TSTP Solution File: SET575+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET575+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 15:25:21 EDT 2023
% Result : Theorem 3.39s 1.16s
% Output : Proof 3.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET575+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:38:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.88/0.94 Prover 1: Preprocessing ...
% 1.88/0.94 Prover 4: Preprocessing ...
% 2.16/0.98 Prover 3: Preprocessing ...
% 2.16/0.98 Prover 0: Preprocessing ...
% 2.16/0.98 Prover 5: Preprocessing ...
% 2.16/0.98 Prover 2: Preprocessing ...
% 2.16/0.98 Prover 6: Preprocessing ...
% 2.67/1.05 Prover 2: Constructing countermodel ...
% 2.67/1.07 Prover 5: Proving ...
% 2.83/1.08 Prover 6: Proving ...
% 2.83/1.08 Prover 3: Constructing countermodel ...
% 2.83/1.08 Prover 1: Constructing countermodel ...
% 2.83/1.11 Prover 4: Constructing countermodel ...
% 2.83/1.11 Prover 0: Proving ...
% 3.39/1.16 Prover 2: proved (512ms)
% 3.39/1.16 Prover 3: proved (511ms)
% 3.39/1.16
% 3.39/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.16
% 3.39/1.16
% 3.39/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.16
% 3.39/1.16 Prover 5: stopped
% 3.39/1.17 Prover 0: stopped
% 3.39/1.17 Prover 6: stopped
% 3.39/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.39/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.39/1.19 Prover 8: Preprocessing ...
% 3.39/1.19 Prover 7: Preprocessing ...
% 3.39/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.39/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.39/1.19 Prover 10: Preprocessing ...
% 3.39/1.19 Prover 11: Preprocessing ...
% 3.39/1.19 Prover 1: Found proof (size 13)
% 3.39/1.19 Prover 1: proved (549ms)
% 3.39/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.39/1.19 Prover 4: stopped
% 3.39/1.20 Prover 10: Constructing countermodel ...
% 3.39/1.20 Prover 10: stopped
% 3.39/1.20 Prover 7: Constructing countermodel ...
% 3.39/1.20 Prover 7: stopped
% 3.39/1.20 Prover 13: Preprocessing ...
% 3.39/1.20 Prover 11: stopped
% 3.39/1.22 Prover 13: Constructing countermodel ...
% 3.39/1.22 Prover 13: stopped
% 3.93/1.23 Prover 8: Warning: ignoring some quantifiers
% 3.93/1.23 Prover 8: Constructing countermodel ...
% 3.93/1.23 Prover 8: stopped
% 3.93/1.23
% 3.93/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/1.23
% 3.93/1.24 % SZS output start Proof for theBenchmark
% 3.93/1.24 Assumptions after simplification:
% 3.93/1.24 ---------------------------------
% 3.93/1.24
% 3.93/1.24 (intersect_defn)
% 3.93/1.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) =
% 3.93/1.28 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~
% 3.93/1.28 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0:
% 3.93/1.28 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 3.93/1.28 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 3.93/1.28
% 3.93/1.28 (prove_th15)
% 3.93/1.28 ? [v0: $i] : ? [v1: $i] : (intersect(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2:
% 3.93/1.28 $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 3.93/1.28 member(v2, v1) = v3)))
% 3.93/1.28
% 3.93/1.28 (function-axioms)
% 3.93/1.28 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 3.93/1.28 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 3.93/1.28 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 3.93/1.28 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 3.93/1.29 = v0))
% 3.93/1.29
% 3.93/1.29 Further assumptions not needed in the proof:
% 3.93/1.29 --------------------------------------------
% 3.93/1.29 symmetry_of_intersect
% 3.93/1.29
% 3.93/1.29 Those formulas are unsatisfiable:
% 3.93/1.29 ---------------------------------
% 3.93/1.29
% 3.93/1.29 Begin of proof
% 3.93/1.29 |
% 3.93/1.29 | ALPHA: (intersect_defn) implies:
% 3.93/1.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) |
% 3.93/1.29 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 &
% 3.93/1.29 | $i(v2)))
% 3.93/1.29 |
% 3.93/1.29 | ALPHA: (function-axioms) implies:
% 3.93/1.29 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 3.93/1.29 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 3.93/1.29 | = v0))
% 3.93/1.29 |
% 3.93/1.29 | DELTA: instantiating (prove_th15) with fresh symbols all_5_0, all_5_1 gives:
% 3.93/1.30 | (3) intersect(all_5_1, all_5_0) = 0 & $i(all_5_0) & $i(all_5_1) & ! [v0:
% 3.93/1.30 | $i] : ( ~ (member(v0, all_5_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 3.93/1.30 | (v1 = 0) & member(v0, all_5_0) = v1))
% 3.93/1.30 |
% 3.93/1.30 | ALPHA: (3) implies:
% 3.93/1.30 | (4) $i(all_5_1)
% 3.93/1.30 | (5) $i(all_5_0)
% 3.93/1.30 | (6) intersect(all_5_1, all_5_0) = 0
% 3.93/1.30 | (7) ! [v0: $i] : ( ~ (member(v0, all_5_1) = 0) | ~ $i(v0) | ? [v1: int]
% 3.93/1.30 | : ( ~ (v1 = 0) & member(v0, all_5_0) = v1))
% 3.93/1.30 |
% 3.93/1.30 | GROUND_INST: instantiating (1) with all_5_1, all_5_0, simplifying with (4),
% 3.93/1.30 | (5), (6) gives:
% 3.93/1.30 | (8) ? [v0: $i] : (member(v0, all_5_0) = 0 & member(v0, all_5_1) = 0 &
% 3.93/1.30 | $i(v0))
% 3.93/1.30 |
% 3.93/1.30 | DELTA: instantiating (8) with fresh symbol all_14_0 gives:
% 3.93/1.30 | (9) member(all_14_0, all_5_0) = 0 & member(all_14_0, all_5_1) = 0 &
% 3.93/1.30 | $i(all_14_0)
% 3.93/1.30 |
% 3.93/1.30 | ALPHA: (9) implies:
% 3.93/1.30 | (10) $i(all_14_0)
% 3.93/1.30 | (11) member(all_14_0, all_5_1) = 0
% 3.93/1.30 | (12) member(all_14_0, all_5_0) = 0
% 3.93/1.30 |
% 3.93/1.30 | GROUND_INST: instantiating (7) with all_14_0, simplifying with (10), (11)
% 3.93/1.30 | gives:
% 3.93/1.30 | (13) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_5_0) = v0)
% 3.93/1.30 |
% 3.93/1.30 | DELTA: instantiating (13) with fresh symbol all_21_0 gives:
% 3.93/1.31 | (14) ~ (all_21_0 = 0) & member(all_14_0, all_5_0) = all_21_0
% 3.93/1.31 |
% 3.93/1.31 | ALPHA: (14) implies:
% 3.93/1.31 | (15) ~ (all_21_0 = 0)
% 3.93/1.31 | (16) member(all_14_0, all_5_0) = all_21_0
% 3.93/1.31 |
% 3.93/1.31 | GROUND_INST: instantiating (2) with 0, all_21_0, all_5_0, all_14_0,
% 3.93/1.31 | simplifying with (12), (16) gives:
% 3.93/1.31 | (17) all_21_0 = 0
% 3.93/1.31 |
% 3.93/1.31 | REDUCE: (15), (17) imply:
% 3.93/1.31 | (18) $false
% 3.93/1.31 |
% 3.93/1.31 | CLOSE: (18) is inconsistent.
% 3.93/1.31 |
% 3.93/1.31 End of proof
% 3.93/1.31 % SZS output end Proof for theBenchmark
% 3.93/1.31
% 3.93/1.31 685ms
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