TSTP Solution File: NUM837+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM837+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:42:17 EDT 2023
% Result : Theorem 3.59s 1.83s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 75 ( 22 unt; 11 typ; 0 def)
% Number of atoms : 124 ( 73 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 332 ( 42 ~; 26 |; 6 &; 230 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 129 ( 0 ^; 108 !; 21 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(vd269_type,type,
vd269: $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vd268_type,type,
vd268: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(less_type,type,
less: $i > $i > $o ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(v1_type,type,
v1: $i ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(vd271_type,type,
vd271: $i ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(120,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)],[24]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(117,plain,
! [A: $i,B: $i] :
( ( A = B )
| ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(65,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(53,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( vsucc @ A )
!= ( vsucc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(105,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(31,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(149,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ( vsucc @ A )
= ( vsucc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( geq @ B @ A )
<=> ( ( greater @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ( geq @ B @ A )
=> ( ( greater @ B @ A )
| ( B = A ) ) )
& ( ( ( greater @ B @ A )
| ( B = A ) )
=> ( geq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(108,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(63,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(127,plain,
! [A: $i,B: $i] :
( B
!= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(72,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ( vsucc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(75,plain,
! [A: $i] :
( ( vsucc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
less @ vd268 @ vd269,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(131,plain,
less @ vd268 @ vd269,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(17,axiom,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(90,plain,
! [A: $i] :
( ( vsucc @ A )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(69,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(101,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(32,axiom,
less @ vd269 @ vd271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(170), 272, 0)') ).
thf(152,plain,
less @ vd269 @ vd271,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(57,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( greater @ B @ A )
<=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( greater @ B @ A )
=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) )
& ( ? [C: $i] :
( B
= ( vplus @ A @ C ) )
=> ( greater @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(38,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
? [A: $i] :
( vd269
= ( vplus @ vd268 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(171)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( vd269
= ( vplus @ vd268 @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(33,plain,
~ ? [A: $i] :
( vd269
= ( vplus @ vd268 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(112,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( vplus @ C @ A )
!= ( vplus @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(123,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( leq @ B @ A )
<=> ( ( less @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( leq @ B @ A )
=> ( ( less @ B @ A )
| ( B = A ) ) )
& ( ( ( less @ B @ A )
| ( B = A ) )
=> ( leq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( less @ B @ A )
<=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( less @ B @ A )
=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( vplus @ B @ C ) )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(36,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(146,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(79,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( vplus @ A @ ( vsucc @ B ) )
= ( vsucc @ ( vplus @ A @ B ) ) )
& ( ( vplus @ A @ v1 )
= ( vsucc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(94,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)],[18]) ).
thf(153,plain,
$false,
inference(e,[status(thm)],[120,117,65,53,105,149,49,81,108,63,127,72,75,131,90,69,101,152,57,61,132,38,33,112,123,40,139,36,146,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM837+1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.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 17:35:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (126ms).
% 1.23/0.97 % [INFO] Running in sequential loop mode.
% 1.70/1.17 % [INFO] eprover registered as external prover.
% 1.70/1.18 % [INFO] cvc4 registered as external prover.
% 1.70/1.18 % [INFO] Scanning for conjecture ...
% 1.77/1.24 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 1.90/1.28 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.09/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.32 % [INFO] Type checking passed.
% 2.09/1.32 % [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 ...
% 3.59/1.83 % External prover 'e' found a proof!
% 3.59/1.83 % [INFO] Killing All external provers ...
% 3.59/1.83 % Time passed: 1310ms (effective reasoning time: 854ms)
% 3.59/1.83 % 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)>
% 3.59/1.83 % Axioms used in derivation (30): ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(goal(88), 0), 2), ass(cond(20, 0), 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(52, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(12, 0), 0), ass(cond(43, 0), 0), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), ass(cond(goal(88), 0), 1), holds(conjunct2(170), 272, 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), holds(conjunct1(170), 270, 0), ass(cond(goal(88), 0), 3), ass(cond(147, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(73, 0), 0), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), ass(cond(158, 0), 0), ass(cond(33, 0), 0), qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), ass(cond(61, 0), 0)
% 3.59/1.83 % No. of inferences in proof: 64
% 3.59/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1310 ms resp. 854 ms w/o parsing
% 3.76/1.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------