TSTP Solution File: GRP302-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP302-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:13:39 EDT 2023
% Result : Unsatisfiable 3.65s 1.83s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 40
% Syntax : Number of formulae : 70 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 127 ( 126 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 288 ( 22 ~; 68 |; 0 &; 198 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(sk_c8_type,type,
sk_c8: $i ).
thf(sk_c7_type,type,
sk_c7: $i ).
thf(sk_c6_type,type,
sk_c6: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(sk_c1_type,type,
sk_c1: $i ).
thf(sk_c3_type,type,
sk_c3: $i ).
thf(sk_c5_type,type,
sk_c5: $i ).
thf(sk_c4_type,type,
sk_c4: $i ).
thf(sk_c2_type,type,
sk_c2: $i ).
thf(identity_type,type,
identity: $i ).
thf(16,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
thf(46,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
thf(53,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(22,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
thf(41,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
thf(44,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
thf(39,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(108,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
thf(35,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(8,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
thf(48,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
thf(43,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
thf(47,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
thf(42,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
thf(37,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
thf(52,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(110,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
thf(38,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
thf(33,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
thf(45,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
thf(32,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,negated_conjecture,
( ( multiply @ sk_c8 @ sk_c7 )
= sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
thf(34,plain,
( ( multiply @ sk_c8 @ sk_c7 )
= sk_c6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(26,negated_conjecture,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ sk_c8 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ A )
!= sk_c8 )
| ( ( multiply @ A @ sk_c7 )
!= sk_c8 )
| ( ( multiply @ B @ sk_c8 )
!= sk_c6 )
| ( ( inverse @ B )
!= sk_c8 )
| ( ( inverse @ sk_c8 )
!= sk_c7 )
| ( ( inverse @ C )
!= sk_c8 )
| ( ( multiply @ C @ sk_c7 )
!= sk_c8 )
| ( ( inverse @ D )
!= E )
| ( ( inverse @ E )
!= sk_c8 )
| ( ( multiply @ D @ sk_c8 )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ sk_c8 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ A )
!= sk_c8 )
| ( ( multiply @ A @ sk_c7 )
!= sk_c8 )
| ( ( multiply @ B @ sk_c8 )
!= sk_c6 )
| ( ( inverse @ B )
!= sk_c8 )
| ( ( inverse @ sk_c8 )
!= sk_c7 )
| ( ( inverse @ C )
!= sk_c8 )
| ( ( multiply @ C @ sk_c7 )
!= sk_c8 )
| ( ( inverse @ D )
!= E )
| ( ( inverse @ E )
!= sk_c8 )
| ( ( multiply @ D @ sk_c8 )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
thf(49,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c8 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
thf(50,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
thf(31,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c8 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
thf(40,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
thf(55,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
thf(36,plain,
( ( ( inverse @ sk_c2 )
= sk_c8 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
thf(30,plain,
( ( ( inverse @ sk_c1 )
= sk_c8 )
| ( ( inverse @ sk_c5 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
thf(51,plain,
( ( ( multiply @ sk_c2 @ sk_c8 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[46,53,41,44,39,108,35,112,48,43,47,42,37,52,110,38,33,45,32,34,54,49,50,31,40,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP302-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n031.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Fri May 19 02:05:27 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (123ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.60/1.18 % [INFO] eprover registered as external prover.
% 1.60/1.18 % [INFO] cvc4 registered as external prover.
% 1.77/1.18 % [INFO] Scanning for conjecture ...
% 1.91/1.26 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.91/1.30 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.91/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.31 % [INFO] Type checking passed.
% 2.18/1.31 % [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 ...
% 3.65/1.83 % External prover 'e' found a proof!
% 3.65/1.83 % [INFO] Killing All external provers ...
% 3.65/1.83 % Time passed: 1299ms (effective reasoning time: 844ms)
% 3.65/1.83 % 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)>
% 3.65/1.83 % Axioms used in derivation (3): left_identity, associativity, left_inverse
% 3.65/1.83 % No. of inferences in proof: 59
% 3.65/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1299 ms resp. 844 ms w/o parsing
% 3.65/1.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------