TSTP Solution File: REL031-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : REL031-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Thu Aug 31 13:36:16 EDT 2023
% Result : Unsatisfiable 1.81s 1.92s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 39 unt; 10 typ; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% 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 : 54 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
join: ( $i * $i ) > $i ).
tff(decl_23,type,
complement: $i > $i ).
tff(decl_24,type,
meet: ( $i * $i ) > $i ).
tff(decl_25,type,
composition: ( $i * $i ) > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
converse: $i > $i ).
tff(decl_28,type,
top: $i ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
sk1: $i ).
tff(decl_31,type,
sk2: $i ).
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(goals_18,negated_conjecture,
join(composition(converse(sk2),sk2),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
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(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(goals_17,negated_conjecture,
join(composition(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
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(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(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(goals_19,negated_conjecture,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
cnf(c_0_11,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_12,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_13,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_15,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12]) ).
cnf(c_0_16,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
join(composition(converse(sk2),sk2),one) = one,
goals_18 ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_19,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_20,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
join(composition(converse(sk1),sk1),one) = one,
goals_17 ).
cnf(c_0_22,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_23,negated_conjecture,
join(one,composition(converse(sk2),sk2)) = one,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_25,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
join(one,composition(converse(sk1),sk1)) = one,
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_28,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_29,negated_conjecture,
join(one,join(composition(converse(sk2),sk2),X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_31,negated_conjecture,
join(X1,composition(converse(sk1),composition(sk1,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_20]) ).
cnf(c_0_32,plain,
converse(composition(X1,composition(X2,converse(X3)))) = composition(X3,converse(composition(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_28]),c_0_27]),c_0_11]) ).
cnf(c_0_33,negated_conjecture,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
goals_19 ).
cnf(c_0_34,negated_conjecture,
join(one,composition(join(converse(sk2),X1),sk2)) = join(one,composition(X1,sk2)),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
join(X1,composition(X1,composition(converse(sk1),sk1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_12]),c_0_32]),c_0_13]) ).
cnf(c_0_36,plain,
composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_37,negated_conjecture,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) != one,
inference(rw,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_23]),c_0_36]),c_0_27]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL031-2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 20:19:12 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.49/0.57 start to proof: theBenchmark
% 1.81/1.92 % Version : CSE_E---1.5
% 1.81/1.92 % Problem : theBenchmark.p
% 1.81/1.92 % Proof found
% 1.81/1.92 % SZS status Theorem for theBenchmark.p
% 1.81/1.92 % SZS output start Proof
% See solution above
% 1.81/1.92 % Total time : 1.337000 s
% 1.81/1.92 % SZS output end Proof
% 1.81/1.92 % Total time : 1.340000 s
%------------------------------------------------------------------------------