TSTP Solution File: NUM842+1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : NUM842+1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n019.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 : Mon Jun 24 13:06:34 EDT 2024
% Result : Theorem 73.39s 11.57s
% Output : Refutation 73.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 55 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 558 ( 50 ~; 67 |; 10 &; 412 @)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 113 ( 0 ^ 108 !; 5 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vd353_type,type,
vd353: $i ).
thf(vd355_type,type,
vd355: $i ).
thf(vd354_type,type,
vd354: $i ).
thf(vd356_type,type,
vd356: $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(sk6_type,type,
sk6: $i > $i > $i ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(149,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)],[31]) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ! [C: $i] : ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(miniscope,[status(thm)],[149]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(1,conjecture,
greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd356 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq(218), 361, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd356 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd356 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
( ( ( greater @ vd355 @ vd356 )
& ( geq @ vd353 @ vd354 ) )
| ( ( geq @ vd355 @ vd356 )
& ( greater @ vd353 @ vd354 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(antec(218))') ).
thf(110,plain,
( ( ( greater @ vd355 @ vd356 )
& ( geq @ vd353 @ vd354 ) )
| ( ( geq @ vd355 @ vd356 )
& ( greater @ vd353 @ vd354 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(111,plain,
( ( greater @ vd355 @ vd356 )
| ( geq @ vd355 @ vd356 ) ),
inference(cnf,[status(esa)],[110]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(49,plain,
! [A: $i,B: $i] :
( ( geq @ A @ B )
=> ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[49]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( greater @ vd355 @ vd356 )
| ( leq @ B @ A )
| ( ( geq @ vd355 @ vd356 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[111,50]) ).
thf(371,plain,
( ( greater @ vd355 @ vd356 )
| ( leq @ vd356 @ vd355 ) ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( vd355 )),bind(B,$thf( vd356 ))]]) ).
thf(6,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(51,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)],[6]) ).
thf(52,plain,
( ! [A: $i,B: $i] :
( ( leq @ B @ A )
=> ( ( less @ B @ A )
| ( B = A ) ) )
& ! [A: $i,B: $i] :
( ( ( less @ B @ A )
| ( B = A ) )
=> ( leq @ B @ A ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( leq @ B @ A )
| ( less @ B @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[52]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( leq @ B @ A )
| ( less @ B @ A ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(1177,plain,
! [B: $i,A: $i] :
( ( greater @ vd355 @ vd356 )
| ( B = A )
| ( less @ B @ A )
| ( ( leq @ vd356 @ vd355 )
!= ( leq @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[371,59]) ).
thf(1178,plain,
( ( greater @ vd355 @ vd356 )
| ( vd356 = vd355 )
| ( less @ vd356 @ vd355 ) ),
inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( vd355 )),bind(B,$thf( vd356 ))]]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(137,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( greater @ B @ A ) ),
inference(cnf,[status(esa)],[137]) ).
thf(5015,plain,
! [B: $i,A: $i] :
( ( greater @ vd355 @ vd356 )
| ( vd356 = vd355 )
| ( greater @ B @ A )
| ( ( less @ vd356 @ vd355 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1178,138]) ).
thf(5016,plain,
( ( greater @ vd355 @ vd356 )
| ( vd356 = vd355 )
| ( greater @ vd355 @ vd356 ) ),
inference(pattern_uni,[status(thm)],[5015:[bind(A,$thf( vd356 )),bind(B,$thf( vd355 ))]]) ).
thf(5037,plain,
( ( greater @ vd355 @ vd356 )
| ( vd356 = vd355 ) ),
inference(simp,[status(thm)],[5016]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greater @ C @ D )
& ( greater @ A @ B ) )
=> ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( greater @ A @ B )
| ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(10312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( greater @ C @ D )
| ~ ( greater @ A @ B )
| ( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ D ) )
!= ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd356 ) ) ) ),
inference(paramod_ordered,[status(thm)],[170,43]) ).
thf(10313,plain,
( ~ ( greater @ vd355 @ vd356 )
| ~ ( greater @ vd353 @ vd354 ) ),
inference(pattern_uni,[status(thm)],[10312:[bind(A,$thf( vd353 )),bind(B,$thf( vd354 )),bind(C,$thf( vd355 )),bind(D,$thf( vd356 ))]]) ).
thf(114,plain,
( ( geq @ vd353 @ vd354 )
| ( greater @ vd353 @ vd354 ) ),
inference(cnf,[status(esa)],[110]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ( greater @ vd353 @ vd354 )
| ( leq @ B @ A )
| ( ( geq @ vd353 @ vd354 )
!= ( geq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[114,50]) ).
thf(440,plain,
( ( greater @ vd353 @ vd354 )
| ( leq @ vd354 @ vd353 ) ),
inference(pattern_uni,[status(thm)],[439:[bind(A,$thf( vd353 )),bind(B,$thf( vd354 ))]]) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ( greater @ vd353 @ vd354 )
| ( B = A )
| ( less @ B @ A )
| ( ( leq @ vd354 @ vd353 )
!= ( leq @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[440,59]) ).
thf(1481,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 = vd353 )
| ( less @ vd354 @ vd353 ) ),
inference(pattern_uni,[status(thm)],[1480:[bind(A,$thf( vd353 )),bind(B,$thf( vd354 ))]]) ).
thf(5027,plain,
! [B: $i,A: $i] :
( ( greater @ vd353 @ vd354 )
| ( vd354 = vd353 )
| ( greater @ B @ A )
| ( ( less @ vd354 @ vd353 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1481,138]) ).
thf(5028,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 = vd353 )
| ( greater @ vd353 @ vd354 ) ),
inference(pattern_uni,[status(thm)],[5027:[bind(A,$thf( vd354 )),bind(B,$thf( vd353 ))]]) ).
thf(5034,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 = vd353 ) ),
inference(simp,[status(thm)],[5028]) ).
thf(112,plain,
( ( greater @ vd355 @ vd356 )
| ( greater @ vd353 @ vd354 ) ),
inference(cnf,[status(esa)],[110]) ).
thf(30,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(142,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)],[30]) ).
thf(143,plain,
( ! [A: $i,B: $i] :
( ( greater @ B @ A )
=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( vplus @ A @ C ) )
=> ( greater @ B @ A ) ) ),
inference(miniscope,[status(thm)],[142]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( greater @ B @ A )
| ( B
= ( vplus @ A @ ( sk6 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ ( sk6 @ B @ A ) )
= B )
| ~ ( greater @ B @ A ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(121,plain,
! [A: $i,B: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(122,plain,
! [B: $i,A: $i] : ( greater @ ( vplus @ A @ B ) @ A ),
inference(cnf,[status(esa)],[121]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( greater @ ( vplus @ A @ B ) @ A )
!= ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd356 ) ) ),
inference(paramod_ordered,[status(thm)],[122,43]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( vplus @ A @ B )
!= ( vplus @ vd353 @ vd355 ) )
| ( A
!= ( vplus @ vd354 @ vd356 ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(311,plain,
! [A: $i] :
( ( vplus @ ( vplus @ vd354 @ vd356 ) @ A )
!= ( vplus @ vd353 @ vd355 ) ),
inference(simp,[status(thm)],[307]) ).
thf(22,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(118,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)],[22]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( vplus @ ( vplus @ A @ B ) @ C )
= ( vplus @ A @ ( vplus @ B @ C ) ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(4118,plain,
! [A: $i] :
( ( vplus @ vd354 @ ( vplus @ vd356 @ A ) )
!= ( vplus @ vd353 @ vd355 ) ),
inference(rewrite,[status(thm)],[311,120]) ).
thf(4354,plain,
! [A: $i] :
( ( vd354 != vd353 )
| ( ( vplus @ vd356 @ A )
!= vd355 ) ),
inference(simp,[status(thm)],[4118]) ).
thf(7800,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ B @ A )
| ( vd354 != vd353 )
| ( B != vd355 )
| ( ( vplus @ A @ ( sk6 @ B @ A ) )
!= ( vplus @ vd356 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[148,4354]) ).
thf(7801,plain,
! [A: $i] :
( ~ ( greater @ A @ vd356 )
| ( vd354 != vd353 )
| ( A != vd355 ) ),
inference(pattern_uni,[status(thm)],[7800:[bind(A,$thf( vd356 )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D @ vd356 ))]]) ).
thf(7966,plain,
( ~ ( greater @ vd355 @ vd356 )
| ( vd354 != vd353 ) ),
inference(simp,[status(thm)],[7801]) ).
thf(8189,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 != vd353 )
| ( ( greater @ vd355 @ vd356 )
!= ( greater @ vd355 @ vd356 ) ) ),
inference(paramod_ordered,[status(thm)],[112,7966]) ).
thf(8190,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 != vd353 ) ),
inference(pattern_uni,[status(thm)],[8189:[]]) ).
thf(8571,plain,
( ( greater @ vd353 @ vd354 )
| ( vd354 != vd354 ) ),
inference(paramod_ordered,[status(thm)],[5034,8190]) ).
thf(8572,plain,
greater @ vd353 @ vd354,
inference(pattern_uni,[status(thm)],[8571:[]]) ).
thf(11498,plain,
( ~ ( greater @ vd355 @ vd356 )
| ~ $true ),
inference(rewrite,[status(thm)],[10313,8572]) ).
thf(11499,plain,
~ ( greater @ vd355 @ vd356 ),
inference(simp,[status(thm)],[11498]) ).
thf(11500,plain,
( $false
| ( vd356 = vd355 ) ),
inference(rewrite,[status(thm)],[5037,11499]) ).
thf(11501,plain,
vd356 = vd355,
inference(simp,[status(thm)],[11500]) ).
thf(11595,plain,
~ ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd355 ) ),
inference(rewrite,[status(thm)],[43,11501]) ).
thf(17794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( ( greater @ ( vplus @ A @ C ) @ ( vplus @ B @ C ) )
!= ( greater @ ( vplus @ vd353 @ vd355 ) @ ( vplus @ vd354 @ vd355 ) ) ) ),
inference(paramod_ordered,[status(thm)],[151,11595]) ).
thf(17795,plain,
~ ( greater @ vd353 @ vd354 ),
inference(pattern_uni,[status(thm)],[17794:[bind(A,$thf( vd353 )),bind(B,$thf( vd354 )),bind(C,$thf( vd355 ))]]) ).
thf(17878,plain,
~ $true,
inference(rewrite,[status(thm)],[17795,8572]) ).
thf(17879,plain,
$false,
inference(simp,[status(thm)],[17878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : NUM842+1 : TPTP v8.2.0. Released v4.1.0.
% 0.05/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Jun 22 19:09:40 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.06 % [INFO] Parsing done (166ms).
% 1.38/1.07 % [INFO] Running in sequential loop mode.
% 1.86/1.34 % [INFO] nitpick registered as external prover.
% 1.86/1.34 % [INFO] Scanning for conjecture ...
% 1.99/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 2.20/1.46 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.34/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/1.52 % [INFO] Type checking passed.
% 2.34/1.52 % [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 ...
% 73.39/11.56 % [INFO] Killing All external provers ...
% 73.39/11.56 % Time passed: 11028ms (effective reasoning time: 10484ms)
% 73.39/11.56 % 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)>
% 73.39/11.57 % Axioms used in derivation (9): ass(cond(goal(193), 0), 2), def(cond(conseq(axiom(3)), 11), 1), ass(cond(189, 0), 0), ass(cond(147, 0), 0), def(cond(conseq(axiom(3)), 17), 1), dis(antec(218)), ass(cond(209, 0), 0), ass(cond(158, 0), 0), ass(cond(33, 0), 0)
% 73.39/11.57 % No. of inferences in proof: 75
% 73.39/11.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11028 ms resp. 10484 ms w/o parsing
% 73.39/11.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 73.39/11.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------