TSTP Solution File: GRP683+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:15:08 EDT 2023
% Result : Theorem 2.90s 1.77s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 21 ( 15 unt; 3 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 189 ( 2 ~; 0 |; 3 &; 184 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
= ( mult @ A @ C ) )
& ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
= ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
= ( mult @ A @ C ) )
& ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
= ( mult @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
= ( mult @ A @ C ) )
& ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
= ( mult @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( ld @ A @ ( mult @ A @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(14,plain,
! [A: $i] :
( ( ld @ A @ ( mult @ A @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= ( ld @ B @ ( mult @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= ( ld @ B @ ( mult @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( rd @ ( mult @ ( mult @ D @ C ) @ ( rd @ B @ A ) ) @ ( rd @ B @ A ) )
= ( mult @ D @ ( rd @ ( mult @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(29,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( rd @ ( mult @ ( mult @ D @ C ) @ ( rd @ B @ A ) ) @ ( rd @ B @ A ) )
= ( mult @ D @ ( rd @ ( mult @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ ( ld @ A @ A ) ) )
= ( rd @ ( mult @ ( rd @ B @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ ( ld @ A @ A ) ) )
= ( rd @ ( mult @ ( rd @ B @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( rd @ ( mult @ A @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(17,plain,
! [A: $i] :
( ( rd @ ( mult @ A @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ld @ ( ld @ D @ C ) @ ( mult @ ( ld @ D @ C ) @ ( mult @ B @ A ) ) )
= ( mult @ ( ld @ D @ ( mult @ D @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(26,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ld @ ( ld @ D @ C ) @ ( mult @ ( ld @ D @ C ) @ ( mult @ B @ A ) ) )
= ( mult @ ( ld @ D @ ( mult @ D @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= ( rd @ ( mult @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= ( rd @ ( mult @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,plain,
$false,
inference(e,[status(thm)],[10,14,20,29,32,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n009.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % 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 01:35:33 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/0.98 % [INFO] Parsing done (115ms).
% 1.12/0.99 % [INFO] Running in sequential loop mode.
% 1.63/1.20 % [INFO] eprover registered as external prover.
% 1.63/1.20 % [INFO] cvc4 registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.80/1.26 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.80/1.28 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.80/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.80/1.30 % [INFO] Type checking passed.
% 1.80/1.31 % [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 ...
% 2.90/1.77 % External prover 'e' found a proof!
% 2.90/1.77 % [INFO] Killing All external provers ...
% 2.90/1.77 % Time passed: 1231ms (effective reasoning time: 774ms)
% 2.90/1.77 % 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)>
% 2.90/1.77 % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 2.90/1.77 % No. of inferences in proof: 18
% 2.90/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1231 ms resp. 774 ms w/o parsing
% 3.36/1.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.36/1.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------