TSTP Solution File: NUM841+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM841+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 : n025.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 11:50:19 EDT 2023
% Result : Theorem 9.51s 2.03s
% Output : Proof 11.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM841+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:44:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.93/1.14 Prover 4: Preprocessing ...
% 2.93/1.14 Prover 1: Preprocessing ...
% 2.93/1.17 Prover 2: Preprocessing ...
% 2.93/1.17 Prover 0: Preprocessing ...
% 2.93/1.17 Prover 6: Preprocessing ...
% 2.93/1.17 Prover 5: Preprocessing ...
% 2.93/1.17 Prover 3: Preprocessing ...
% 6.78/1.65 Prover 1: Warning: ignoring some quantifiers
% 6.78/1.67 Prover 6: Proving ...
% 6.78/1.68 Prover 3: Warning: ignoring some quantifiers
% 6.78/1.68 Prover 5: Proving ...
% 6.78/1.69 Prover 1: Constructing countermodel ...
% 6.78/1.70 Prover 3: Constructing countermodel ...
% 7.30/1.73 Prover 4: Warning: ignoring some quantifiers
% 7.76/1.79 Prover 4: Constructing countermodel ...
% 7.76/1.82 Prover 2: Proving ...
% 8.51/1.89 Prover 0: Proving ...
% 9.51/2.02 Prover 3: proved (1383ms)
% 9.51/2.03
% 9.51/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.51/2.03
% 9.51/2.03 Prover 2: stopped
% 9.51/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.51/2.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.51/2.04 Prover 5: stopped
% 9.51/2.04 Prover 0: stopped
% 9.51/2.04 Prover 6: stopped
% 9.51/2.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.51/2.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.51/2.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.94/2.12 Prover 8: Preprocessing ...
% 9.94/2.13 Prover 13: Preprocessing ...
% 9.94/2.13 Prover 7: Preprocessing ...
% 9.94/2.13 Prover 11: Preprocessing ...
% 9.94/2.14 Prover 10: Preprocessing ...
% 9.94/2.17 Prover 1: Found proof (size 45)
% 9.94/2.17 Prover 1: proved (1537ms)
% 9.94/2.17 Prover 4: stopped
% 9.94/2.19 Prover 10: stopped
% 9.94/2.20 Prover 7: stopped
% 9.94/2.20 Prover 11: stopped
% 9.94/2.21 Prover 13: stopped
% 9.94/2.26 Prover 8: Warning: ignoring some quantifiers
% 9.94/2.27 Prover 8: Constructing countermodel ...
% 11.15/2.28 Prover 8: stopped
% 11.15/2.28
% 11.15/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.15/2.28
% 11.15/2.30 % SZS output start Proof for theBenchmark
% 11.15/2.30 Assumptions after simplification:
% 11.15/2.30 ---------------------------------
% 11.15/2.30
% 11.15/2.30 (ass(cond(33, 0), 0))
% 11.46/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 11.46/2.34 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.46/2.34 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) &
% 11.46/2.34 $i(v4)))
% 11.46/2.34
% 11.46/2.34 (ass(cond(61, 0), 0))
% 11.46/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 11.46/2.34 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 11.46/2.34
% 11.46/2.34 (def(cond(conseq(axiom(3)), 11), 1))
% 11.46/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2)
% 11.46/2.34 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~
% 11.46/2.34 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~
% 11.46/2.34 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 11.46/2.34
% 11.46/2.34 (holds(212, 350, 0))
% 11.46/2.34 $i(vd345) & $i(vd347) & $i(vd344) & ? [v0: $i] : ? [v1: $i] : (greater(v0,
% 11.46/2.34 v1) = 0 & vplus(vd345, vd347) = v1 & vplus(vd344, vd347) = v0 & $i(v1) &
% 11.46/2.34 $i(v0))
% 11.46/2.34
% 11.46/2.34 (holds(213, 351, 0))
% 11.46/2.34 $i(vd345) & $i(vd347) & ? [v0: $i] : (vplus(vd345, vd347) = v0 & vplus(vd347,
% 11.46/2.34 vd345) = v0 & $i(v0))
% 11.46/2.34
% 11.46/2.34 (holds(213, 351, 1))
% 11.46/2.34 $i(vd348) & $i(vd345) & $i(vd347) & ? [v0: $i] : ? [v1: $i] : (greater(v0,
% 11.46/2.34 v1) = 0 & vplus(vd348, vd345) = v1 & vplus(vd347, vd345) = v0 & $i(v1) &
% 11.46/2.34 $i(v0))
% 11.46/2.34
% 11.46/2.34 (holds(213, 351, 2))
% 11.46/2.34 $i(vd348) & $i(vd345) & ? [v0: $i] : (vplus(vd348, vd345) = v0 & vplus(vd345,
% 11.46/2.34 vd348) = v0 & $i(v0))
% 11.46/2.34
% 11.46/2.34 (holds(214, 352, 0))
% 11.46/2.34 $i(vd348) & $i(vd345) & $i(vd347) & $i(vd344) & ? [v0: $i] : ? [v1: $i] : ?
% 11.46/2.34 [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vplus(vd345, vd348) = v1 &
% 11.46/2.34 vplus(vd344, vd347) = v0 & $i(v1) & $i(v0))
% 11.46/2.34
% 11.46/2.34 (function-axioms)
% 11.46/2.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.46/2.35 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 11.46/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.46/2.35 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 11.46/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.46/2.35 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 11.46/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.46/2.35 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 11.46/2.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2)
% 11.46/2.35 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 11.46/2.35 : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0: $i] :
% 11.46/2.35 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) =
% 11.46/2.35 v0))
% 11.46/2.35
% 11.46/2.35 Further assumptions not needed in the proof:
% 11.46/2.35 --------------------------------------------
% 11.46/2.35 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 11.46/2.35 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 11.46/2.35 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0),
% 11.46/2.35 0), ass(cond(6, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0),
% 11.46/2.35 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0),
% 11.46/2.35 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0),
% 11.46/2.35 ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0),
% 11.46/2.35 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1),
% 11.46/2.35 ass(cond(goal(202), 0), 2), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0),
% 11.46/2.35 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 11.46/2.35 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1),
% 11.46/2.35 def(cond(conseq(axiom(3)), 17), 1), holds(conjunct1(211), 346, 0),
% 11.46/2.35 holds(conjunct2(211), 349, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 11.46/2.35 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 11.46/2.35 holds(definiens(29), 44, 0))), qu(restrictor(axiom(1)),
% 11.46/2.35 holds(scope(axiom(1)), 2, 0))
% 11.46/2.35
% 11.46/2.35 Those formulas are unsatisfiable:
% 11.46/2.35 ---------------------------------
% 11.46/2.35
% 11.46/2.35 Begin of proof
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (holds(213, 351, 2)) implies:
% 11.46/2.35 | (1) ? [v0: $i] : (vplus(vd348, vd345) = v0 & vplus(vd345, vd348) = v0 &
% 11.46/2.35 | $i(v0))
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (holds(213, 351, 1)) implies:
% 11.46/2.35 | (2) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vplus(vd348, vd345)
% 11.46/2.35 | = v1 & vplus(vd347, vd345) = v0 & $i(v1) & $i(v0))
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (holds(213, 351, 0)) implies:
% 11.46/2.35 | (3) ? [v0: $i] : (vplus(vd345, vd347) = v0 & vplus(vd347, vd345) = v0 &
% 11.46/2.35 | $i(v0))
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (holds(212, 350, 0)) implies:
% 11.46/2.35 | (4) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vplus(vd345, vd347)
% 11.46/2.35 | = v1 & vplus(vd344, vd347) = v0 & $i(v1) & $i(v0))
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies:
% 11.46/2.35 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~
% 11.46/2.35 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 11.46/2.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1,
% 11.46/2.35 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0,
% 11.46/2.35 | v3) = v1) | ~ $i(v3)))
% 11.46/2.35 |
% 11.46/2.35 | ALPHA: (holds(214, 352, 0)) implies:
% 11.46/2.35 | (7) $i(vd344)
% 11.46/2.35 | (8) $i(vd347)
% 11.46/2.35 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & greater(v0,
% 11.46/2.35 | v1) = v2 & vplus(vd345, vd348) = v1 & vplus(vd344, vd347) = v0 &
% 11.46/2.36 | $i(v1) & $i(v0))
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (function-axioms) implies:
% 11.46/2.36 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.46/2.36 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 11.46/2.36 |
% 11.46/2.36 | DELTA: instantiating (1) with fresh symbol all_37_0 gives:
% 11.46/2.36 | (11) vplus(vd348, vd345) = all_37_0 & vplus(vd345, vd348) = all_37_0 &
% 11.46/2.36 | $i(all_37_0)
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (11) implies:
% 11.46/2.36 | (12) vplus(vd345, vd348) = all_37_0
% 11.46/2.36 | (13) vplus(vd348, vd345) = all_37_0
% 11.46/2.36 |
% 11.46/2.36 | DELTA: instantiating (3) with fresh symbol all_39_0 gives:
% 11.46/2.36 | (14) vplus(vd345, vd347) = all_39_0 & vplus(vd347, vd345) = all_39_0 &
% 11.46/2.36 | $i(all_39_0)
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (14) implies:
% 11.46/2.36 | (15) vplus(vd347, vd345) = all_39_0
% 11.46/2.36 | (16) vplus(vd345, vd347) = all_39_0
% 11.46/2.36 |
% 11.46/2.36 | DELTA: instantiating (2) with fresh symbols all_42_0, all_42_1 gives:
% 11.46/2.36 | (17) greater(all_42_1, all_42_0) = 0 & vplus(vd348, vd345) = all_42_0 &
% 11.46/2.36 | vplus(vd347, vd345) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (17) implies:
% 11.46/2.36 | (18) $i(all_42_1)
% 11.46/2.36 | (19) $i(all_42_0)
% 11.46/2.36 | (20) vplus(vd347, vd345) = all_42_1
% 11.46/2.36 | (21) vplus(vd348, vd345) = all_42_0
% 11.46/2.36 | (22) greater(all_42_1, all_42_0) = 0
% 11.46/2.36 |
% 11.46/2.36 | DELTA: instantiating (4) with fresh symbols all_44_0, all_44_1 gives:
% 11.46/2.36 | (23) greater(all_44_1, all_44_0) = 0 & vplus(vd345, vd347) = all_44_0 &
% 11.46/2.36 | vplus(vd344, vd347) = all_44_1 & $i(all_44_0) & $i(all_44_1)
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (23) implies:
% 11.46/2.36 | (24) vplus(vd344, vd347) = all_44_1
% 11.46/2.36 | (25) vplus(vd345, vd347) = all_44_0
% 11.46/2.36 | (26) greater(all_44_1, all_44_0) = 0
% 11.46/2.36 |
% 11.46/2.36 | DELTA: instantiating (9) with fresh symbols all_49_0, all_49_1, all_49_2
% 11.46/2.36 | gives:
% 11.46/2.36 | (27) ~ (all_49_0 = 0) & greater(all_49_2, all_49_1) = all_49_0 &
% 11.46/2.36 | vplus(vd345, vd348) = all_49_1 & vplus(vd344, vd347) = all_49_2 &
% 11.46/2.36 | $i(all_49_1) & $i(all_49_2)
% 11.46/2.36 |
% 11.46/2.36 | ALPHA: (27) implies:
% 11.46/2.36 | (28) ~ (all_49_0 = 0)
% 11.46/2.36 | (29) vplus(vd344, vd347) = all_49_2
% 11.46/2.36 | (30) vplus(vd345, vd348) = all_49_1
% 11.46/2.36 | (31) greater(all_49_2, all_49_1) = all_49_0
% 11.46/2.36 |
% 11.46/2.36 | GROUND_INST: instantiating (10) with all_44_1, all_49_2, vd347, vd344,
% 11.46/2.36 | simplifying with (24), (29) gives:
% 11.46/2.36 | (32) all_49_2 = all_44_1
% 11.46/2.36 |
% 11.46/2.36 | GROUND_INST: instantiating (10) with all_39_0, all_42_1, vd345, vd347,
% 11.46/2.36 | simplifying with (15), (20) gives:
% 11.46/2.36 | (33) all_42_1 = all_39_0
% 11.46/2.36 |
% 11.46/2.36 | GROUND_INST: instantiating (10) with all_39_0, all_44_0, vd347, vd345,
% 11.46/2.36 | simplifying with (16), (25) gives:
% 11.46/2.36 | (34) all_44_0 = all_39_0
% 11.46/2.36 |
% 11.46/2.36 | GROUND_INST: instantiating (10) with all_37_0, all_49_1, vd348, vd345,
% 11.46/2.36 | simplifying with (12), (30) gives:
% 11.46/2.36 | (35) all_49_1 = all_37_0
% 11.46/2.36 |
% 11.46/2.36 | GROUND_INST: instantiating (10) with all_37_0, all_42_0, vd345, vd348,
% 11.46/2.36 | simplifying with (13), (21) gives:
% 11.46/2.36 | (36) all_42_0 = all_37_0
% 11.46/2.36 |
% 11.46/2.36 | REDUCE: (31), (32), (35) imply:
% 11.46/2.36 | (37) greater(all_44_1, all_37_0) = all_49_0
% 11.46/2.36 |
% 11.46/2.36 | REDUCE: (26), (34) imply:
% 11.46/2.36 | (38) greater(all_44_1, all_39_0) = 0
% 11.46/2.36 |
% 11.46/2.36 | REDUCE: (22), (33), (36) imply:
% 11.46/2.37 | (39) greater(all_39_0, all_37_0) = 0
% 11.46/2.37 |
% 11.46/2.37 | REDUCE: (19), (36) imply:
% 11.46/2.37 | (40) $i(all_37_0)
% 11.46/2.37 |
% 11.46/2.37 | REDUCE: (18), (33) imply:
% 11.46/2.37 | (41) $i(all_39_0)
% 11.46/2.37 |
% 11.46/2.37 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd344, vd347, all_44_1,
% 11.46/2.37 | simplifying with (7), (8), (24) gives:
% 11.46/2.37 | (42) vplus(vd347, vd344) = all_44_1 & $i(all_44_1)
% 11.46/2.37 |
% 11.46/2.37 | ALPHA: (42) implies:
% 11.46/2.37 | (43) $i(all_44_1)
% 11.46/2.37 |
% 11.46/2.37 | GROUND_INST: instantiating (5) with all_37_0, all_39_0, simplifying with (39),
% 11.46/2.37 | (40), (41) gives:
% 11.46/2.37 | (44) ? [v0: $i] : (vplus(all_37_0, v0) = all_39_0 & $i(v0))
% 11.46/2.37 |
% 11.46/2.37 | GROUND_INST: instantiating (6) with all_37_0, all_44_1, all_49_0, simplifying
% 11.46/2.37 | with (37), (40), (43) gives:
% 11.46/2.37 | (45) all_49_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_37_0, v0) = all_44_1) | ~
% 11.46/2.37 | $i(v0))
% 11.46/2.37 |
% 11.46/2.37 | GROUND_INST: instantiating (5) with all_39_0, all_44_1, simplifying with (38),
% 11.46/2.37 | (41), (43) gives:
% 11.46/2.37 | (46) ? [v0: $i] : (vplus(all_39_0, v0) = all_44_1 & $i(v0))
% 11.46/2.37 |
% 11.46/2.37 | DELTA: instantiating (44) with fresh symbol all_63_0 gives:
% 11.46/2.37 | (47) vplus(all_37_0, all_63_0) = all_39_0 & $i(all_63_0)
% 11.46/2.37 |
% 11.46/2.37 | ALPHA: (47) implies:
% 11.46/2.37 | (48) $i(all_63_0)
% 11.46/2.37 | (49) vplus(all_37_0, all_63_0) = all_39_0
% 11.46/2.37 |
% 11.46/2.37 | DELTA: instantiating (46) with fresh symbol all_67_0 gives:
% 11.46/2.37 | (50) vplus(all_39_0, all_67_0) = all_44_1 & $i(all_67_0)
% 11.46/2.37 |
% 11.46/2.37 | ALPHA: (50) implies:
% 11.46/2.37 | (51) $i(all_67_0)
% 11.46/2.37 | (52) vplus(all_39_0, all_67_0) = all_44_1
% 11.46/2.37 |
% 11.46/2.37 | BETA: splitting (45) gives:
% 11.46/2.37 |
% 11.46/2.37 | Case 1:
% 11.46/2.37 | |
% 11.46/2.37 | | (53) all_49_0 = 0
% 11.46/2.37 | |
% 11.46/2.37 | | REDUCE: (28), (53) imply:
% 11.46/2.37 | | (54) $false
% 11.46/2.37 | |
% 11.46/2.37 | | CLOSE: (54) is inconsistent.
% 11.46/2.37 | |
% 11.46/2.37 | Case 2:
% 11.46/2.37 | |
% 11.46/2.37 | | (55) ! [v0: $i] : ( ~ (vplus(all_37_0, v0) = all_44_1) | ~ $i(v0))
% 11.46/2.37 | |
% 11.46/2.37 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_37_0, all_63_0,
% 11.46/2.37 | | all_67_0, all_39_0, all_44_1, simplifying with (40), (48),
% 11.46/2.37 | | (49), (51), (52) gives:
% 11.46/2.37 | | (56) ? [v0: $i] : (vplus(all_63_0, all_67_0) = v0 & vplus(all_37_0, v0)
% 11.46/2.37 | | = all_44_1 & $i(v0) & $i(all_44_1))
% 11.46/2.37 | |
% 11.46/2.37 | | DELTA: instantiating (56) with fresh symbol all_82_0 gives:
% 11.46/2.37 | | (57) vplus(all_63_0, all_67_0) = all_82_0 & vplus(all_37_0, all_82_0) =
% 11.46/2.37 | | all_44_1 & $i(all_82_0) & $i(all_44_1)
% 11.46/2.37 | |
% 11.46/2.37 | | ALPHA: (57) implies:
% 11.46/2.37 | | (58) $i(all_82_0)
% 11.46/2.37 | | (59) vplus(all_37_0, all_82_0) = all_44_1
% 11.46/2.37 | |
% 11.46/2.37 | | GROUND_INST: instantiating (55) with all_82_0, simplifying with (58), (59)
% 11.46/2.37 | | gives:
% 11.46/2.37 | | (60) $false
% 11.46/2.37 | |
% 11.46/2.37 | | CLOSE: (60) is inconsistent.
% 11.46/2.37 | |
% 11.46/2.37 | End of split
% 11.46/2.37 |
% 11.46/2.37 End of proof
% 11.46/2.37 % SZS output end Proof for theBenchmark
% 11.46/2.37
% 11.46/2.37 1758ms
%------------------------------------------------------------------------------