TSTP Solution File: GRP029-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP029-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:13:02 EDT 2023
% Result : Unsatisfiable 3.35s 1.83s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 39 ( 11 unt; 6 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 296 ( 42 ~; 40 |; 0 &; 214 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 94 ( 0 ^; 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(not_right_identity_type,type,
not_right_identity: $i > $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( inverse @ A ) @ ( inverse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( inverse @ A ) @ ( inverse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(29,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ A @ D )
| ( product @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( product @ ( not_right_identity @ A ) @ A @ ( not_right_identity @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
thf(17,plain,
! [A: $i] :
~ ( product @ ( not_right_identity @ A ) @ A @ ( not_right_identity @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ A @ C @ D )
| ( product @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(35,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(31,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(43,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ C @ A ) @ ( multiply @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ C @ A ) @ ( multiply @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(38,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( product @ C @ D @ A )
| ( product @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(30,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[25,29,41,17,27,39,35,31,43,23,38,21,33,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP029-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n016.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 02:26:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.06 % [INFO] Parsing done (135ms).
% 1.43/1.07 % [INFO] Running in sequential loop mode.
% 1.85/1.28 % [INFO] eprover registered as external prover.
% 1.85/1.28 % [INFO] cvc4 registered as external prover.
% 1.85/1.28 % [INFO] Scanning for conjecture ...
% 1.85/1.34 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 2.12/1.37 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.12/1.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.12/1.39 % [INFO] Type checking passed.
% 2.12/1.40 % [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 ...
% 3.35/1.83 % External prover 'e' found a proof!
% 3.35/1.83 % [INFO] Killing All external provers ...
% 3.35/1.83 % Time passed: 1282ms (effective reasoning time: 761ms)
% 3.35/1.83 % 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)>
% 3.35/1.83 % Axioms used in derivation (15): total_function1, product_substitution2, inverse_substitution, left_identity, left_inverse, reflexivity, associativity1, total_function2, symmetry, multiply_substitution1, product_substitution3, product_substitution1, multiply_substitution2, transitivity, associativity2
% 3.35/1.83 % No. of inferences in proof: 33
% 3.35/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1282 ms resp. 761 ms w/o parsing
% 3.45/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.45/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------