TSTP Solution File: NUM854+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:42:23 EDT 2023
% Result : Theorem 3.36s 1.87s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 37
% Syntax : Number of formulae : 66 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 102 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 346 ( 26 ~; 20 |; 4 &; 274 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 110 !; 18 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd508_type,type,
vd508: $i ).
thf(vd511_type,type,
vd511: $i ).
thf(vd509_type,type,
vd509: $i ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(vd512_type,type,
vd512: $i ).
thf(v1_type,type,
v1: $i ).
thf(9,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(56,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(52,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
greater @ vd511 @ vd512,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).
thf(85,plain,
greater @ vd511 @ vd512,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( vmul @ A @ ( vsucc @ B ) )
= ( vplus @ ( vmul @ A @ B ) @ A ) )
& ( ( vmul @ A @ v1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(97,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)],[23]) ).
thf(6,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(41,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ B @ C )
=> ( greater @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ B @ C )
=> ( greater @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,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(86,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)],[21]) ).
thf(13,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(66,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
greater @ vd508 @ vd509,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
thf(112,plain,
greater @ vd508 @ vd509,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(72,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(104,plain,
! [A: $i] :
( ( vmul @ v1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,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(30,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( greater @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ B @ C )
=> ( less @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ B @ C )
=> ( less @ ( vmul @ B @ A ) @ ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vmul @ A @ B )
= ( vmul @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vmul @ A @ B )
= ( vmul @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ( greater @ ( vmul @ vd508 @ vd511 ) @ ( vmul @ vd509 @ vd511 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(74,plain,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,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(38,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)],[5]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(70,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(109,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( vmul @ B @ A )
= ( vmul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 1)') ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( vmul @ B @ A )
= ( vmul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,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(34,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)],[4]) ).
thf(7,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(45,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)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vmul @ A @ B ) @ ( vmul @ C @ B ) )
=> ( less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(81,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(116,plain,
$false,
inference(e,[status(thm)],[56,52,85,97,41,59,86,66,112,72,104,30,107,68,93,29,61,74,38,70,109,77,34,45,64,113,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.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 17:21:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.02 % [INFO] Parsing done (143ms).
% 1.28/1.03 % [INFO] Running in sequential loop mode.
% 1.74/1.22 % [INFO] eprover registered as external prover.
% 1.74/1.23 % [INFO] cvc4 registered as external prover.
% 1.74/1.23 % [INFO] Scanning for conjecture ...
% 1.74/1.28 % [INFO] Found a conjecture and 26 axioms. Running axiom selection ...
% 1.97/1.32 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 1.97/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 1.97/1.37 % [INFO] Type checking passed.
% 1.97/1.37 % [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 ...
% 3.36/1.87 % External prover 'e' found a proof!
% 3.36/1.87 % [INFO] Killing All external provers ...
% 3.36/1.87 % Time passed: 1351ms (effective reasoning time: 837ms)
% 3.36/1.87 % 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)>
% 3.36/1.87 % Axioms used in derivation (26): def(cond(conseq(axiom(3)), 11), 1), ass(cond(270, 0), 0), ass(cond(goal(88), 0), 2), ass(cond(147, 0), 0), ass(cond(conjunct1(307), 0), 0), ass(cond(281, 0), 0), ass(cond(253, 0), 0), ass(cond(290, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(conjunct2(conjunct2(307)), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(299, 0), 0), ass(cond(299, 0), 2), ass(cond(299, 0), 1), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), holds(conjunct1(314), 510, 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), ass(cond(goal(88), 0), 3), ass(cond(goal(88), 0), 0), holds(conjunct2(314), 513, 0), ass(cond(261, 0), 0), ass(cond(conjunct1(conjunct2(307)), 0), 0)
% 3.36/1.87 % No. of inferences in proof: 56
% 3.36/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1351 ms resp. 837 ms w/o parsing
% 3.77/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.77/1.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------