : 2.372s
%------------------------------------------------------------------------------