TSTP Solution File: NUM845+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:42:19 EDT 2023
% Result : Theorem 3.51s 1.81s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 37 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 55 ( 54 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 480 ( 2 ~; 0 |; 4 &; 455 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(vd411_type,type,
vd411: $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(v1_type,type,
v1: $i ).
thf(11,axiom,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(46,plain,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 2)') ).
thf(28,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).
thf(22,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 3)') ).
thf(31,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vsucc @ ( vplus @ vd411 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
thf(43,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(58,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 5)') ).
thf(37,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 1)') ).
thf(25,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ vd411 @ ( vsucc @ A ) ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ vd411 ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 4)') ).
thf(34,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ A @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ A ) @ ( vplus @ ( vsucc @ vd411 ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ A ) )
= ( vplus @ ( vmul @ vd411 @ ( vsucc @ A ) ) @ ( vsucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 6)') ).
thf(40,plain,
! [A: $i] :
( ( ( vmul @ ( vsucc @ vd411 ) @ A )
= ( vplus @ ( vmul @ vd411 @ A ) @ A ) )
=> ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ A ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ A ) @ A ) @ ( vsucc @ vd411 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(55,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[46,61,28,22,48,31,43,58,37,25,34,64,17,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 17:22:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.02 % [INFO] Parsing done (141ms).
% 1.30/1.03 % [INFO] Running in sequential loop mode.
% 1.63/1.22 % [INFO] eprover registered as external prover.
% 1.79/1.22 % [INFO] cvc4 registered as external prover.
% 1.79/1.23 % [INFO] Scanning for conjecture ...
% 1.92/1.28 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.92/1.30 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.92/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.92/1.34 % [INFO] Type checking passed.
% 1.92/1.34 % [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 ...
% 3.31/1.80 % External prover 'e' found a proof!
% 3.31/1.80 % [INFO] Killing All external provers ...
% 3.31/1.80 % Time passed: 1285ms (effective reasoning time: 774ms)
% 3.31/1.80 % 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)>
% 3.51/1.80 % Axioms used in derivation (14): ass(cond(conseq(263), 1), 4), ass(cond(conseq(263), 1), 7), ass(cond(conseq(263), 1), 6), ass(cond(conseq(263), 1), 1), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(61, 0), 0), holds(264, 412, 2), ass(cond(conseq(263), 1), 3), ass(cond(43, 0), 0), ass(cond(conseq(263), 1), 5), ass(cond(conseq(263), 1), 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), ass(cond(conseq(263), 1), 2), ass(cond(33, 0), 0)
% 3.51/1.80 % No. of inferences in proof: 32
% 3.51/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1285 ms resp. 774 ms w/o parsing
% 3.51/1.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.51/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------