TSTP Solution File: GRP697-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP697-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:15:10 EDT 2023
% Result : Unsatisfiable 55.52s 9.70s
% Output : Refutation 55.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 33 ( 25 unt; 8 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 146 ( 2 ~; 0 |; 0 &; 144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% 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(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(i_type,type,
i: $i > $i ).
thf(6,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(24,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
= ( i @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
= ( i @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( mult @ ( mult @ a @ b ) @ ( mult @ b @ ( mult @ c @ b ) ) )
!= ( mult @ ( mult @ a @ ( mult @ b @ ( mult @ b @ c ) ) ) @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(13,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ b @ ( mult @ c @ b ) ) )
!= ( mult @ ( mult @ a @ ( mult @ b @ ( mult @ b @ c ) ) ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(26,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
thf(34,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
thf(36,plain,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32922,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,22,18,16,26,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP697-1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n022.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 01:48:49 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/0.97 % [INFO] Parsing done (114ms).
% 1.28/0.98 % [INFO] Running in sequential loop mode.
% 1.75/1.19 % [INFO] eprover registered as external prover.
% 1.75/1.19 % [INFO] cvc4 registered as external prover.
% 1.75/1.20 % [INFO] Scanning for conjecture ...
% 1.91/1.25 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.91/1.27 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.91/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.29 % [INFO] Type checking passed.
% 1.91/1.29 % [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 ...
% 55.52/9.69 % External prover 'e' found a proof!
% 55.52/9.69 % [INFO] Killing All external provers ...
% 55.52/9.70 % Time passed: 9162ms (effective reasoning time: 8709ms)
% 55.52/9.70 % 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)>
% 55.52/9.70 % Axioms used in derivation (11): c05, c11, c08, c01, c03, c06, c02, c07, c10, c09, c04
% 55.52/9.70 % No. of inferences in proof: 25
% 55.52/9.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9162 ms resp. 8709 ms w/o parsing
% 55.52/9.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.52/9.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------