TSTP Solution File: NUM851+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM851+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 : n018.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 11:50:24 EDT 2023
% Result : Theorem 9.45s 2.02s
% Output : Proof 11.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 17:20:44 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.06/1.16 Prover 1: Preprocessing ...
% 3.06/1.16 Prover 4: Preprocessing ...
% 3.44/1.20 Prover 6: Preprocessing ...
% 3.44/1.20 Prover 2: Preprocessing ...
% 3.44/1.20 Prover 0: Preprocessing ...
% 3.44/1.20 Prover 5: Preprocessing ...
% 3.44/1.20 Prover 3: Preprocessing ...
% 7.04/1.69 Prover 1: Warning: ignoring some quantifiers
% 7.24/1.77 Prover 1: Constructing countermodel ...
% 7.24/1.79 Prover 5: Proving ...
% 7.89/1.82 Prover 6: Proving ...
% 7.89/1.83 Prover 4: Warning: ignoring some quantifiers
% 7.89/1.85 Prover 3: Warning: ignoring some quantifiers
% 7.89/1.87 Prover 3: Constructing countermodel ...
% 8.49/1.91 Prover 4: Constructing countermodel ...
% 8.49/1.97 Prover 0: Proving ...
% 9.24/1.99 Prover 2: Proving ...
% 9.45/2.02 Prover 3: proved (1395ms)
% 9.45/2.02
% 9.45/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.45/2.02
% 9.45/2.05 Prover 5: stopped
% 9.45/2.06 Prover 2: stopped
% 9.45/2.06 Prover 0: stopped
% 9.45/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.45/2.07 Prover 6: stopped
% 9.45/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.45/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.45/2.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.45/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.45/2.11 Prover 7: Preprocessing ...
% 9.45/2.14 Prover 10: Preprocessing ...
% 9.45/2.15 Prover 1: Found proof (size 33)
% 9.45/2.16 Prover 1: proved (1531ms)
% 9.45/2.16 Prover 4: stopped
% 9.45/2.16 Prover 8: Preprocessing ...
% 9.45/2.17 Prover 13: Preprocessing ...
% 9.45/2.18 Prover 10: stopped
% 9.45/2.18 Prover 7: stopped
% 9.45/2.18 Prover 11: Preprocessing ...
% 10.49/2.23 Prover 13: stopped
% 10.49/2.25 Prover 11: stopped
% 10.49/2.29 Prover 8: Warning: ignoring some quantifiers
% 11.21/2.31 Prover 8: Constructing countermodel ...
% 11.21/2.32 Prover 8: stopped
% 11.21/2.32
% 11.21/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.21/2.32
% 11.21/2.33 % SZS output start Proof for theBenchmark
% 11.21/2.33 Assumptions after simplification:
% 11.21/2.33 ---------------------------------
% 11.21/2.33
% 11.21/2.33 (ass(cond(270, 0), 0))
% 11.21/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 11.21/2.36 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 11.21/2.36
% 11.21/2.36 (ass(cond(281, 0), 0))
% 11.21/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.21/2.36 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) =
% 11.21/2.36 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) =
% 11.21/2.36 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5)))
% 11.21/2.36
% 11.21/2.36 (holds(conseq_conjunct1(conseq(302)), 474, 0))
% 11.21/2.36 vplus(vd471, vd473) = vd470 & $i(vd470) & $i(vd473) & $i(vd471)
% 11.21/2.36
% 11.21/2.36 (holds(conseq_conjunct2(conseq(302)), 475, 0))
% 11.21/2.36 $i(vd470) & $i(vd469) & $i(vd473) & $i(vd471) & ? [v0: $i] : ? [v1: $i] :
% 11.21/2.36 (vplus(vd471, vd473) = v1 & vmul(v1, vd469) = v0 & vmul(vd470, vd469) = v0 &
% 11.21/2.36 $i(v1) & $i(v0))
% 11.21/2.36
% 11.21/2.36 (holds(conseq_conjunct2(conseq(302)), 475, 1))
% 11.21/2.37 $i(vd469) & $i(vd473) & $i(vd471) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 11.21/2.37 ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v1) & vplus(v2, v3) = v4 & vplus(vd471,
% 11.21/2.37 vd473) = v0 & vmul(v0, vd469) = v1 & vmul(vd473, vd469) = v3 & vmul(vd471,
% 11.21/2.37 vd469) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.21/2.37
% 11.21/2.37 (function-axioms)
% 11.21/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.21/2.37 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 11.21/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.21/2.37 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 11.21/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.21/2.37 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 11.21/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.21/2.37 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 11.21/2.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2)
% 11.21/2.37 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 11.21/2.37 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) &
% 11.21/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) |
% 11.21/2.37 ~ (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.21/2.37 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 11.21/2.37
% 11.21/2.37 Further assumptions not needed in the proof:
% 11.21/2.37 --------------------------------------------
% 11.21/2.37 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 11.21/2.37 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 11.21/2.37 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 11.21/2.37 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 11.21/2.37 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(290, 0), 0), ass(cond(33,
% 11.21/2.37 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0),
% 11.21/2.37 ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0),
% 11.21/2.37 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0),
% 11.21/2.37 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0),
% 11.21/2.37 ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0),
% 11.21/2.37 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1),
% 11.21/2.37 ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0),
% 11.21/2.37 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88),
% 11.21/2.37 0), 3), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12),
% 11.21/2.37 1), def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 11.21/2.37 holds(antec(302), 472, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 11.21/2.37 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 11.21/2.37 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 11.21/2.37 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))),
% 11.21/2.37 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 11.21/2.37
% 11.21/2.37 Those formulas are unsatisfiable:
% 11.21/2.37 ---------------------------------
% 11.21/2.37
% 11.21/2.37 Begin of proof
% 11.21/2.37 |
% 11.21/2.37 | ALPHA: (holds(conseq_conjunct2(conseq(302)), 475, 0)) implies:
% 11.21/2.38 | (1) ? [v0: $i] : ? [v1: $i] : (vplus(vd471, vd473) = v1 & vmul(v1, vd469)
% 11.21/2.38 | = v0 & vmul(vd470, vd469) = v0 & $i(v1) & $i(v0))
% 11.21/2.38 |
% 11.21/2.38 | ALPHA: (holds(conseq_conjunct1(conseq(302)), 474, 0)) implies:
% 11.21/2.38 | (2) vplus(vd471, vd473) = vd470
% 11.21/2.38 |
% 11.21/2.38 | ALPHA: (holds(conseq_conjunct2(conseq(302)), 475, 1)) implies:
% 11.21/2.38 | (3) $i(vd471)
% 11.21/2.38 | (4) $i(vd473)
% 11.21/2.38 | (5) $i(vd469)
% 11.21/2.38 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 11.21/2.38 | ~ (v4 = v1) & vplus(v2, v3) = v4 & vplus(vd471, vd473) = v0 &
% 11.21/2.38 | vmul(v0, vd469) = v1 & vmul(vd473, vd469) = v3 & vmul(vd471, vd469) =
% 11.21/2.38 | v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.21/2.38 |
% 11.21/2.38 | ALPHA: (function-axioms) implies:
% 11.21/2.38 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.21/2.38 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 11.21/2.38 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.21/2.38 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 11.21/2.38 |
% 11.21/2.38 | DELTA: instantiating (1) with fresh symbols all_52_0, all_52_1 gives:
% 11.21/2.38 | (9) vplus(vd471, vd473) = all_52_0 & vmul(all_52_0, vd469) = all_52_1 &
% 11.21/2.38 | vmul(vd470, vd469) = all_52_1 & $i(all_52_0) & $i(all_52_1)
% 11.21/2.38 |
% 11.21/2.38 | ALPHA: (9) implies:
% 11.21/2.38 | (10) $i(all_52_0)
% 11.21/2.38 | (11) vmul(all_52_0, vd469) = all_52_1
% 11.21/2.38 | (12) vplus(vd471, vd473) = all_52_0
% 11.21/2.38 |
% 11.21/2.38 | DELTA: instantiating (6) with fresh symbols all_59_0, all_59_1, all_59_2,
% 11.21/2.38 | all_59_3, all_59_4 gives:
% 11.21/2.38 | (13) ~ (all_59_0 = all_59_3) & vplus(all_59_2, all_59_1) = all_59_0 &
% 11.21/2.38 | vplus(vd471, vd473) = all_59_4 & vmul(all_59_4, vd469) = all_59_3 &
% 11.21/2.38 | vmul(vd473, vd469) = all_59_1 & vmul(vd471, vd469) = all_59_2 &
% 11.21/2.38 | $i(all_59_0) & $i(all_59_1) & $i(all_59_2) & $i(all_59_3) &
% 11.21/2.38 | $i(all_59_4)
% 11.21/2.38 |
% 11.21/2.38 | ALPHA: (13) implies:
% 11.21/2.39 | (14) ~ (all_59_0 = all_59_3)
% 11.21/2.39 | (15) vmul(vd471, vd469) = all_59_2
% 11.21/2.39 | (16) vmul(vd473, vd469) = all_59_1
% 11.21/2.39 | (17) vmul(all_59_4, vd469) = all_59_3
% 11.21/2.39 | (18) vplus(vd471, vd473) = all_59_4
% 11.21/2.39 | (19) vplus(all_59_2, all_59_1) = all_59_0
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (8) with all_52_0, all_59_4, vd473, vd471,
% 11.21/2.39 | simplifying with (12), (18) gives:
% 11.21/2.39 | (20) all_59_4 = all_52_0
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (8) with vd470, all_59_4, vd473, vd471, simplifying
% 11.21/2.39 | with (2), (18) gives:
% 11.21/2.39 | (21) all_59_4 = vd470
% 11.21/2.39 |
% 11.21/2.39 | COMBINE_EQS: (20), (21) imply:
% 11.21/2.39 | (22) all_52_0 = vd470
% 11.21/2.39 |
% 11.21/2.39 | SIMP: (22) implies:
% 11.21/2.39 | (23) all_52_0 = vd470
% 11.21/2.39 |
% 11.21/2.39 | REDUCE: (17), (21) imply:
% 11.21/2.39 | (24) vmul(vd470, vd469) = all_59_3
% 11.21/2.39 |
% 11.21/2.39 | REDUCE: (11), (23) imply:
% 11.21/2.39 | (25) vmul(vd470, vd469) = all_52_1
% 11.21/2.39 |
% 11.21/2.39 | REDUCE: (10), (23) imply:
% 11.21/2.39 | (26) $i(vd470)
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (7) with all_52_1, all_59_3, vd469, vd470,
% 11.21/2.39 | simplifying with (24), (25) gives:
% 11.21/2.39 | (27) all_59_3 = all_52_1
% 11.21/2.39 |
% 11.21/2.39 | REDUCE: (14), (27) imply:
% 11.21/2.39 | (28) ~ (all_59_0 = all_52_1)
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd471, vd469, all_59_2,
% 11.21/2.39 | simplifying with (3), (5), (15) gives:
% 11.21/2.39 | (29) vmul(vd469, vd471) = all_59_2 & $i(all_59_2)
% 11.21/2.39 |
% 11.21/2.39 | ALPHA: (29) implies:
% 11.21/2.39 | (30) vmul(vd469, vd471) = all_59_2
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd473, vd469, all_59_1,
% 11.21/2.39 | simplifying with (4), (5), (16) gives:
% 11.21/2.39 | (31) vmul(vd469, vd473) = all_59_1 & $i(all_59_1)
% 11.21/2.39 |
% 11.21/2.39 | ALPHA: (31) implies:
% 11.21/2.39 | (32) vmul(vd469, vd473) = all_59_1
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd470, vd469, all_52_1,
% 11.21/2.39 | simplifying with (5), (25), (26) gives:
% 11.21/2.39 | (33) vmul(vd469, vd470) = all_52_1 & $i(all_52_1)
% 11.21/2.39 |
% 11.21/2.39 | ALPHA: (33) implies:
% 11.21/2.39 | (34) vmul(vd469, vd470) = all_52_1
% 11.21/2.39 |
% 11.21/2.39 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd469, vd471, vd473,
% 11.21/2.39 | all_59_2, all_59_1, all_59_0, simplifying with (3), (4), (5),
% 11.21/2.39 | (19), (30), (32) gives:
% 11.21/2.39 | (35) ? [v0: $i] : (vplus(vd471, vd473) = v0 & vmul(vd469, v0) = all_59_0 &
% 11.21/2.39 | $i(v0) & $i(all_59_0))
% 11.21/2.39 |
% 11.21/2.39 | DELTA: instantiating (35) with fresh symbol all_83_0 gives:
% 11.21/2.39 | (36) vplus(vd471, vd473) = all_83_0 & vmul(vd469, all_83_0) = all_59_0 &
% 11.21/2.39 | $i(all_83_0) & $i(all_59_0)
% 11.21/2.39 |
% 11.21/2.39 | ALPHA: (36) implies:
% 11.21/2.40 | (37) vmul(vd469, all_83_0) = all_59_0
% 11.21/2.40 | (38) vplus(vd471, vd473) = all_83_0
% 11.21/2.40 |
% 11.21/2.40 | GROUND_INST: instantiating (8) with vd470, all_83_0, vd473, vd471, simplifying
% 11.21/2.40 | with (2), (38) gives:
% 11.21/2.40 | (39) all_83_0 = vd470
% 11.21/2.40 |
% 11.21/2.40 | REDUCE: (37), (39) imply:
% 11.21/2.40 | (40) vmul(vd469, vd470) = all_59_0
% 11.21/2.40 |
% 11.21/2.40 | GROUND_INST: instantiating (7) with all_52_1, all_59_0, vd470, vd469,
% 11.21/2.40 | simplifying with (34), (40) gives:
% 11.21/2.40 | (41) all_59_0 = all_52_1
% 11.21/2.40 |
% 11.21/2.40 | REDUCE: (28), (41) imply:
% 11.21/2.40 | (42) $false
% 11.66/2.40 |
% 11.66/2.40 | CLOSE: (42) is inconsistent.
% 11.66/2.40 |
% 11.66/2.40 End of proof
% 11.66/2.40 % SZS output end Proof for theBenchmark
% 11.66/2.40
% 11.66/2.40 1793ms
%------------------------------------------------------------------------------