TSTP Solution File: NUM848+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM848+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:42:21 EDT 2023
% Result : Theorem 3.45s 1.85s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 26 unt; 10 typ; 0 def)
% Number of atoms : 42 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 307 ( 4 ~; 0 |; 4 &; 295 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd436_type,type,
vd436: $i ).
thf(vd437_type,type,
vd437: $i ).
thf(vd439_type,type,
vd439: $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(vskolem2_type,type,
vskolem2: $i > $i ).
thf(9,axiom,
( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
thf(33,plain,
( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(284, 438, 2)') ).
thf(45,plain,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,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(35,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)],[10]) ).
thf(1,conjecture,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 4)') ).
thf(2,negated_conjecture,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
!= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
!= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
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(23,plain,
! [A: $i,B: $i] :
( ( less @ A @ ( vplus @ B @ v1 ) )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,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(42,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)],[11]) ).
thf(5,axiom,
( ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 3)') ).
thf(25,plain,
( ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(20,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 1)') ).
thf(57,plain,
( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(284, 438, 1)') ).
thf(29,plain,
( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,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(59,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
thf(27,plain,
( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(50,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)],[14]) ).
thf(8,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 0)') ).
thf(31,plain,
( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(47,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(62,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(71,plain,
$false,
inference(e,[status(thm)],[33,45,35,18,23,42,25,20,57,29,59,27,50,31,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM848+2 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n005.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 17:10:39 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.02 % [INFO] Parsing done (136ms).
% 1.29/1.03 % [INFO] Running in sequential loop mode.
% 1.73/1.23 % [INFO] eprover registered as external prover.
% 1.73/1.23 % [INFO] cvc4 registered as external prover.
% 1.73/1.24 % [INFO] Scanning for conjecture ...
% 1.73/1.29 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.98/1.33 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.98/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 1.98/1.36 % [INFO] Type checking passed.
% 1.98/1.36 % [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 ...
% 3.45/1.85 % External prover 'e' found a proof!
% 3.45/1.85 % [INFO] Killing All external provers ...
% 3.45/1.85 % Time passed: 1332ms (effective reasoning time: 811ms)
% 3.45/1.85 % 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)>
% 3.45/1.85 % Axioms used in derivation (15): qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), holds(286, 441, 1), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(20, 0), 0), holds(285, 440, 0), ass(cond(33, 0), 0), ass(cond(61, 0), 0), ass(cond(241, 0), 0), ass(cond(43, 0), 0), holds(284, 438, 1), holds(286, 441, 3), holds(286, 441, 2), holds(284, 438, 2), holds(286, 441, 0), ass(cond(52, 0), 0)
% 3.45/1.85 % No. of inferences in proof: 34
% 3.45/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1332 ms resp. 811 ms w/o parsing
% 3.45/1.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.45/1.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------