TSTP Solution File: NUM855+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 : Thu Aug 31 11:50:26 EDT 2023
% Result : Theorem 10.57s 2.12s
% Output : Proof 12.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n009.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
% 0.12/0.33 % DateTime : Fri Aug 25 14:31:21 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.51/1.15 Prover 1: Preprocessing ...
% 3.51/1.15 Prover 4: Preprocessing ...
% 3.51/1.19 Prover 5: Preprocessing ...
% 3.51/1.19 Prover 2: Preprocessing ...
% 3.51/1.20 Prover 3: Preprocessing ...
% 3.51/1.20 Prover 0: Preprocessing ...
% 3.51/1.21 Prover 6: Preprocessing ...
% 7.55/1.70 Prover 1: Warning: ignoring some quantifiers
% 7.68/1.77 Prover 5: Proving ...
% 7.68/1.78 Prover 1: Constructing countermodel ...
% 7.68/1.79 Prover 6: Proving ...
% 7.68/1.80 Prover 3: Warning: ignoring some quantifiers
% 8.42/1.84 Prover 4: Warning: ignoring some quantifiers
% 8.42/1.84 Prover 3: Constructing countermodel ...
% 8.99/1.95 Prover 4: Constructing countermodel ...
% 8.99/1.96 Prover 0: Proving ...
% 9.58/2.00 Prover 2: Proving ...
% 10.57/2.11 Prover 3: proved (1492ms)
% 10.57/2.11
% 10.57/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.57/2.12
% 10.57/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.57/2.12 Prover 2: stopped
% 10.57/2.12 Prover 5: stopped
% 10.57/2.12 Prover 0: stopped
% 10.57/2.12 Prover 6: stopped
% 10.57/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.57/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.57/2.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.57/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.57/2.20 Prover 11: Preprocessing ...
% 10.57/2.20 Prover 7: Preprocessing ...
% 10.57/2.20 Prover 13: Preprocessing ...
% 10.57/2.21 Prover 8: Preprocessing ...
% 11.29/2.22 Prover 10: Preprocessing ...
% 11.29/2.23 Prover 1: Found proof (size 45)
% 11.29/2.23 Prover 1: proved (1614ms)
% 11.29/2.23 Prover 4: stopped
% 11.29/2.25 Prover 7: stopped
% 11.29/2.27 Prover 10: stopped
% 11.29/2.27 Prover 13: stopped
% 11.29/2.28 Prover 11: stopped
% 11.88/2.36 Prover 8: Warning: ignoring some quantifiers
% 11.88/2.37 Prover 8: Constructing countermodel ...
% 12.30/2.38 Prover 8: stopped
% 12.30/2.38
% 12.30/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.30/2.38
% 12.30/2.40 % SZS output start Proof for theBenchmark
% 12.38/2.40 Assumptions after simplification:
% 12.38/2.40 ---------------------------------
% 12.38/2.40
% 12.38/2.40 (ass(cond(270, 0), 0))
% 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 12.45/2.43 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 12.45/2.43
% 12.45/2.43 (ass(cond(33, 0), 0))
% 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 12.45/2.43 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.45/2.43 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) &
% 12.45/2.43 $i(v4)))
% 12.45/2.43
% 12.45/2.43 (def(cond(conseq(axiom(3)), 11), 1))
% 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2)
% 12.45/2.43 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~
% 12.45/2.43 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~
% 12.45/2.43 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 12.45/2.43
% 12.45/2.43 (holds(conjunct1(315), 514, 0))
% 12.45/2.43 $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : (greater(v0,
% 12.45/2.43 v1) = 0 & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & $i(v1) &
% 12.45/2.43 $i(v0))
% 12.45/2.43
% 12.45/2.43 (holds(conjunct2(315), 515, 0))
% 12.45/2.43 $i(vd509) & $i(vd511) & ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511,
% 12.45/2.43 vd509) = v0 & $i(v0))
% 12.45/2.43
% 12.45/2.43 (holds(conjunct2(315), 515, 1))
% 12.45/2.43 $i(vd512) & $i(vd509) & $i(vd511) & ? [v0: $i] : ? [v1: $i] : (greater(v0,
% 12.45/2.43 v1) = 0 & vmul(vd512, vd509) = v1 & vmul(vd511, vd509) = v0 & $i(v1) &
% 12.45/2.43 $i(v0))
% 12.45/2.43
% 12.45/2.43 (holds(conjunct2(315), 515, 2))
% 12.45/2.44 $i(vd512) & $i(vd509) & ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509,
% 12.45/2.44 vd512) = v0 & $i(v0))
% 12.45/2.44
% 12.45/2.44 (holds(conseq_conjunct2(315), 516, 0))
% 12.45/2.44 $i(vd512) & $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : ?
% 12.45/2.44 [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vmul(vd509, vd512) = v1 &
% 12.45/2.44 vmul(vd508, vd511) = v0 & $i(v1) & $i(v0))
% 12.45/2.44
% 12.45/2.44 (function-axioms)
% 12.45/2.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.45/2.44 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 12.45/2.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.45/2.44 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 12.45/2.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~
% 12.45/2.44 (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.45/2.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2)
% 12.45/2.44 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.45/2.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3,
% 12.45/2.44 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.45/2.44 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2)
% 12.45/2.44 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.45/2.44 (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 12.45/2.44 ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 12.45/2.44
% 12.45/2.44 Further assumptions not needed in the proof:
% 12.45/2.44 --------------------------------------------
% 12.45/2.44 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 12.45/2.44 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 12.45/2.44 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 12.45/2.44 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 12.45/2.44 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290,
% 12.45/2.44 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(299, 0), 2),
% 12.45/2.44 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0),
% 12.45/2.44 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0),
% 12.45/2.44 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)),
% 12.45/2.44 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 12.45/2.44 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 12.45/2.44 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 12.45/2.44 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 12.45/2.44 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 12.45/2.44 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 12.45/2.44 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1),
% 12.45/2.44 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 12.45/2.44 holds(conjunct1(314), 510, 0), holds(conjunct2(314), 513, 0),
% 12.45/2.44 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 12.45/2.44 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 12.45/2.44 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 12.45/2.44 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)),
% 12.45/2.44 holds(scope(axiom(1)), 2, 0))
% 12.45/2.44
% 12.45/2.44 Those formulas are unsatisfiable:
% 12.45/2.44 ---------------------------------
% 12.45/2.44
% 12.45/2.44 Begin of proof
% 12.45/2.44 |
% 12.45/2.44 | ALPHA: (holds(conjunct2(315), 515, 2)) implies:
% 12.45/2.44 | (1) ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, vd512) = v0 &
% 12.45/2.44 | $i(v0))
% 12.45/2.44 |
% 12.45/2.44 | ALPHA: (holds(conjunct2(315), 515, 1)) implies:
% 12.45/2.45 | (2) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd512, vd509) =
% 12.45/2.45 | v1 & vmul(vd511, vd509) = v0 & $i(v1) & $i(v0))
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (holds(conjunct2(315), 515, 0)) implies:
% 12.45/2.45 | (3) ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, vd509) = v0 &
% 12.45/2.45 | $i(v0))
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (holds(conjunct1(315), 514, 0)) implies:
% 12.45/2.45 | (4) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd509, vd511) =
% 12.45/2.45 | v1 & vmul(vd508, vd511) = v0 & $i(v1) & $i(v0))
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies:
% 12.45/2.45 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~
% 12.45/2.45 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 12.45/2.45 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1,
% 12.45/2.45 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0,
% 12.45/2.45 | v3) = v1) | ~ $i(v3)))
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (holds(conseq_conjunct2(315), 516, 0)) implies:
% 12.45/2.45 | (7) $i(vd508)
% 12.45/2.45 | (8) $i(vd511)
% 12.45/2.45 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & greater(v0,
% 12.45/2.45 | v1) = v2 & vmul(vd509, vd512) = v1 & vmul(vd508, vd511) = v0 &
% 12.45/2.45 | $i(v1) & $i(v0))
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (function-axioms) implies:
% 12.45/2.45 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.45/2.45 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 12.45/2.45 |
% 12.45/2.45 | DELTA: instantiating (1) with fresh symbol all_54_0 gives:
% 12.45/2.45 | (11) vmul(vd512, vd509) = all_54_0 & vmul(vd509, vd512) = all_54_0 &
% 12.45/2.45 | $i(all_54_0)
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (11) implies:
% 12.45/2.45 | (12) vmul(vd509, vd512) = all_54_0
% 12.45/2.45 | (13) vmul(vd512, vd509) = all_54_0
% 12.45/2.45 |
% 12.45/2.45 | DELTA: instantiating (3) with fresh symbol all_56_0 gives:
% 12.45/2.45 | (14) vmul(vd509, vd511) = all_56_0 & vmul(vd511, vd509) = all_56_0 &
% 12.45/2.45 | $i(all_56_0)
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (14) implies:
% 12.45/2.45 | (15) vmul(vd511, vd509) = all_56_0
% 12.45/2.45 | (16) vmul(vd509, vd511) = all_56_0
% 12.45/2.45 |
% 12.45/2.45 | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1 gives:
% 12.45/2.45 | (17) greater(all_63_1, all_63_0) = 0 & vmul(vd512, vd509) = all_63_0 &
% 12.45/2.45 | vmul(vd511, vd509) = all_63_1 & $i(all_63_0) & $i(all_63_1)
% 12.45/2.45 |
% 12.45/2.45 | ALPHA: (17) implies:
% 12.45/2.45 | (18) $i(all_63_1)
% 12.45/2.45 | (19) $i(all_63_0)
% 12.45/2.45 | (20) vmul(vd511, vd509) = all_63_1
% 12.45/2.45 | (21) vmul(vd512, vd509) = all_63_0
% 12.45/2.46 | (22) greater(all_63_1, all_63_0) = 0
% 12.45/2.46 |
% 12.45/2.46 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1 gives:
% 12.45/2.46 | (23) greater(all_65_1, all_65_0) = 0 & vmul(vd509, vd511) = all_65_0 &
% 12.45/2.46 | vmul(vd508, vd511) = all_65_1 & $i(all_65_0) & $i(all_65_1)
% 12.45/2.46 |
% 12.45/2.46 | ALPHA: (23) implies:
% 12.45/2.46 | (24) vmul(vd508, vd511) = all_65_1
% 12.45/2.46 | (25) vmul(vd509, vd511) = all_65_0
% 12.45/2.46 | (26) greater(all_65_1, all_65_0) = 0
% 12.45/2.46 |
% 12.45/2.46 | DELTA: instantiating (9) with fresh symbols all_68_0, all_68_1, all_68_2
% 12.45/2.46 | gives:
% 12.45/2.46 | (27) ~ (all_68_0 = 0) & greater(all_68_2, all_68_1) = all_68_0 &
% 12.45/2.46 | vmul(vd509, vd512) = all_68_1 & vmul(vd508, vd511) = all_68_2 &
% 12.45/2.46 | $i(all_68_1) & $i(all_68_2)
% 12.45/2.46 |
% 12.45/2.46 | ALPHA: (27) implies:
% 12.45/2.46 | (28) ~ (all_68_0 = 0)
% 12.45/2.46 | (29) vmul(vd508, vd511) = all_68_2
% 12.45/2.46 | (30) vmul(vd509, vd512) = all_68_1
% 12.45/2.46 | (31) greater(all_68_2, all_68_1) = all_68_0
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (10) with all_65_1, all_68_2, vd511, vd508,
% 12.45/2.46 | simplifying with (24), (29) gives:
% 12.45/2.46 | (32) all_68_2 = all_65_1
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (10) with all_56_0, all_63_1, vd509, vd511,
% 12.45/2.46 | simplifying with (15), (20) gives:
% 12.45/2.46 | (33) all_63_1 = all_56_0
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (10) with all_56_0, all_65_0, vd511, vd509,
% 12.45/2.46 | simplifying with (16), (25) gives:
% 12.45/2.46 | (34) all_65_0 = all_56_0
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (10) with all_54_0, all_68_1, vd512, vd509,
% 12.45/2.46 | simplifying with (12), (30) gives:
% 12.45/2.46 | (35) all_68_1 = all_54_0
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (10) with all_54_0, all_63_0, vd509, vd512,
% 12.45/2.46 | simplifying with (13), (21) gives:
% 12.45/2.46 | (36) all_63_0 = all_54_0
% 12.45/2.46 |
% 12.45/2.46 | REDUCE: (31), (32), (35) imply:
% 12.45/2.46 | (37) greater(all_65_1, all_54_0) = all_68_0
% 12.45/2.46 |
% 12.45/2.46 | REDUCE: (26), (34) imply:
% 12.45/2.46 | (38) greater(all_65_1, all_56_0) = 0
% 12.45/2.46 |
% 12.45/2.46 | REDUCE: (22), (33), (36) imply:
% 12.45/2.46 | (39) greater(all_56_0, all_54_0) = 0
% 12.45/2.46 |
% 12.45/2.46 | REDUCE: (19), (36) imply:
% 12.45/2.46 | (40) $i(all_54_0)
% 12.45/2.46 |
% 12.45/2.46 | REDUCE: (18), (33) imply:
% 12.45/2.46 | (41) $i(all_56_0)
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd508, vd511, all_65_1,
% 12.45/2.46 | simplifying with (7), (8), (24) gives:
% 12.45/2.46 | (42) vmul(vd511, vd508) = all_65_1 & $i(all_65_1)
% 12.45/2.46 |
% 12.45/2.46 | ALPHA: (42) implies:
% 12.45/2.46 | (43) $i(all_65_1)
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (5) with all_54_0, all_56_0, simplifying with (39),
% 12.45/2.46 | (40), (41) gives:
% 12.45/2.46 | (44) ? [v0: $i] : (vplus(all_54_0, v0) = all_56_0 & $i(v0))
% 12.45/2.46 |
% 12.45/2.46 | GROUND_INST: instantiating (6) with all_54_0, all_65_1, all_68_0, simplifying
% 12.45/2.46 | with (37), (40), (43) gives:
% 12.45/2.47 | (45) all_68_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~
% 12.45/2.47 | $i(v0))
% 12.45/2.47 |
% 12.45/2.47 | GROUND_INST: instantiating (5) with all_56_0, all_65_1, simplifying with (38),
% 12.45/2.47 | (41), (43) gives:
% 12.45/2.47 | (46) ? [v0: $i] : (vplus(all_56_0, v0) = all_65_1 & $i(v0))
% 12.45/2.47 |
% 12.45/2.47 | DELTA: instantiating (44) with fresh symbol all_82_0 gives:
% 12.45/2.47 | (47) vplus(all_54_0, all_82_0) = all_56_0 & $i(all_82_0)
% 12.45/2.47 |
% 12.45/2.47 | ALPHA: (47) implies:
% 12.45/2.47 | (48) $i(all_82_0)
% 12.45/2.47 | (49) vplus(all_54_0, all_82_0) = all_56_0
% 12.45/2.47 |
% 12.45/2.47 | DELTA: instantiating (46) with fresh symbol all_86_0 gives:
% 12.45/2.47 | (50) vplus(all_56_0, all_86_0) = all_65_1 & $i(all_86_0)
% 12.45/2.47 |
% 12.45/2.47 | ALPHA: (50) implies:
% 12.45/2.47 | (51) $i(all_86_0)
% 12.45/2.47 | (52) vplus(all_56_0, all_86_0) = all_65_1
% 12.45/2.47 |
% 12.45/2.47 | BETA: splitting (45) gives:
% 12.45/2.47 |
% 12.45/2.47 | Case 1:
% 12.45/2.47 | |
% 12.45/2.47 | | (53) all_68_0 = 0
% 12.45/2.47 | |
% 12.45/2.47 | | REDUCE: (28), (53) imply:
% 12.45/2.47 | | (54) $false
% 12.45/2.47 | |
% 12.45/2.47 | | CLOSE: (54) is inconsistent.
% 12.45/2.47 | |
% 12.45/2.47 | Case 2:
% 12.45/2.47 | |
% 12.45/2.47 | | (55) ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~ $i(v0))
% 12.45/2.47 | |
% 12.45/2.47 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_54_0, all_82_0,
% 12.45/2.47 | | all_86_0, all_56_0, all_65_1, simplifying with (40), (48),
% 12.45/2.47 | | (49), (51), (52) gives:
% 12.45/2.47 | | (56) ? [v0: $i] : (vplus(all_82_0, all_86_0) = v0 & vplus(all_54_0, v0)
% 12.45/2.47 | | = all_65_1 & $i(v0) & $i(all_65_1))
% 12.45/2.47 | |
% 12.45/2.47 | | DELTA: instantiating (56) with fresh symbol all_101_0 gives:
% 12.45/2.47 | | (57) vplus(all_82_0, all_86_0) = all_101_0 & vplus(all_54_0, all_101_0) =
% 12.45/2.47 | | all_65_1 & $i(all_101_0) & $i(all_65_1)
% 12.45/2.47 | |
% 12.45/2.47 | | ALPHA: (57) implies:
% 12.45/2.47 | | (58) $i(all_101_0)
% 12.45/2.47 | | (59) vplus(all_54_0, all_101_0) = all_65_1
% 12.45/2.47 | |
% 12.45/2.47 | | GROUND_INST: instantiating (55) with all_101_0, simplifying with (58), (59)
% 12.45/2.47 | | gives:
% 12.45/2.47 | | (60) $false
% 12.45/2.47 | |
% 12.45/2.47 | | CLOSE: (60) is inconsistent.
% 12.45/2.47 | |
% 12.45/2.47 | End of split
% 12.45/2.47 |
% 12.45/2.47 End of proof
% 12.45/2.47 % SZS output end Proof for theBenchmark
% 12.45/2.47
% 12.45/2.47 1876ms
%------------------------------------------------------------------------------