TSTP Solution File: GRP751-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP751-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:15:19 EDT 2023
% Result : Unsatisfiable 9.44s 2.73s
% Output : Refutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 23 ( 17 unt; 6 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 138 ( 2 ~; 0 |; 0 &; 136 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ C ) )
= ( mult @ ( mult @ A @ C ) @ ( mult @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ C ) )
= ( mult @ ( mult @ A @ C ) @ ( mult @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( mult @ A @ A ) ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ A @ B ) @ ( mult @ ( mult @ A @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( mult @ A @ A ) ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ A @ B ) @ ( mult @ ( mult @ A @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( mult @ a @ ( mult @ b @ c ) )
!= ( mult @ ( mult @ ( rd @ a @ a ) @ b ) @ ( mult @ a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(9,plain,
( ( mult @ a @ ( mult @ b @ c ) )
!= ( mult @ ( mult @ ( rd @ a @ a ) @ b ) @ ( mult @ a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ A ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ A ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1542,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,22,12,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP751-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:01:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (104ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.47/1.14 % [INFO] eprover registered as external prover.
% 1.47/1.15 % [INFO] cvc4 registered as external prover.
% 1.47/1.15 % [INFO] Scanning for conjecture ...
% 1.68/1.20 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.75/1.22 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.75/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.23 % [INFO] Type checking passed.
% 1.84/1.23 % [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 ...
% 9.44/2.73 % External prover 'e' found a proof!
% 9.44/2.73 % [INFO] Killing All external provers ...
% 9.44/2.73 % Time passed: 2210ms (effective reasoning time: 1769ms)
% 9.44/2.73 % 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)>
% 9.44/2.73 % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 9.44/2.73 % No. of inferences in proof: 17
% 9.44/2.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2210 ms resp. 1769 ms w/o parsing
% 9.44/2.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.44/2.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------