TSTP Solution File: GRP493-1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP493-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 May 20 21:04:08 EDT 2024
% Result : Unsatisfiable 158.71s 23.33s
% Output : Refutation 158.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 52 unt; 5 typ; 0 def)
% Number of atoms : 82 ( 81 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 548 ( 22 ~; 15 |; 0 &; 511 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 ^ 93 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(identity_type,type,
identity: $i ).
thf(double_divide_type,type,
double_divide: $i > $i > $i ).
thf(5,axiom,
! [A: $i] :
( identity
= ( double_divide @ A @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(15,plain,
! [A: $i] :
( identity
= ( double_divide @ A @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [A: $i] :
( ( double_divide @ A @ ( inverse @ A ) )
= identity ),
inference(lifteq,[status(thm)],[15]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( double_divide @ ( double_divide @ B @ A ) @ identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( double_divide @ ( double_divide @ B @ A ) @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ B @ A ) @ identity )
= ( multiply @ A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( inverse @ A )
= ( double_divide @ A @ identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(13,plain,
! [A: $i] :
( ( inverse @ A )
= ( double_divide @ A @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [A: $i] :
( ( double_divide @ A @ identity )
= ( inverse @ A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( inverse @ ( double_divide @ B @ A ) )
= ( multiply @ A @ B ) ),
inference(rewrite,[status(thm)],[12,14]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ B @ C )
= ( inverse @ identity ) )
| ( ( double_divide @ A @ ( inverse @ A ) )
!= ( double_divide @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,23]) ).
thf(27,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= ( inverse @ identity ) ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( D )),bind(B,$thf( inverse @ D )),bind(C,$thf( D ))]]) ).
thf(35,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= ( inverse @ identity ) ),
inference(simp,[status(thm)],[27]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( double_divide @ C @ ( multiply @ A @ B ) )
= identity )
| ( ( inverse @ ( double_divide @ B @ A ) )
!= ( inverse @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,16]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ A @ B ) @ ( multiply @ B @ A ) )
= identity ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( double_divide @ D @ E ))]]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ A @ B ) @ ( multiply @ B @ A ) )
= identity ),
inference(simp,[status(thm)],[25]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( double_divide @ B @ C ) @ ( inverse @ identity ) )
= identity )
| ( ( multiply @ ( inverse @ A ) @ A )
!= ( multiply @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,34]) ).
thf(234,plain,
! [A: $i] :
( ( double_divide @ ( double_divide @ A @ ( inverse @ A ) ) @ ( inverse @ identity ) )
= identity ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( inverse @ D ))]]) ).
thf(262,plain,
! [A: $i] :
( ( double_divide @ ( double_divide @ A @ ( inverse @ A ) ) @ ( inverse @ identity ) )
= identity ),
inference(simp,[status(thm)],[234]) ).
thf(442,plain,
( ( double_divide @ identity @ ( inverse @ identity ) )
= identity ),
inference(rewrite,[status(thm)],[262,16]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ ( double_divide @ B @ C ) @ ( double_divide @ identity @ identity ) ) @ ( double_divide @ A @ C ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ ( double_divide @ B @ C ) @ ( double_divide @ identity @ identity ) ) @ ( double_divide @ A @ C ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ ( double_divide @ B @ C ) @ ( double_divide @ identity @ identity ) ) @ ( double_divide @ A @ C ) ) )
= B ),
inference(lifteq,[status(thm)],[9]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ ( double_divide @ B @ C ) @ ( inverse @ identity ) ) @ ( double_divide @ A @ C ) ) )
= B ),
inference(rewrite,[status(thm)],[10,14]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ identity @ ( double_divide @ ( double_divide @ ( double_divide @ C @ D ) @ ( inverse @ identity ) ) @ ( double_divide @ B @ D ) ) )
= C )
| ( ( double_divide @ A @ ( inverse @ A ) )
!= ( double_divide @ identity @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,74]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( double_divide @ identity @ ( double_divide @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ identity ) ) @ ( double_divide @ ( inverse @ identity ) @ B ) ) )
= A ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( identity )),bind(B,$thf( inverse @ identity )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( double_divide @ identity @ ( double_divide @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ identity ) ) @ ( double_divide @ ( inverse @ identity ) @ B ) ) )
= A ),
inference(simp,[status(thm)],[96]) ).
thf(6353,plain,
! [B: $i,A: $i] :
( ( ( double_divide @ identity @ ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ ( inverse @ identity ) @ B ) ) )
= A )
| ( ( double_divide @ identity @ ( inverse @ identity ) )
!= ( double_divide @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[442,119]) ).
thf(6354,plain,
( ( double_divide @ identity @ ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[6353:[bind(A,$thf( identity )),bind(B,$thf( inverse @ identity ))]]) ).
thf(6674,plain,
( ( double_divide @ identity @ ( double_divide @ identity @ ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) ) ) )
= identity ),
inference(rewrite,[status(thm)],[6354,442]) ).
thf(6785,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ B )
= ( inverse @ identity ) )
| ( ( double_divide @ identity @ ( double_divide @ identity @ ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) ) ) )
!= ( double_divide @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6674,23]) ).
thf(6786,plain,
( ( multiply @ ( double_divide @ identity @ ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) ) ) @ identity )
= ( inverse @ identity ) ),
inference(pattern_uni,[status(thm)],[6785:[bind(A,$thf( double_divide @ identity @ ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) ) )),bind(B,$thf( identity ))]]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( double_divide @ identity @ B ) @ ( double_divide @ ( double_divide @ ( double_divide @ C @ D ) @ ( inverse @ identity ) ) @ identity ) )
= C )
| ( ( double_divide @ A @ ( inverse @ A ) )
!= ( double_divide @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,74]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ B ) @ ( double_divide @ ( double_divide @ ( double_divide @ A @ ( inverse @ B ) ) @ ( inverse @ identity ) ) @ identity ) )
= A ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( inverse @ E ))]]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ B ) @ ( double_divide @ ( double_divide @ ( double_divide @ A @ ( inverse @ B ) ) @ ( inverse @ identity ) ) @ identity ) )
= A ),
inference(simp,[status(thm)],[98]) ).
thf(7059,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ B ) @ ( inverse @ ( double_divide @ ( double_divide @ A @ ( inverse @ B ) ) @ ( inverse @ identity ) ) ) )
= A ),
inference(rewrite,[status(thm)],[120,14]) ).
thf(7272,plain,
! [B: $i,A: $i] :
( ( ( double_divide @ ( double_divide @ identity @ B ) @ ( inverse @ ( double_divide @ identity @ ( inverse @ identity ) ) ) )
= A )
| ( ( double_divide @ identity @ ( inverse @ identity ) )
!= ( double_divide @ A @ ( inverse @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[442,7059]) ).
thf(7273,plain,
( ( double_divide @ ( double_divide @ identity @ identity ) @ ( inverse @ ( double_divide @ identity @ ( inverse @ identity ) ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[7272:[bind(A,$thf( identity )),bind(B,$thf( identity ))]]) ).
thf(7737,plain,
( ( double_divide @ ( inverse @ identity ) @ ( inverse @ identity ) )
= identity ),
inference(rewrite,[status(thm)],[7273,442,14]) ).
thf(9351,plain,
( ( multiply @ ( double_divide @ identity @ identity ) @ identity )
= ( inverse @ identity ) ),
inference(rewrite,[status(thm)],[6786,7737]) ).
thf(9416,plain,
! [B: $i,A: $i] :
( ( ( inverse @ ( double_divide @ B @ A ) )
= ( inverse @ identity ) )
| ( ( multiply @ ( double_divide @ identity @ identity ) @ identity )
!= ( multiply @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9351,23]) ).
thf(9417,plain,
( ( inverse @ ( double_divide @ identity @ ( double_divide @ identity @ identity ) ) )
= ( inverse @ identity ) ),
inference(pattern_uni,[status(thm)],[9416:[bind(A,$thf( double_divide @ identity @ identity )),bind(B,$thf( identity ))]]) ).
thf(9821,plain,
( ( inverse @ ( double_divide @ identity @ ( inverse @ identity ) ) )
= ( inverse @ identity ) ),
inference(rewrite,[status(thm)],[9417,14]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( inverse @ A ) @ ( multiply @ C @ B ) )
= identity )
| ( ( double_divide @ A @ identity )
!= ( double_divide @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,34]) ).
thf(220,plain,
! [A: $i] :
( ( double_divide @ ( inverse @ A ) @ ( multiply @ identity @ A ) )
= identity ),
inference(pattern_uni,[status(thm)],[219:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( inverse @ ( inverse @ A ) )
= ( multiply @ B @ C ) )
| ( ( double_divide @ A @ identity )
!= ( double_divide @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,23]) ).
thf(32,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= ( inverse @ ( inverse @ A ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( identity )),bind(C,$thf( A ))]]) ).
thf(270,plain,
! [A: $i] :
( ( double_divide @ ( inverse @ A ) @ ( inverse @ ( inverse @ A ) ) )
= identity ),
inference(rewrite,[status(thm)],[220,32]) ).
thf(9871,plain,
! [A: $i] :
( ( ( double_divide @ ( inverse @ identity ) @ ( inverse @ ( inverse @ A ) ) )
= identity )
| ( ( inverse @ ( double_divide @ identity @ ( inverse @ identity ) ) )
!= ( inverse @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9821,270]) ).
thf(9872,plain,
( ( double_divide @ ( inverse @ identity ) @ ( inverse @ ( inverse @ ( double_divide @ identity @ ( inverse @ identity ) ) ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[9871:[bind(A,$thf( double_divide @ identity @ ( inverse @ identity ) ))]]) ).
thf(11298,plain,
( ( double_divide @ ( inverse @ identity ) @ ( inverse @ ( inverse @ identity ) ) )
= identity ),
inference(rewrite,[status(thm)],[9872,9821]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( double_divide @ ( double_divide @ identity @ B ) @ ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ B @ D ) ) )
= C )
| ( ( double_divide @ A @ ( inverse @ A ) )
!= ( double_divide @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,74]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ A @ ( inverse @ B ) ) ) )
= B ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( inverse @ E ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ A @ ( inverse @ B ) ) ) )
= B ),
inference(simp,[status(thm)],[102]) ).
thf(8208,plain,
! [B: $i,A: $i] :
( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ identity @ ( double_divide @ A @ ( inverse @ B ) ) ) )
= B ),
inference(rewrite,[status(thm)],[121,442]) ).
thf(11354,plain,
! [B: $i,A: $i] :
( ( ( double_divide @ ( double_divide @ identity @ A ) @ ( double_divide @ identity @ identity ) )
= B )
| ( ( double_divide @ ( inverse @ identity ) @ ( inverse @ ( inverse @ identity ) ) )
!= ( double_divide @ A @ ( inverse @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11298,8208]) ).
thf(11355,plain,
( ( double_divide @ ( double_divide @ identity @ ( inverse @ identity ) ) @ ( double_divide @ identity @ identity ) )
= ( inverse @ identity ) ),
inference(pattern_uni,[status(thm)],[11354:[bind(A,$thf( inverse @ identity )),bind(B,$thf( inverse @ identity ))]]) ).
thf(17812,plain,
( ( double_divide @ identity @ ( inverse @ identity ) )
= ( inverse @ identity ) ),
inference(rewrite,[status(thm)],[11355,442,14]) ).
thf(17816,plain,
( ( inverse @ identity )
= identity ),
inference(rewrite,[status(thm)],[442,17812]) ).
thf(1,negated_conjecture,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
thf(6,plain,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= identity ),
inference(lifteq,[status(thm)],[7]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( inverse @ ( double_divide @ B @ A ) )
!= identity )
| ( ( multiply @ A @ B )
!= ( multiply @ ( inverse @ a1 ) @ a1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,8]) ).
thf(30,plain,
( ( inverse @ ( double_divide @ a1 @ ( inverse @ a1 ) ) )
!= identity ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( inverse @ a1 )),bind(B,$thf( a1 ))]]) ).
thf(36,plain,
( ( inverse @ identity )
!= identity ),
inference(rewrite,[status(thm)],[30,16]) ).
thf(18290,plain,
$false,
inference(simplifyReflect,[status(thm)],[17816,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP493-1 : TPTP v8.2.0. Released v2.6.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 06:11:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.18/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.27 % [INFO] Parsing done (172ms).
% 1.51/1.29 % [INFO] Running in sequential loop mode.
% 2.21/1.74 % [INFO] nitpick registered as external prover.
% 2.21/1.75 % [INFO] Scanning for conjecture ...
% 2.41/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.41/1.88 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.41/1.89 % [INFO] Problem is propositional (TPTP CNF).
% 2.41/1.90 % [INFO] Type checking passed.
% 2.60/1.90 % [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 ...
% 158.71/23.31 % [INFO] Killing All external provers ...
% 158.71/23.32 % Time passed: 22779ms (effective reasoning time: 22023ms)
% 158.71/23.33 % Axioms used in derivation (4): identity, multiply, inverse, single_axiom
% 158.71/23.33 % No. of inferences in proof: 67
% 158.71/23.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22779 ms resp. 22023 ms w/o parsing
% 158.82/23.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 158.82/23.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------