TSTP Solution File: NUM841+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:42:18 EDT 2023
% Result : Theorem 3.77s 2.02s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 36
% Syntax : Number of formulae : 64 ( 26 unt; 10 typ; 0 def)
% Number of atoms : 86 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 310 ( 12 ~; 8 |; 3 &; 266 @)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 91 ( 0 ^; 86 !; 5 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vd344_type,type,
vd344: $i ).
thf(vd347_type,type,
vd347: $i ).
thf(vd345_type,type,
vd345: $i ).
thf(vd348_type,type,
vd348: $i ).
thf(v1_type,type,
v1: $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(vskolem2_type,type,
vskolem2: $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(56,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
=> ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(96,plain,
! [A: $i] :
( ( vplus @ v1 @ A )
= ( vsucc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,axiom,
greater @ vd344 @ vd345,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).
thf(44,plain,
greater @ vd344 @ vd345,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(39,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(91,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd347 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(212, 350, 0)') ).
thf(63,plain,
greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd347 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,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(67,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)],[16]) ).
thf(26,axiom,
( ( vplus @ vd345 @ vd347 )
= ( vplus @ vd347 @ vd345 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 0)') ).
thf(99,plain,
( ( vplus @ vd345 @ vd347 )
= ( vplus @ vd347 @ vd345 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
greater @ vd347 @ vd348,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).
thf(55,plain,
greater @ vd347 @ vd348,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( vplus @ A @ C )
= ( vplus @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
( ( vplus @ vd348 @ vd345 )
= ( vplus @ vd345 @ vd348 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 2)') ).
thf(101,plain,
( ( vplus @ vd348 @ vd345 )
= ( vplus @ vd345 @ vd348 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( less @ A @ B )
=> ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( less @ A @ B )
=> ( less @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,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(93,plain,
! [A: $i,B: $i] :
( ( vplus @ ( vsucc @ A ) @ B )
= ( vsucc @ ( vplus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(78,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( vplus @ A @ C )
= ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(29,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( vsucc @ ( vskolem2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(214, 352, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ( greater @ ( vplus @ vd344 @ vd347 ) @ ( vplus @ vd345 @ vd348 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(70,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,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(32,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)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( greater @ B @ A )
<=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(45,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)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( vplus @ B @ A )
= ( vplus @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(72,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
greater @ ( vplus @ vd347 @ vd345 ) @ ( vplus @ vd348 @ vd345 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 1)') ).
thf(43,plain,
greater @ ( vplus @ vd347 @ vd345 ) @ ( vplus @ vd348 @ vd345 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(58,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(163,plain,
$false,
inference(cvc4,[status(thm)],[56,52,60,96,44,39,91,63,67,99,55,83,101,88,93,78,29,28,70,32,45,64,72,43,75,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n029.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 17:50:59 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.96 % [INFO] Parsing done (118ms).
% 1.16/0.97 % [INFO] Running in sequential loop mode.
% 1.60/1.22 % [INFO] eprover registered as external prover.
% 1.75/1.22 % [INFO] cvc4 registered as external prover.
% 1.75/1.23 % [INFO] Scanning for conjecture ...
% 1.90/1.29 % [INFO] Found a conjecture and 25 axioms. Running axiom selection ...
% 1.90/1.33 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.23/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.23/1.38 % [INFO] Type checking passed.
% 2.23/1.38 % [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 ...
% 3.77/2.02 % External prover 'cvc4' found a proof!
% 3.77/2.02 % [INFO] Killing All external provers ...
% 3.77/2.02 % Time passed: 1512ms (effective reasoning time: 1044ms)
% 3.77/2.02 % 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)>
% 3.77/2.02 % Axioms used in derivation (25): ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 2), def(cond(conseq(axiom(3)), 11), 1), holds(213, 351, 0), ass(cond(goal(130), 0), 0), ass(cond(goal(88), 0), 3), ass(cond(goal(202), 0), 2), ass(cond(goal(202), 0), 1), ass(cond(52, 0), 0), ass(cond(61, 0), 0), holds(conjunct1(211), 346, 0), ass(cond(140, 0), 0), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(147, 0), 0), ass(cond(20, 0), 0), holds(213, 351, 1), ass(cond(33, 0), 0), holds(213, 351, 2), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), holds(conjunct2(211), 349, 0), ass(cond(43, 0), 0), holds(212, 350, 0)
% 3.77/2.02 % No. of inferences in proof: 54
% 3.77/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1512 ms resp. 1044 ms w/o parsing
% 4.11/2.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.11/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------