TSTP Solution File: KRS003_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS003_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 05:50:58 EDT 2023
% Result : Theorem 5.67s 1.55s
% Output : Proof 7.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS003_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n015.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 : Mon Aug 28 02:24:09 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.33/1.06 Prover 1: Preprocessing ...
% 2.33/1.07 Prover 4: Preprocessing ...
% 2.83/1.11 Prover 5: Preprocessing ...
% 2.83/1.11 Prover 3: Preprocessing ...
% 2.83/1.11 Prover 0: Preprocessing ...
% 2.83/1.11 Prover 2: Preprocessing ...
% 2.83/1.11 Prover 6: Preprocessing ...
% 3.76/1.35 Prover 2: Proving ...
% 3.76/1.35 Prover 5: Proving ...
% 3.76/1.37 Prover 1: Constructing countermodel ...
% 3.76/1.37 Prover 6: Constructing countermodel ...
% 3.76/1.39 Prover 3: Constructing countermodel ...
% 5.09/1.44 Prover 0: Proving ...
% 5.09/1.45 Prover 4: Constructing countermodel ...
% 5.09/1.50 Prover 6: gave up
% 5.09/1.50 Prover 3: gave up
% 5.09/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.09/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.67/1.53 Prover 7: Preprocessing ...
% 5.67/1.53 Prover 1: gave up
% 5.67/1.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.67/1.55 Prover 2: proved (906ms)
% 5.67/1.55 Prover 5: proved (904ms)
% 5.67/1.55
% 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55
% 5.67/1.55 Prover 8: Preprocessing ...
% 5.67/1.55
% 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55
% 5.67/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.67/1.55 Prover 0: stopped
% 5.67/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.67/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.67/1.57 Prover 9: Preprocessing ...
% 6.19/1.59 Prover 10: Preprocessing ...
% 6.19/1.59 Prover 13: Preprocessing ...
% 6.19/1.61 Prover 11: Preprocessing ...
% 6.19/1.61 Prover 7: Constructing countermodel ...
% 6.19/1.62 Prover 13: Warning: ignoring some quantifiers
% 6.19/1.63 Prover 7: gave up
% 6.19/1.63 Prover 13: Constructing countermodel ...
% 6.19/1.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.19/1.64 Prover 10: Constructing countermodel ...
% 6.19/1.65 Prover 8: Warning: ignoring some quantifiers
% 6.19/1.66 Prover 8: Constructing countermodel ...
% 6.19/1.66 Prover 10: gave up
% 6.19/1.67 Prover 16: Preprocessing ...
% 6.86/1.69 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.97/1.69 Prover 16: Warning: ignoring some quantifiers
% 6.97/1.70 Prover 16: Constructing countermodel ...
% 7.14/1.72 Prover 19: Preprocessing ...
% 7.23/1.73 Prover 9: Constructing countermodel ...
% 7.23/1.73 Prover 8: gave up
% 7.23/1.73 Prover 9: stopped
% 7.23/1.74 Prover 13: Found proof (size 25)
% 7.23/1.74 Prover 13: proved (179ms)
% 7.23/1.74 Prover 4: stopped
% 7.23/1.74 Prover 16: stopped
% 7.23/1.77 Prover 11: Constructing countermodel ...
% 7.23/1.77 Prover 19: Warning: ignoring some quantifiers
% 7.23/1.78 Prover 19: Constructing countermodel ...
% 7.23/1.79 Prover 19: stopped
% 7.23/1.79 Prover 11: stopped
% 7.23/1.79
% 7.23/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.23/1.79
% 7.23/1.79 % SZS output start Proof for theBenchmark
% 7.23/1.80 Assumptions after simplification:
% 7.23/1.80 ---------------------------------
% 7.23/1.80
% 7.23/1.80 (clause_11)
% 7.23/1.80 ! [v0: real] : ! [v1: real] : ! [v2: unreal] : ( ~ real(v1) | ~ real(v0) |
% 7.23/1.80 ~ unreal(v2) | ~ s(v2, v1) | ~ s(v2, v0) | ~ s1most(v2) | equalish(v1,
% 7.23/1.80 v0))
% 7.23/1.80
% 7.23/1.80 (clause_15)
% 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ e(v0) | c(v0))
% 7.23/1.80
% 7.23/1.80 (clause_16)
% 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ f(v0) | d(v0))
% 7.23/1.80
% 7.23/1.80 (clause_1__clause_2)
% 7.23/1.80 unreal(exist) & e(exist) & f(exist)
% 7.23/1.80
% 7.23/1.80 (clause_3)
% 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ c(v0) | s2least(v0))
% 7.23/1.80
% 7.23/1.80 (clause_5)
% 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r2(v0) = v1) | ~ unreal(v0) | ~
% 7.75/1.83 s2least(v0) | ? [v2: real] : (u1r1(v0) = v2 & real(v2) & ~ equalish(v1,
% 7.75/1.83 v2))) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1:
% 7.75/1.83 real] : ? [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) &
% 7.75/1.83 real(v1) & ~ equalish(v1, v2)))
% 7.75/1.83
% 7.75/1.83 (clause_6)
% 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r1(v0) = v1) | ~ unreal(v0) | ~
% 7.75/1.83 s2least(v0) | s(v0, v1)) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0)
% 7.75/1.83 | ? [v1: real] : (u1r1(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.83
% 7.75/1.83 (clause_7)
% 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r2(v0) = v1) | ~ unreal(v0) | ~
% 7.75/1.83 s2least(v0) | s(v0, v1)) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0)
% 7.75/1.83 | ? [v1: real] : (u1r2(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.83
% 7.75/1.83 (clause_9)
% 7.75/1.83 ! [v0: unreal] : ( ~ unreal(v0) | ~ d(v0) | s1most(v0))
% 7.75/1.83
% 7.75/1.83 (function-axioms)
% 7.75/1.84 ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ (u3r2(v2) =
% 7.75/1.84 v1) | ~ (u3r2(v2) = v0)) & ! [v0: real] : ! [v1: real] : ! [v2:
% 7.75/1.84 unreal] : (v1 = v0 | ~ (u3r1(v2) = v1) | ~ (u3r1(v2) = v0)) & ! [v0:
% 7.75/1.84 real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ (u1r2(v2) = v1) | ~
% 7.75/1.84 (u1r2(v2) = v0)) & ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 =
% 7.75/1.84 v0 | ~ (u1r1(v2) = v1) | ~ (u1r1(v2) = v0))
% 7.75/1.84
% 7.75/1.84 Further assumptions not needed in the proof:
% 7.75/1.84 --------------------------------------------
% 7.75/1.84 clause_10, clause_12, clause_13, clause_14, clause_4, clause_8
% 7.75/1.84
% 7.75/1.84 Those formulas are unsatisfiable:
% 7.75/1.84 ---------------------------------
% 7.75/1.84
% 7.75/1.84 Begin of proof
% 7.75/1.84 |
% 7.75/1.84 | ALPHA: (clause_5) implies:
% 7.75/1.84 | (1) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] : ?
% 7.75/1.84 | [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) & real(v1) &
% 7.75/1.84 | ~ equalish(v1, v2)))
% 7.75/1.84 |
% 7.75/1.84 | ALPHA: (clause_6) implies:
% 7.75/1.84 | (2) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] :
% 7.75/1.84 | (u1r1(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.84 |
% 7.75/1.84 | ALPHA: (clause_7) implies:
% 7.75/1.84 | (3) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] :
% 7.75/1.84 | (u1r2(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.84 |
% 7.75/1.84 | ALPHA: (clause_1__clause_2) implies:
% 7.75/1.84 | (4) f(exist)
% 7.75/1.84 | (5) e(exist)
% 7.75/1.84 | (6) unreal(exist)
% 7.75/1.84 |
% 7.75/1.84 | ALPHA: (function-axioms) implies:
% 7.75/1.84 | (7) ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~
% 7.75/1.84 | (u1r1(v2) = v1) | ~ (u1r1(v2) = v0))
% 7.75/1.85 | (8) ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~
% 7.75/1.85 | (u1r2(v2) = v1) | ~ (u1r2(v2) = v0))
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (clause_16) with exist, simplifying with (4), (6)
% 7.75/1.85 | gives:
% 7.75/1.85 | (9) d(exist)
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (clause_15) with exist, simplifying with (5), (6)
% 7.75/1.85 | gives:
% 7.75/1.85 | (10) c(exist)
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (clause_9) with exist, simplifying with (6), (9)
% 7.75/1.85 | gives:
% 7.75/1.85 | (11) s1most(exist)
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (clause_3) with exist, simplifying with (6), (10)
% 7.75/1.85 | gives:
% 7.75/1.85 | (12) s2least(exist)
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (1) with exist, simplifying with (6), (12) gives:
% 7.75/1.85 | (13) ? [v0: real] : ? [v1: real] : (u1r2(exist) = v0 & u1r1(exist) = v1 &
% 7.75/1.85 | real(v1) & real(v0) & ~ equalish(v0, v1))
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (3) with exist, simplifying with (6), (12) gives:
% 7.75/1.85 | (14) ? [v0: real] : (u1r2(exist) = v0 & real(v0) & s(exist, v0))
% 7.75/1.85 |
% 7.75/1.85 | GROUND_INST: instantiating (2) with exist, simplifying with (6), (12) gives:
% 7.75/1.85 | (15) ? [v0: real] : (u1r1(exist) = v0 & real(v0) & s(exist, v0))
% 7.75/1.85 |
% 7.75/1.85 | DELTA: instantiating (15) with fresh symbol all_42_0 gives:
% 7.75/1.85 | (16) u1r1(exist) = all_42_0 & real(all_42_0) & s(exist, all_42_0)
% 7.75/1.85 |
% 7.75/1.85 | ALPHA: (16) implies:
% 7.75/1.85 | (17) s(exist, all_42_0)
% 7.75/1.85 | (18) u1r1(exist) = all_42_0
% 7.75/1.85 |
% 7.75/1.85 | DELTA: instantiating (14) with fresh symbol all_44_0 gives:
% 7.75/1.85 | (19) u1r2(exist) = all_44_0 & real(all_44_0) & s(exist, all_44_0)
% 7.75/1.85 |
% 7.75/1.85 | ALPHA: (19) implies:
% 7.75/1.85 | (20) s(exist, all_44_0)
% 7.75/1.85 | (21) u1r2(exist) = all_44_0
% 7.75/1.85 |
% 7.75/1.85 | DELTA: instantiating (13) with fresh symbols all_46_0, all_46_1 gives:
% 7.75/1.86 | (22) u1r2(exist) = all_46_1 & u1r1(exist) = all_46_0 & real(all_46_0) &
% 7.75/1.86 | real(all_46_1) & ~ equalish(all_46_1, all_46_0)
% 7.75/1.86 |
% 7.75/1.86 | ALPHA: (22) implies:
% 7.75/1.86 | (23) ~ equalish(all_46_1, all_46_0)
% 7.75/1.86 | (24) real(all_46_1)
% 7.75/1.86 | (25) real(all_46_0)
% 7.75/1.86 | (26) u1r1(exist) = all_46_0
% 7.75/1.86 | (27) u1r2(exist) = all_46_1
% 7.75/1.86 |
% 7.75/1.86 | GROUND_INST: instantiating (7) with all_42_0, all_46_0, exist, simplifying
% 7.75/1.86 | with (18), (26) gives:
% 7.75/1.86 | (28) all_46_0 = all_42_0
% 7.75/1.86 |
% 7.75/1.86 | GROUND_INST: instantiating (8) with all_44_0, all_46_1, exist, simplifying
% 7.75/1.86 | with (21), (27) gives:
% 7.75/1.86 | (29) all_46_1 = all_44_0
% 7.75/1.86 |
% 7.75/1.86 | REDUCE: (25), (28) imply:
% 7.75/1.86 | (30) real(all_42_0)
% 7.75/1.86 |
% 7.75/1.86 | REDUCE: (24), (29) imply:
% 7.75/1.86 | (31) real(all_44_0)
% 7.75/1.86 |
% 7.75/1.86 | REDUCE: (23), (28), (29) imply:
% 7.75/1.86 | (32) ~ equalish(all_44_0, all_42_0)
% 7.75/1.86 |
% 7.75/1.86 | GROUND_INST: instantiating (clause_11) with all_42_0, all_44_0, exist,
% 7.75/1.86 | simplifying with (6), (11), (17), (20), (30), (31), (32) gives:
% 7.75/1.86 | (33) $false
% 7.75/1.86 |
% 7.75/1.86 | CLOSE: (33) is inconsistent.
% 7.75/1.86 |
% 7.75/1.86 End of proof
% 7.75/1.86 % SZS output end Proof for theBenchmark
% 7.75/1.86
% 7.75/1.86 1251ms
%------------------------------------------------------------------------------