TSTP Solution File: GRP201-1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRP201-1 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : Mon Jun 24 07:06:01 EDT 2024
% Result : Unsatisfiable 6.21s 2.53s
% Output : Refutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 30 ( 21 unt; 9 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 102 ( 2 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 ^ 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(identity_type,type,
identity: $i ).
thf(left_division_type,type,
left_division: $i > $i > $i ).
thf(right_division_type,type,
right_division: $i > $i > $i ).
thf(right_inverse_type,type,
right_inverse: $i > $i ).
thf(left_inverse_type,type,
left_inverse: $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( right_division @ ( multiply @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( right_division @ ( multiply @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(14,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( left_division @ A @ ( multiply @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( left_division @ A @ ( multiply @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( multiply @ ( left_inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(28,plain,
! [A: $i] :
( ( multiply @ ( left_inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( right_division @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( multiply @ ( right_division @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ ( left_division @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( left_division @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(16,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( multiply @ ( multiply @ ( multiply @ a @ b ) @ a ) @ c )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ a @ c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang3) ).
thf(11,plain,
( ( multiply @ ( multiply @ ( multiply @ a @ b ) @ a ) @ c )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ a @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( multiply @ A @ ( right_inverse @ A ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(26,plain,
! [A: $i] :
( ( multiply @ A @ ( right_inverse @ A ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ B )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ B )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(586,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,22,18,16,11,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP201-1 : TPTP v8.2.0. Released v2.2.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 20 07:13:55 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.01 % [INFO] Parsing done (99ms).
% 1.27/1.02 % [INFO] Running in sequential loop mode.
% 1.61/1.24 % [INFO] eprover registered as external prover.
% 1.70/1.24 % [INFO] Scanning for conjecture ...
% 1.70/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.70/1.31 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.70/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.70/1.33 % [INFO] Type checking passed.
% 1.70/1.33 % [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 ...
% 6.21/2.52 % External prover 'e' found a proof!
% 6.21/2.52 % [INFO] Killing All external provers ...
% 6.21/2.52 % Time passed: 2007ms (effective reasoning time: 1501ms)
% 6.21/2.53 % Axioms used in derivation (9): left_division_multiply, left_identity, right_division_multiply, multiply_left_division, left_inverse, moufang2, right_identity, right_inverse, multiply_right_division
% 6.21/2.53 % No. of inferences in proof: 21
% 6.21/2.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2007 ms resp. 1501 ms w/o parsing
% 6.66/2.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.66/2.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------