TSTP Solution File: GRP037-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP037-3 : 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 : n028.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 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 31 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
subgroup_member: $i > $o ).
tff(decl_27,type,
another_identity: $i ).
tff(decl_28,type,
another_inverse: $i > $i ).
tff(decl_29,type,
a: $i ).
cnf(product_right_cancellation,hypothesis,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(another_right_identity,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_right_identity) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(product_left_cancellation,hypothesis,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(another_left_inverse,hypothesis,
( product(another_inverse(X1),X1,another_identity)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_inverse) ).
cnf(prove_two_inverses_are_equal,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
cnf(c_0_8,hypothesis,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_9,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_10,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
another_right_identity ).
cnf(c_0_11,hypothesis,
subgroup_member(a),
a_is_in_subgroup ).
cnf(c_0_12,hypothesis,
( identity = X1
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,hypothesis,
product(a,another_identity,a),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_15,hypothesis,
identity = another_identity,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_17,plain,
product(inverse(X1),X1,another_identity),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
( product(another_inverse(X1),X1,another_identity)
| ~ subgroup_member(X1) ),
another_left_inverse ).
cnf(c_0_19,hypothesis,
( X1 = inverse(X2)
| ~ product(X1,X2,another_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
product(another_inverse(a),a,another_identity),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_21,negated_conjecture,
inverse(a) != another_inverse(a),
prove_two_inverses_are_equal ).
cnf(c_0_22,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 02:59:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.57 % Version : CSE_E---1.5
% 0.18/0.57 % Problem : theBenchmark.p
% 0.18/0.57 % Proof found
% 0.18/0.57 % SZS status Theorem for theBenchmark.p
% 0.18/0.57 % SZS output start Proof
% See solution above
% 0.18/0.58 % Total time : 0.013000 s
% 0.18/0.58 % SZS output end Proof
% 0.18/0.58 % Total time : 0.016000 s
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