TSTP Solution File: NUM844+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM844+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 3.29s 1.72s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of formulae : 53 ( 30 unt; 11 typ; 0 def)
% Number of atoms : 54 ( 45 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 298 ( 10 ~; 0 |; 4 &; 276 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd411_type,type,
vd411: $i ).
thf(vd413_type,type,
vd413: $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(v1_type,type,
v1: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(14,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(60,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)],[14]) ).
thf(7,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(33,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)],[7]) ).
thf(16,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(65,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,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(53,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)],[13]) ).
thf(20,axiom,
( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 1)') ).
thf(77,plain,
( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ vd413 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 0)') ).
thf(49,plain,
( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ vd413 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ vd413 )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(265, 414, 0)') ).
thf(63,plain,
( ( vmul @ ( vsucc @ vd411 ) @ vd413 )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 0)') ).
thf(31,plain,
( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(72,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(40,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( geq @ A @ ( vplus @ B @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 2)') ).
thf(75,plain,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(51,plain,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(79,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(68,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(42,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(24,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(46,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 1)') ).
thf(29,plain,
( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 3)') ).
thf(2,negated_conjecture,
( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
!= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
!= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(27,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(82,plain,
$false,
inference(e,[status(thm)],[60,33,65,53,77,49,63,31,72,40,75,51,79,68,42,24,46,29,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM844+2 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 16:30:18 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (128ms).
% 1.24/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.18 % [INFO] eprover registered as external prover.
% 1.71/1.18 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.87/1.28 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.87/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.31 % [INFO] Type checking passed.
% 1.87/1.31 % [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 ...
% 3.29/1.72 % External prover 'e' found a proof!
% 3.29/1.72 % [INFO] Killing All external provers ...
% 3.29/1.72 % Time passed: 1215ms (effective reasoning time: 747ms)
% 3.29/1.72 % 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)>
% 3.29/1.72 % Axioms used in derivation (19): ass(cond(6, 0), 0), holds(266, 415, 2), holds(265, 414, 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), holds(266, 415, 0), ass(cond(253, 0), 0), ass(cond(52, 0), 0), ass(cond(61, 0), 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(43, 0), 0), holds(266, 415, 1), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), holds(264, 412, 1), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), holds(264, 412, 2), holds(264, 412, 0)
% 3.29/1.72 % No. of inferences in proof: 42
% 3.29/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1215 ms resp. 747 ms w/o parsing
% 3.29/1.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.29/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------