TSTP Solution File: GRP667+6 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP667+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:15:05 EDT 2023
% Result : Theorem 36.38s 6.47s
% Output : Refutation 36.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 19 unt; 5 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 251 ( 2 ~; 9 |; 0 &; 240 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% 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(unit_type,type,
unit: $i ).
thf(f_type,type,
f: $i > $i ).
thf(11,axiom,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
thf(45,plain,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ! [A: $i,B: $i,C: $i] :
( ( mult @ C @ ( mult @ A @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ C @ A ) @ C ) @ B ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ C @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ C ) @ B ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ C @ ( mult @ A @ B ) ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ C @ ( mult @ ( mult @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i,C: $i] :
( ( mult @ C @ ( mult @ A @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ C @ A ) @ C ) @ B ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ C @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ C ) @ B ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ C @ ( mult @ A @ B ) ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ C @ ( mult @ ( mult @ A @ B ) @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( mult @ C @ ( mult @ A @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ C @ A ) @ C ) @ B ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ C @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ C ) @ B ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ ( mult @ C @ ( mult @ A @ B ) ) @ C ) )
| ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ A ) @ ( mult @ B @ C ) )
= ( mult @ C @ ( mult @ ( mult @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(33,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(36,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13807,plain,
$false,
inference(e,[status(thm)],[45,27,12,39,42,24,21,33,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP667+6 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n021.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 02:05:13 EDT 2023
% 0.16/0.38 % CPUTime :
% 1.03/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.06 % [INFO] Parsing done (137ms).
% 1.31/1.07 % [INFO] Running in sequential loop mode.
% 1.69/1.27 % [INFO] eprover registered as external prover.
% 1.69/1.27 % [INFO] cvc4 registered as external prover.
% 1.69/1.27 % [INFO] Scanning for conjecture ...
% 1.91/1.33 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.91/1.36 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.91/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.37 % [INFO] Type checking passed.
% 2.13/1.38 % [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 ...
% 36.38/6.47 % External prover 'e' found a proof!
% 36.38/6.47 % [INFO] Killing All external provers ...
% 36.38/6.47 % Time passed: 5931ms (effective reasoning time: 5403ms)
% 36.38/6.47 % 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)>
% 36.38/6.47 % Axioms used in derivation (9): f08, f03, f02, f07, f06, f05, f01, f04, f09
% 36.38/6.47 % No. of inferences in proof: 22
% 36.38/6.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5931 ms resp. 5403 ms w/o parsing
% 36.38/6.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.38/6.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------