%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL008-2 : 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 : n024.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 05:04:12 PM UTC 2026
% Result : Unsatisfiable 1.99s 1.86s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 47 unt; 0 nHn; 8 RR)
% Number of literals : 55 ( 54 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 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 : 77 ( 0 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(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/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/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(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/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(goals_14,negated_conjecture,
( join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
cnf(c_0_13,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_14,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_15,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_17,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_19,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_20,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_21,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_22,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_23,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_25,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_27,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_20]),c_0_24]) ).
cnf(c_0_28,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_30,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_31,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_33,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,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_32,c_0_27]),c_0_26]),c_0_28]),c_0_19]) ).
cnf(c_0_35,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_36,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_37,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
composition(converse(X1),join(converse(X2),converse(X3))) = join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_35]),c_0_36]),c_0_13]),c_0_13]),c_0_36]) ).
cnf(c_0_39,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
goals_14 ).
cnf(c_0_41,plain,
composition(X1,join(converse(X2),converse(X3))) = join(composition(X1,converse(X2)),composition(X1,converse(X3))),
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_42,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_19]),c_0_19]),c_0_30]) ).
cnf(c_0_44,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_30]) ).
cnf(c_0_45,plain,
composition(X1,join(converse(X2),X3)) = join(composition(X1,converse(X2)),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_16]) ).
cnf(c_0_46,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_16]) ).
cnf(c_0_49,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[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)],[c_0_47,c_0_48]),c_0_49]),c_0_46]),c_0_48]),c_0_49]),c_0_46]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : REL008-2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.07/0.27 % Computer : n024.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon May 4 20:40:12 EDT 2026
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % start to proof: theBenchmark
% 1.99/1.86 % Version : CSE_E---1.7
% 1.99/1.86 % Problem : theBenchmark.p
% 1.99/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.99/1.86 % SZS output start CNFRefutation
% See solution above
% 1.99/1.87 % Total time : 1.361s
%------------------------------------------------------------------------------