TSTP Solution File: GRP039-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP039-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 00:13:47 EDT 2023
% Result : Unsatisfiable 0.50s 1.00s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 30
% Syntax : Number of formulae : 101 ( 29 unt; 10 typ; 0 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 193 ( 93 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
subgroup_member: $i > $o ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
element_in_O2: ( $i * $i ) > $i ).
tff(decl_26,type,
inverse: $i > $i ).
tff(decl_27,type,
identity: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
a: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
d: $i ).
cnf(closure_of_product,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(product_right_cancellation,axiom,
( equalish(X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(well_defined,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(property_of_O2,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(subgroup_member_substitution,axiom,
( subgroup_member(X2)
| ~ equalish(X1,X2)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_substitution) ).
cnf(element_in_O2_substitution2,axiom,
( equalish(element_in_O2(X1,X3),element_in_O2(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_in_O2_substitution2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(element_in_O2_substitution1,axiom,
( equalish(element_in_O2(X3,X1),element_in_O2(X3,X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_in_O2_substitution1) ).
cnf(c_0_20,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
closure_of_product ).
cnf(c_0_21,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_22,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_23,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_24,negated_conjecture,
~ subgroup_member(d),
prove_d_is_in_subgroup ).
cnf(c_0_25,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_26,axiom,
( equalish(X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_27,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_28,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_29,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_30,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_23]),c_0_24]) ).
cnf(c_0_31,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
well_defined ).
cnf(c_0_32,negated_conjecture,
( product(a,c,X1)
| ~ equalish(d,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_33,plain,
( equalish(X1,X2)
| ~ product(inverse(X1),X2,identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_35,negated_conjecture,
( product(b,inverse(a),X1)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_36,negated_conjecture,
( equalish(c,X1)
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_37,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_38,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( equalish(X1,c)
| ~ product(b,inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_40,negated_conjecture,
( product(a,c,X1)
| ~ equalish(d,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_41,plain,
equalish(X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( product(b,inverse(a),X1)
| ~ equalish(c,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
equalish(c,element_in_O2(a,d)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_24]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( equalish(X1,c)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( product(a,c,X1)
| ~ equalish(inverse(inverse(d)),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_47,negated_conjecture,
( product(b,inverse(a),X1)
| ~ equalish(element_in_O2(a,d),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| equalish(element_in_O2(X1,X2),X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_49,axiom,
( subgroup_member(X2)
| ~ equalish(X1,X2)
| ~ subgroup_member(X1) ),
subgroup_member_substitution ).
cnf(c_0_50,negated_conjecture,
equalish(element_in_O2(a,d),c),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_51,axiom,
( equalish(element_in_O2(X1,X3),element_in_O2(X2,X3))
| ~ equalish(X1,X2) ),
element_in_O2_substitution2 ).
cnf(c_0_52,negated_conjecture,
( equalish(X1,d)
| ~ product(a,c,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_53,negated_conjecture,
product(a,c,inverse(inverse(inverse(inverse(d))))),
inference(spm,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_54,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_27]) ).
cnf(c_0_55,negated_conjecture,
( product(b,inverse(a),X1)
| ~ product(a,X1,d) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_38]),c_0_24]) ).
cnf(c_0_56,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,d,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_57,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_58,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_60,plain,
( subgroup_member(element_in_O2(X1,X2))
| ~ subgroup_member(element_in_O2(X3,X2))
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
equalish(inverse(inverse(inverse(inverse(d)))),d),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_63,negated_conjecture,
( product(X1,a,X2)
| ~ product(b,identity,X2)
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_65,plain,
( product(X1,inverse(X2),X3)
| ~ product(X4,identity,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_34]) ).
cnf(c_0_66,negated_conjecture,
( product(X1,c,d)
| ~ product(identity,a,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,negated_conjecture,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_24]),c_0_38]) ).
cnf(c_0_68,axiom,
( equalish(element_in_O2(X3,X1),element_in_O2(X3,X2))
| ~ equalish(X1,X2) ),
element_in_O2_substitution1 ).
cnf(c_0_69,plain,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X3)
| subgroup_member(X2)
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
~ subgroup_member(inverse(inverse(inverse(inverse(d))))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_24]) ).
cnf(c_0_71,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_72,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_57]) ).
cnf(c_0_73,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_57]) ).
cnf(c_0_74,negated_conjecture,
( product(X1,a,b)
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_75,plain,
( product(X1,inverse(X2),X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(identity,a,X1)
| ~ subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_66]),c_0_67])]),c_0_24]) ).
cnf(c_0_77,plain,
( subgroup_member(element_in_O2(X1,X2))
| ~ subgroup_member(element_in_O2(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( subgroup_member(element_in_O2(d,X1))
| subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_61]),c_0_70]) ).
cnf(c_0_79,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_81,negated_conjecture,
( product(inverse(X1),a,b)
| ~ product(d,X1,a) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( ~ subgroup_member(X1)
| ~ equalish(a,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_72]) ).
cnf(c_0_83,negated_conjecture,
( subgroup_member(element_in_O2(d,X1))
| subgroup_member(X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,plain,
equalish(inverse(inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_79,c_0_41]) ).
cnf(c_0_85,negated_conjecture,
( product(X1,b,a)
| ~ product(d,X1,a) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
~ subgroup_member(inverse(inverse(a))),
inference(spm,[status(thm)],[c_0_82,c_0_41]) ).
cnf(c_0_87,negated_conjecture,
( subgroup_member(inverse(inverse(X1)))
| subgroup_member(element_in_O2(d,X1)) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
product(element_in_O2(d,a),b,a),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_37]),c_0_38]),c_0_24]) ).
cnf(c_0_89,negated_conjecture,
subgroup_member(element_in_O2(d,a)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_88]),c_0_22]),c_0_89])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP039-6 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 01:38:25 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.50/1.00 % Version : CSE_E---1.5
% 0.50/1.00 % Problem : theBenchmark.p
% 0.50/1.00 % Proof found
% 0.50/1.00 % SZS status Theorem for theBenchmark.p
% 0.50/1.00 % SZS output start Proof
% See solution above
% 0.50/1.01 % Total time : 0.467000 s
% 0.50/1.01 % SZS output end Proof
% 0.50/1.01 % Total time : 0.469000 s
%------------------------------------------------------------------------------