TSTP Solution File: KLE072+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 05:34:27 EDT 2023
% Result : Theorem 6.80s 1.63s
% Output : Proof 8.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 11:41:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.52/1.02 Prover 1: Preprocessing ...
% 2.52/1.02 Prover 4: Preprocessing ...
% 2.52/1.07 Prover 6: Preprocessing ...
% 2.52/1.07 Prover 3: Preprocessing ...
% 2.52/1.07 Prover 5: Preprocessing ...
% 2.52/1.07 Prover 0: Preprocessing ...
% 2.52/1.07 Prover 2: Preprocessing ...
% 5.23/1.40 Prover 1: Constructing countermodel ...
% 5.23/1.40 Prover 6: Constructing countermodel ...
% 5.23/1.41 Prover 3: Constructing countermodel ...
% 5.23/1.44 Prover 4: Constructing countermodel ...
% 5.23/1.45 Prover 0: Proving ...
% 5.23/1.46 Prover 5: Proving ...
% 6.56/1.59 Prover 2: Proving ...
% 6.80/1.63 Prover 3: proved (996ms)
% 6.80/1.63 Prover 0: proved (1003ms)
% 6.80/1.63
% 6.80/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.80/1.63
% 6.80/1.64
% 6.80/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.80/1.64
% 6.80/1.64 Prover 2: stopped
% 6.80/1.64 Prover 5: stopped
% 6.80/1.65 Prover 6: stopped
% 6.80/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.80/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.80/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.80/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.80/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.80/1.68 Prover 7: Preprocessing ...
% 6.80/1.69 Prover 10: Preprocessing ...
% 6.80/1.70 Prover 8: Preprocessing ...
% 6.80/1.70 Prover 11: Preprocessing ...
% 7.37/1.71 Prover 13: Preprocessing ...
% 7.37/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.37/1.78 Prover 8: Constructing countermodel ...
% 8.00/1.78 Prover 7: Constructing countermodel ...
% 8.00/1.80 Prover 4: Found proof (size 33)
% 8.00/1.80 Prover 4: proved (1171ms)
% 8.00/1.81 Prover 10: Constructing countermodel ...
% 8.00/1.81 Prover 13: Warning: ignoring some quantifiers
% 8.00/1.81 Prover 7: stopped
% 8.00/1.81 Prover 1: Found proof (size 42)
% 8.00/1.81 Prover 1: proved (1178ms)
% 8.00/1.81 Prover 8: stopped
% 8.00/1.81 Prover 10: stopped
% 8.00/1.81 Prover 13: Constructing countermodel ...
% 8.00/1.81 Prover 11: Constructing countermodel ...
% 8.00/1.82 Prover 13: stopped
% 8.00/1.82 Prover 11: stopped
% 8.00/1.82
% 8.00/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.00/1.82
% 8.00/1.83 % SZS output start Proof for theBenchmark
% 8.00/1.83 Assumptions after simplification:
% 8.00/1.83 ---------------------------------
% 8.00/1.83
% 8.00/1.83 (additive_commutativity)
% 8.00/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 8.00/1.86 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 8.00/1.86 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 8.00/1.86 (addition(v1, v0) = v2 & $i(v2)))
% 8.00/1.86
% 8.00/1.86 (domain2)
% 8.00/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 8.00/1.86 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 8.00/1.86 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 8.00/1.86 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.00/1.86 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 8.00/1.86 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) =
% 8.00/1.86 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 8.00/1.86
% 8.00/1.86 (domain5)
% 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.00/1.87 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~
% 8.00/1.87 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5
% 8.00/1.87 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.00/1.87 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 8.00/1.87 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 &
% 8.00/1.87 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 8.00/1.87
% 8.00/1.87 (goals)
% 8.00/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.00/1.87 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 8.00/1.87 ? [v11: $i] : ( ~ (v11 = v6) & domain(v9) = v10 & domain(v7) = v8 &
% 8.00/1.87 domain(v5) = v6 & domain(v2) = v4 & multiplication(v3, v4) = v5 &
% 8.00/1.87 multiplication(v1, v4) = v9 & multiplication(v0, v4) = v7 & addition(v8,
% 8.00/1.87 v10) = v11 & addition(v0, v1) = v3 & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 8.00/1.87 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.00/1.87
% 8.00/1.87 (left_distributivity)
% 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.00/1.87 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 8.00/1.87 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 8.00/1.87 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 8.00/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.00/1.87 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 8.00/1.87 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 8.00/1.87 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 8.00/1.87 & $i(v4)))
% 8.00/1.87
% 8.00/1.87 (function-axioms)
% 8.00/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.00/1.88 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 8.00/1.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.00/1.88 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 8.00/1.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 8.00/1.88 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.00/1.88 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 8.00/1.88
% 8.00/1.88 Further assumptions not needed in the proof:
% 8.00/1.88 --------------------------------------------
% 8.00/1.88 additive_associativity, additive_idempotence, additive_identity, domain1,
% 8.00/1.88 domain3, domain4, left_annihilation, multiplicative_associativity,
% 8.00/1.88 multiplicative_left_identity, multiplicative_right_identity, order,
% 8.00/1.88 right_annihilation, right_distributivity
% 8.00/1.88
% 8.00/1.88 Those formulas are unsatisfiable:
% 8.00/1.88 ---------------------------------
% 8.00/1.88
% 8.00/1.88 Begin of proof
% 8.00/1.88 |
% 8.00/1.88 | ALPHA: (additive_commutativity) implies:
% 8.56/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 8.56/1.88 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 8.56/1.88 |
% 8.56/1.88 | ALPHA: (left_distributivity) implies:
% 8.56/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 8.56/1.88 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~
% 8.56/1.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 8.56/1.88 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 8.56/1.88 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 8.56/1.88 |
% 8.56/1.88 | ALPHA: (domain2) implies:
% 8.56/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) =
% 8.56/1.88 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.56/1.88 | $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 &
% 8.56/1.88 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 8.56/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1)
% 8.56/1.89 | = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 8.56/1.89 | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 &
% 8.56/1.89 | multiplication(v0, v1) = v4 & $i(v5) & $i(v4)))
% 8.56/1.89 |
% 8.56/1.89 | ALPHA: (domain5) implies:
% 8.56/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 8.56/1.89 | ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) =
% 8.56/1.89 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 &
% 8.56/1.89 | addition(v0, v1) = v5 & $i(v5) & $i(v4)))
% 8.56/1.89 |
% 8.56/1.89 | ALPHA: (function-axioms) implies:
% 8.56/1.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 8.56/1.89 | v1) | ~ (domain(v2) = v0))
% 8.56/1.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.56/1.89 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 8.56/1.89 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.56/1.89 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 8.56/1.89 |
% 8.56/1.89 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2,
% 8.56/1.89 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9,
% 8.56/1.89 | all_20_10, all_20_11 gives:
% 8.56/1.89 | (9) ~ (all_20_0 = all_20_5) & domain(all_20_2) = all_20_1 &
% 8.56/1.89 | domain(all_20_4) = all_20_3 & domain(all_20_6) = all_20_5 &
% 8.56/1.89 | domain(all_20_9) = all_20_7 & multiplication(all_20_8, all_20_7) =
% 8.56/1.89 | all_20_6 & multiplication(all_20_10, all_20_7) = all_20_2 &
% 8.56/1.89 | multiplication(all_20_11, all_20_7) = all_20_4 & addition(all_20_3,
% 8.56/1.89 | all_20_1) = all_20_0 & addition(all_20_11, all_20_10) = all_20_8 &
% 8.56/1.89 | $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & $i(all_20_3) &
% 8.56/1.89 | $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & $i(all_20_7) &
% 8.56/1.89 | $i(all_20_8) & $i(all_20_9) & $i(all_20_10) & $i(all_20_11)
% 8.56/1.89 |
% 8.56/1.89 | ALPHA: (9) implies:
% 8.62/1.89 | (10) ~ (all_20_0 = all_20_5)
% 8.62/1.89 | (11) $i(all_20_11)
% 8.62/1.89 | (12) $i(all_20_10)
% 8.62/1.89 | (13) $i(all_20_9)
% 8.62/1.89 | (14) $i(all_20_7)
% 8.62/1.89 | (15) $i(all_20_4)
% 8.62/1.89 | (16) $i(all_20_2)
% 8.62/1.89 | (17) addition(all_20_11, all_20_10) = all_20_8
% 8.62/1.89 | (18) addition(all_20_3, all_20_1) = all_20_0
% 8.62/1.89 | (19) multiplication(all_20_11, all_20_7) = all_20_4
% 8.62/1.90 | (20) multiplication(all_20_10, all_20_7) = all_20_2
% 8.62/1.90 | (21) multiplication(all_20_8, all_20_7) = all_20_6
% 8.62/1.90 | (22) domain(all_20_9) = all_20_7
% 8.62/1.90 | (23) domain(all_20_6) = all_20_5
% 8.62/1.90 | (24) domain(all_20_4) = all_20_3
% 8.62/1.90 | (25) domain(all_20_2) = all_20_1
% 8.62/1.90 |
% 8.62/1.90 | GROUND_INST: instantiating (1) with all_20_10, all_20_11, all_20_8,
% 8.62/1.90 | simplifying with (11), (12), (17) gives:
% 8.62/1.90 | (26) addition(all_20_10, all_20_11) = all_20_8 & $i(all_20_8)
% 8.62/1.90 |
% 8.62/1.90 | ALPHA: (26) implies:
% 8.62/1.90 | (27) $i(all_20_8)
% 8.62/1.90 |
% 8.62/1.90 | GROUND_INST: instantiating (2) with all_20_11, all_20_10, all_20_7, all_20_8,
% 8.62/1.90 | all_20_6, simplifying with (11), (12), (14), (17), (21) gives:
% 8.62/1.90 | (28) ? [v0: $i] : ? [v1: $i] : (multiplication(all_20_10, all_20_7) = v1
% 8.62/1.90 | & multiplication(all_20_11, all_20_7) = v0 & addition(v0, v1) =
% 8.62/1.90 | all_20_6 & $i(v1) & $i(v0) & $i(all_20_6))
% 8.62/1.90 |
% 8.62/1.90 | GROUND_INST: instantiating (3) with all_20_8, all_20_7, all_20_6, simplifying
% 8.62/1.90 | with (14), (21), (27) gives:
% 8.62/1.90 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 8.62/1.90 | domain(all_20_6) = v0 & domain(all_20_7) = v1 &
% 8.62/1.90 | multiplication(all_20_8, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 8.62/1.90 |
% 8.62/1.90 | GROUND_INST: instantiating (4) with all_20_8, all_20_9, all_20_7, all_20_6,
% 8.62/1.90 | simplifying with (13), (21), (22), (27) gives:
% 8.62/1.90 | (30) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_6) = v1 &
% 8.62/1.90 | multiplication(all_20_8, all_20_9) = v0 & $i(v1) & $i(v0))
% 8.62/1.90 |
% 8.62/1.90 | GROUND_INST: instantiating (5) with all_20_4, all_20_2, all_20_3, all_20_1,
% 8.62/1.90 | all_20_0, simplifying with (15), (16), (18), (24), (25) gives:
% 8.62/1.90 | (31) ? [v0: $i] : (domain(v0) = all_20_0 & addition(all_20_4, all_20_2) =
% 8.62/1.90 | v0 & $i(v0) & $i(all_20_0))
% 8.62/1.90 |
% 8.62/1.90 | DELTA: instantiating (31) with fresh symbol all_38_0 gives:
% 8.62/1.90 | (32) domain(all_38_0) = all_20_0 & addition(all_20_4, all_20_2) = all_38_0
% 8.62/1.90 | & $i(all_38_0) & $i(all_20_0)
% 8.62/1.90 |
% 8.62/1.90 | ALPHA: (32) implies:
% 8.62/1.90 | (33) addition(all_20_4, all_20_2) = all_38_0
% 8.62/1.90 | (34) domain(all_38_0) = all_20_0
% 8.62/1.90 |
% 8.62/1.90 | DELTA: instantiating (30) with fresh symbols all_44_0, all_44_1 gives:
% 8.62/1.90 | (35) domain(all_44_1) = all_44_0 & domain(all_20_6) = all_44_0 &
% 8.62/1.90 | multiplication(all_20_8, all_20_9) = all_44_1 & $i(all_44_0) &
% 8.62/1.90 | $i(all_44_1)
% 8.62/1.90 |
% 8.62/1.90 | ALPHA: (35) implies:
% 8.62/1.90 | (36) domain(all_20_6) = all_44_0
% 8.62/1.90 |
% 8.62/1.90 | DELTA: instantiating (28) with fresh symbols all_46_0, all_46_1 gives:
% 8.62/1.91 | (37) multiplication(all_20_10, all_20_7) = all_46_0 &
% 8.62/1.91 | multiplication(all_20_11, all_20_7) = all_46_1 & addition(all_46_1,
% 8.62/1.91 | all_46_0) = all_20_6 & $i(all_46_0) & $i(all_46_1) & $i(all_20_6)
% 8.62/1.91 |
% 8.62/1.91 | ALPHA: (37) implies:
% 8.62/1.91 | (38) addition(all_46_1, all_46_0) = all_20_6
% 8.62/1.91 | (39) multiplication(all_20_11, all_20_7) = all_46_1
% 8.62/1.91 | (40) multiplication(all_20_10, all_20_7) = all_46_0
% 8.62/1.91 |
% 8.62/1.91 | DELTA: instantiating (29) with fresh symbols all_50_0, all_50_1, all_50_2
% 8.62/1.91 | gives:
% 8.62/1.91 | (41) domain(all_50_0) = all_50_2 & domain(all_20_6) = all_50_2 &
% 8.62/1.91 | domain(all_20_7) = all_50_1 & multiplication(all_20_8, all_50_1) =
% 8.62/1.91 | all_50_0 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2)
% 8.62/1.91 |
% 8.62/1.91 | ALPHA: (41) implies:
% 8.62/1.91 | (42) domain(all_20_6) = all_50_2
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (8) with all_20_4, all_46_1, all_20_7, all_20_11,
% 8.62/1.91 | simplifying with (19), (39) gives:
% 8.62/1.91 | (43) all_46_1 = all_20_4
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (8) with all_20_2, all_46_0, all_20_7, all_20_10,
% 8.62/1.91 | simplifying with (20), (40) gives:
% 8.62/1.91 | (44) all_46_0 = all_20_2
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (6) with all_20_5, all_50_2, all_20_6, simplifying
% 8.62/1.91 | with (23), (42) gives:
% 8.62/1.91 | (45) all_50_2 = all_20_5
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (6) with all_44_0, all_50_2, all_20_6, simplifying
% 8.62/1.91 | with (36), (42) gives:
% 8.62/1.91 | (46) all_50_2 = all_44_0
% 8.62/1.91 |
% 8.62/1.91 | COMBINE_EQS: (45), (46) imply:
% 8.62/1.91 | (47) all_44_0 = all_20_5
% 8.62/1.91 |
% 8.62/1.91 | REDUCE: (38), (43), (44) imply:
% 8.62/1.91 | (48) addition(all_20_4, all_20_2) = all_20_6
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (7) with all_38_0, all_20_6, all_20_2, all_20_4,
% 8.62/1.91 | simplifying with (33), (48) gives:
% 8.62/1.91 | (49) all_38_0 = all_20_6
% 8.62/1.91 |
% 8.62/1.91 | REDUCE: (34), (49) imply:
% 8.62/1.91 | (50) domain(all_20_6) = all_20_0
% 8.62/1.91 |
% 8.62/1.91 | GROUND_INST: instantiating (6) with all_20_5, all_20_0, all_20_6, simplifying
% 8.62/1.91 | with (23), (50) gives:
% 8.62/1.91 | (51) all_20_0 = all_20_5
% 8.62/1.91 |
% 8.62/1.91 | REDUCE: (10), (51) imply:
% 8.62/1.91 | (52) $false
% 8.62/1.91 |
% 8.62/1.91 | CLOSE: (52) is inconsistent.
% 8.62/1.91 |
% 8.62/1.91 End of proof
% 8.62/1.91 % SZS output end Proof for theBenchmark
% 8.62/1.91
% 8.62/1.91 1302ms
%------------------------------------------------------------------------------