TSTP Solution File: GRP048-10 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRP048-10 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.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 07:05:19 EDT 2024
% Result : Unsatisfiable 13.87s 3.88s
% Output : Refutation 13.87s
% 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 : 206 ( 2 ~; 0 |; 0 &; 204 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 54 ( 0 ^ 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_type,type,
equalish: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(true_type,type,
true: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(product_type,type,
product: $i > $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ B @ E ) @ true @ ( ifeq @ ( product @ F @ D @ A ) @ true @ ( product @ F @ E @ C ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(24,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ B @ E ) @ true @ ( ifeq @ ( product @ F @ D @ A ) @ true @ ( product @ F @ E @ C ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( equalish @ A @ B ) @ true @ ( ifeq @ ( product @ C @ D @ A ) @ true @ ( product @ C @ D @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( equalish @ A @ B ) @ true @ ( ifeq @ ( product @ C @ D @ A ) @ true @ ( product @ C @ D @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ A @ B @ D ) @ true @ ( equalish @ D @ C ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ A @ B @ D ) @ true @ ( equalish @ D @ C ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( product @ ( inverse @ A ) @ A @ identity )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(18,plain,
! [A: $i] :
( ( product @ ( inverse @ A ) @ A @ identity )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( product @ identity @ A @ A )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(16,plain,
! [A: $i] :
( ( product @ identity @ A @ A )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( equalish @ ( inverse @ a ) @ ( inverse @ b ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
thf(11,plain,
( ( equalish @ ( inverse @ a ) @ ( inverse @ b ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ C @ E ) @ true @ ( ifeq @ ( product @ D @ A @ F ) @ true @ ( product @ F @ B @ E ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(26,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ C @ E ) @ true @ ( ifeq @ ( product @ D @ A @ F ) @ true @ ( product @ F @ B @ E ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
( ( equalish @ a @ b )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
thf(30,plain,
( ( equalish @ a @ b )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2820,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,22,18,16,11,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP048-10 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 07:24:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (103ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.58/1.18 % [INFO] eprover registered as external prover.
% 1.68/1.18 % [INFO] Scanning for conjecture ...
% 1.68/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.82/1.25 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.89/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.27 % [INFO] Type checking passed.
% 1.89/1.27 % [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 ...
% 13.87/3.88 % External prover 'e' found a proof!
% 13.87/3.88 % [INFO] Killing All external provers ...
% 13.87/3.88 % Time passed: 3358ms (effective reasoning time: 2907ms)
% 13.87/3.88 % Axioms used in derivation (9): total_function1, a_equals_b, ifeq_axiom, left_identity, product_substitution3, left_inverse, associativity1, total_function2, associativity2
% 13.87/3.88 % No. of inferences in proof: 21
% 13.87/3.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3358 ms resp. 2907 ms w/o parsing
% 13.87/3.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.87/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------