TSTP Solution File: GRP101-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 : Fri May 19 11:13:09 EDT 2023
% Result : Unsatisfiable 3.07s 1.70s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 22 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 100 ( 8 ~; 6 |; 0 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(identity_type,type,
identity: $i ).
thf(a2_type,type,
a2: $i ).
thf(a3_type,type,
a3: $i ).
thf(b3_type,type,
b3: $i ).
thf(c3_type,type,
c3: $i ).
thf(a4_type,type,
a4: $i ).
thf(b4_type,type,
b4: $i ).
thf(double_divide_type,type,
double_divide: $i > $i > $i ).
thf(1,negated_conjecture,
( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(6,plain,
( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity )
| ( ( multiply @ identity @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ A @ ( double_divide @ ( double_divide @ B @ ( double_divide @ C @ A ) ) @ ( double_divide @ C @ identity ) ) ) @ ( double_divide @ identity @ identity ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ A @ ( double_divide @ ( double_divide @ B @ ( double_divide @ C @ A ) ) @ ( double_divide @ C @ identity ) ) ) @ ( double_divide @ identity @ identity ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( inverse @ A )
= ( double_divide @ A @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(13,plain,
! [A: $i] :
( ( inverse @ A )
= ( double_divide @ A @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( double_divide @ ( double_divide @ B @ A ) @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( double_divide @ ( double_divide @ B @ A ) @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( identity
= ( double_divide @ A @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(15,plain,
! [A: $i] :
( identity
= ( double_divide @ A @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 01:56:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.99 % [INFO] Parsing done (109ms).
% 1.11/0.99 % [INFO] Running in sequential loop mode.
% 1.66/1.20 % [INFO] eprover registered as external prover.
% 1.66/1.20 % [INFO] cvc4 registered as external prover.
% 1.66/1.20 % [INFO] Scanning for conjecture ...
% 1.83/1.26 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.83/1.28 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.83/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.29 % [INFO] Type checking passed.
% 1.83/1.29 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.07/1.70 % External prover 'e' found a proof!
% 3.07/1.70 % [INFO] Killing All external provers ...
% 3.07/1.70 % Time passed: 1162ms (effective reasoning time: 704ms)
% 3.07/1.70 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.07/1.70 % Axioms used in derivation (4): single_axiom, inverse, multiply, identity
% 3.07/1.70 % No. of inferences in proof: 11
% 3.07/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1162 ms resp. 704 ms w/o parsing
% 3.07/1.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.07/1.72 % [INFO] Killing All external provers ...
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