TSTP Solution File: GRP292-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP292-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:13:38 EDT 2023
% Result : Unsatisfiable 3.52s 1.84s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of formulae : 59 ( 7 unt; 10 typ; 0 def)
% Number of atoms : 105 ( 104 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 264 ( 18 ~; 56 |; 0 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(sk_c7_type,type,
sk_c7: $i ).
thf(sk_c6_type,type,
sk_c6: $i ).
thf(sk_c5_type,type,
sk_c5: $i ).
thf(sk_c3_type,type,
sk_c3: $i ).
thf(sk_c4_type,type,
sk_c4: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(sk_c1_type,type,
sk_c1: $i ).
thf(sk_c2_type,type,
sk_c2: $i ).
thf(identity_type,type,
identity: $i ).
thf(22,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(89,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
thf(41,plain,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
thf(39,plain,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(91,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
thf(35,plain,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ sk_c7 @ sk_c6 )
!= sk_c5 )
| ( ( multiply @ A @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ A )
!= sk_c7 )
| ( ( multiply @ B @ sk_c5 )
!= sk_c6 )
| ( ( inverse @ B )
!= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
!= sk_c7 )
| ( ( multiply @ C @ D )
!= sk_c6 )
| ( ( inverse @ C )
!= D )
| ( ( multiply @ D @ sk_c5 )
!= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ sk_c7 @ sk_c6 )
!= sk_c5 )
| ( ( multiply @ A @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ A )
!= sk_c7 )
| ( ( multiply @ B @ sk_c5 )
!= sk_c6 )
| ( ( inverse @ B )
!= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
!= sk_c7 )
| ( ( multiply @ C @ D )
!= sk_c6 )
| ( ( inverse @ C )
!= D )
| ( ( multiply @ D @ sk_c5 )
!= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
thf(43,plain,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
thf(42,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
thf(37,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
thf(25,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(93,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)],[24]) ).
thf(1,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
thf(29,plain,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
thf(33,plain,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
thf(28,plain,
( ( ( inverse @ sk_c2 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
thf(38,plain,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
thf(45,plain,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
thf(32,plain,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c5 @ sk_c6 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
thf(34,plain,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
thf(44,plain,
( ( ( multiply @ sk_c7 @ sk_c6 )
= sk_c5 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
thf(27,plain,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
thf(40,plain,
( ( ( multiply @ sk_c2 @ sk_c5 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
thf(26,plain,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
thf(36,plain,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
thf(30,plain,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c4 )
= sk_c6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(101,plain,
$false,
inference(e,[status(thm)],[89,41,39,91,35,31,43,42,37,25,93,29,33,28,38,45,32,34,44,27,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP292-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.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 02:04:58 EDT 2023
% 0.17/0.38 % CPUTime :
% 1.00/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.04 % [INFO] Parsing done (144ms).
% 1.34/1.05 % [INFO] Running in sequential loop mode.
% 1.80/1.25 % [INFO] eprover registered as external prover.
% 1.80/1.25 % [INFO] cvc4 registered as external prover.
% 1.80/1.26 % [INFO] Scanning for conjecture ...
% 2.01/1.33 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 2.01/1.37 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.23/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.38 % [INFO] Type checking passed.
% 2.23/1.38 % [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 ...
% 3.52/1.84 % External prover 'e' found a proof!
% 3.52/1.84 % [INFO] Killing All external provers ...
% 3.52/1.84 % Time passed: 1303ms (effective reasoning time: 785ms)
% 3.52/1.84 % 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)>
% 3.52/1.84 % Axioms used in derivation (3): left_identity, left_inverse, associativity
% 3.52/1.84 % No. of inferences in proof: 49
% 3.52/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1303 ms resp. 785 ms w/o parsing
% 3.52/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------