TSTP Solution File: GRP039-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 00:13:46 EDT 2023
% Result : Unsatisfiable 0.42s 0.61s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 66 ( 41 unt; 9 typ; 0 def)
% Number of atoms : 87 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 26 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
subgroup_member: $i > $o ).
tff(decl_26,type,
element_in_O2: ( $i * $i ) > $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
c: $i ).
tff(decl_30,type,
d: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(a_times_c_is_d,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(closure_of_multiply,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
cnf(b_in_O2,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
cnf(prove_d_in_O2,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
cnf(property_of_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| multiply(X1,element_in_O2(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_14,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_15,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_16,negated_conjecture,
multiply(a,c) = d,
a_times_c_is_d ).
cnf(c_0_17,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_18,negated_conjecture,
multiply(b,inverse(a)) = c,
b_times_a_inverse_is_c ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_21,negated_conjecture,
multiply(a,multiply(c,X1)) = multiply(d,X1),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
multiply(b,multiply(inverse(a),X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
multiply(inverse(a),d) = c,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_25,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
multiply(d,multiply(X1,inverse(multiply(c,X1)))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
cnf(c_0_27,negated_conjecture,
multiply(c,d) = multiply(b,c),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
multiply(d,inverse(c)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_20]) ).
cnf(c_0_29,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
closure_of_multiply ).
cnf(c_0_30,negated_conjecture,
multiply(c,a) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_20]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
multiply(d,multiply(d,inverse(multiply(b,c)))) = a,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
multiply(inverse(d),a) = inverse(c),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_33,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
subgroup_member(b),
b_in_O2 ).
cnf(c_0_35,negated_conjecture,
~ subgroup_member(d),
prove_d_in_O2 ).
cnf(c_0_36,negated_conjecture,
multiply(c,multiply(a,inverse(b))) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
multiply(d,inverse(multiply(b,c))) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_31]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_34])]) ).
cnf(c_0_39,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_40,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_16]),c_0_35]) ).
cnf(c_0_41,plain,
( subgroup_member(multiply(X1,multiply(X2,X3)))
| ~ subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_13]) ).
cnf(c_0_42,negated_conjecture,
multiply(inverse(d),multiply(a,X1)) = multiply(inverse(c),X1),
inference(spm,[status(thm)],[c_0_13,c_0_32]) ).
cnf(c_0_43,negated_conjecture,
multiply(a,inverse(b)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_36]),c_0_20]) ).
cnf(c_0_44,negated_conjecture,
multiply(inverse(d),inverse(c)) = inverse(multiply(b,c)),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_45,plain,
( subgroup_member(X1)
| ~ subgroup_member(multiply(X2,X1))
| ~ subgroup_member(inverse(X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_46,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_47,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| multiply(X1,element_in_O2(X1,X2)) = X2 ),
property_of_O2 ).
cnf(c_0_48,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_49,plain,
( subgroup_member(X1)
| ~ subgroup_member(multiply(X1,X2))
| ~ subgroup_member(inverse(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_17]),c_0_20]) ).
cnf(c_0_50,negated_conjecture,
multiply(inverse(c),inverse(b)) = inverse(multiply(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_51,negated_conjecture,
~ subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_34])]),c_0_46]) ).
cnf(c_0_52,plain,
( subgroup_member(multiply(X1,X2))
| subgroup_member(X3)
| subgroup_member(X2)
| ~ subgroup_member(multiply(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
~ subgroup_member(inverse(multiply(b,c))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_25]),c_0_34])]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( subgroup_member(multiply(c,X1))
| subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_34])]),c_0_46]) ).
cnf(c_0_55,negated_conjecture,
~ subgroup_member(multiply(b,c)),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_27]),c_0_55]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:45:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.42/0.61 % Version : CSE_E---1.5
% 0.42/0.61 % Problem : theBenchmark.p
% 0.42/0.61 % Proof found
% 0.42/0.61 % SZS status Theorem for theBenchmark.p
% 0.42/0.61 % SZS output start Proof
% See solution above
% 0.42/0.61 % Total time : 0.019000 s
% 0.42/0.61 % SZS output end Proof
% 0.42/0.61 % Total time : 0.022000 s
%------------------------------------------------------------------------------