TSTP Solution File: SEU134+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU134+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 17:42:41 EDT 2023
% Result : Theorem 3.97s 1.22s
% Output : Proof 4.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU134+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 01:13:41 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.46/0.86 Prover 4: Preprocessing ...
% 1.46/0.86 Prover 1: Preprocessing ...
% 1.92/0.90 Prover 3: Preprocessing ...
% 1.92/0.90 Prover 6: Preprocessing ...
% 1.92/0.90 Prover 2: Preprocessing ...
% 1.92/0.90 Prover 0: Preprocessing ...
% 1.92/0.90 Prover 5: Preprocessing ...
% 2.97/1.08 Prover 1: Warning: ignoring some quantifiers
% 2.97/1.09 Prover 2: Proving ...
% 2.97/1.09 Prover 3: Warning: ignoring some quantifiers
% 2.97/1.09 Prover 5: Proving ...
% 2.97/1.10 Prover 3: Constructing countermodel ...
% 2.97/1.10 Prover 6: Proving ...
% 2.97/1.10 Prover 4: Constructing countermodel ...
% 2.97/1.10 Prover 1: Constructing countermodel ...
% 2.97/1.10 Prover 0: Proving ...
% 3.97/1.22 Prover 3: proved (677ms)
% 3.97/1.22
% 3.97/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.22
% 3.97/1.23 Prover 6: stopped
% 3.97/1.23 Prover 0: proved (690ms)
% 3.97/1.23
% 3.97/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.23
% 3.97/1.23 Prover 2: stopped
% 3.97/1.23 Prover 5: proved (687ms)
% 3.97/1.23
% 3.97/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.23
% 3.97/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.97/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.97/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.97/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.97/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.97/1.25 Prover 10: Preprocessing ...
% 3.97/1.26 Prover 13: Preprocessing ...
% 3.97/1.26 Prover 11: Preprocessing ...
% 3.97/1.26 Prover 7: Preprocessing ...
% 4.67/1.27 Prover 8: Preprocessing ...
% 4.67/1.27 Prover 4: Found proof (size 28)
% 4.67/1.27 Prover 4: proved (728ms)
% 4.67/1.28 Prover 1: stopped
% 4.67/1.28 Prover 13: stopped
% 4.85/1.30 Prover 11: stopped
% 4.85/1.30 Prover 10: Warning: ignoring some quantifiers
% 4.85/1.31 Prover 10: Constructing countermodel ...
% 4.85/1.31 Prover 7: Warning: ignoring some quantifiers
% 4.85/1.31 Prover 10: stopped
% 4.85/1.31 Prover 7: Constructing countermodel ...
% 4.85/1.32 Prover 7: stopped
% 4.85/1.32 Prover 8: Warning: ignoring some quantifiers
% 4.85/1.33 Prover 8: Constructing countermodel ...
% 4.85/1.33 Prover 8: stopped
% 4.85/1.33
% 4.85/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.85/1.33
% 4.85/1.34 % SZS output start Proof for theBenchmark
% 4.85/1.34 Assumptions after simplification:
% 4.85/1.34 ---------------------------------
% 4.85/1.34
% 4.85/1.34 (l32_xboole_1)
% 4.85/1.38 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 4.85/1.38 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 4.85/1.38 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 4.85/1.38 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 4.85/1.38 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & !
% 4.85/1.38 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1)
% 4.85/1.38 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 4.85/1.38 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) =
% 4.85/1.38 empty_set)
% 4.85/1.38
% 4.85/1.38 (t37_xboole_1)
% 4.85/1.38 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 4.85/1.38 (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) & $i(v0)
% 4.85/1.38 & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = 0))))
% 4.85/1.38
% 4.85/1.38 (function-axioms)
% 4.85/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.85/1.39 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.85/1.39 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.85/1.39 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.85/1.39 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.85/1.39
% 4.85/1.39 Further assumptions not needed in the proof:
% 4.85/1.39 --------------------------------------------
% 4.85/1.39 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_xboole_0, fc1_xboole_0,
% 4.85/1.39 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t3_boole, t4_boole, t6_boole,
% 4.85/1.39 t7_boole, t8_boole
% 4.85/1.39
% 4.85/1.39 Those formulas are unsatisfiable:
% 4.85/1.39 ---------------------------------
% 4.85/1.39
% 4.85/1.39 Begin of proof
% 4.85/1.39 |
% 4.85/1.39 | ALPHA: (l32_xboole_1) implies:
% 4.85/1.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.85/1.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = empty_set)
% 4.85/1.39 | & set_difference(v0, v1) = v3 & $i(v3)))
% 4.85/1.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 4.85/1.39 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 4.85/1.39 | : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 4.85/1.39 |
% 4.85/1.39 | ALPHA: (t37_xboole_1) implies:
% 4.85/1.39 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 4.85/1.39 | (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) &
% 4.85/1.39 | $i(v0) & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 =
% 4.85/1.39 | 0))))
% 4.85/1.39 |
% 4.85/1.39 | ALPHA: (function-axioms) implies:
% 4.85/1.40 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.85/1.40 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 4.85/1.40 | = v0))
% 4.85/1.40 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.85/1.40 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 4.85/1.40 |
% 4.85/1.40 | DELTA: instantiating (3) with fresh symbols all_16_0, all_16_1, all_16_2,
% 4.85/1.40 | all_16_3 gives:
% 4.85/1.40 | (6) set_difference(all_16_3, all_16_2) = all_16_1 & subset(all_16_3,
% 4.85/1.40 | all_16_2) = all_16_0 & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) &
% 4.85/1.40 | ((all_16_0 = 0 & ~ (all_16_1 = empty_set)) | (all_16_1 = empty_set &
% 4.85/1.40 | ~ (all_16_0 = 0)))
% 4.85/1.40 |
% 4.85/1.40 | ALPHA: (6) implies:
% 4.85/1.40 | (7) $i(all_16_3)
% 4.85/1.40 | (8) $i(all_16_2)
% 4.85/1.40 | (9) subset(all_16_3, all_16_2) = all_16_0
% 4.85/1.40 | (10) set_difference(all_16_3, all_16_2) = all_16_1
% 4.85/1.40 | (11) (all_16_0 = 0 & ~ (all_16_1 = empty_set)) | (all_16_1 = empty_set &
% 4.85/1.40 | ~ (all_16_0 = 0))
% 4.85/1.40 |
% 4.85/1.40 | GROUND_INST: instantiating (1) with all_16_3, all_16_2, all_16_0, simplifying
% 4.85/1.40 | with (7), (8), (9) gives:
% 4.85/1.40 | (12) all_16_0 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) &
% 4.85/1.40 | set_difference(all_16_3, all_16_2) = v0 & $i(v0))
% 4.85/1.40 |
% 4.85/1.40 | GROUND_INST: instantiating (2) with all_16_3, all_16_2, all_16_1, simplifying
% 4.85/1.40 | with (7), (8), (10) gives:
% 4.85/1.41 | (13) all_16_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_16_3,
% 4.85/1.41 | all_16_2) = v0)
% 4.85/1.41 |
% 4.85/1.41 | BETA: splitting (11) gives:
% 4.85/1.41 |
% 4.85/1.41 | Case 1:
% 4.85/1.41 | |
% 4.85/1.41 | | (14) all_16_0 = 0 & ~ (all_16_1 = empty_set)
% 4.85/1.41 | |
% 4.85/1.41 | | ALPHA: (14) implies:
% 4.85/1.41 | | (15) all_16_0 = 0
% 4.85/1.41 | | (16) ~ (all_16_1 = empty_set)
% 4.85/1.41 | |
% 4.85/1.41 | | REDUCE: (9), (15) imply:
% 4.85/1.41 | | (17) subset(all_16_3, all_16_2) = 0
% 4.85/1.41 | |
% 4.85/1.41 | | BETA: splitting (13) gives:
% 4.85/1.41 | |
% 4.85/1.41 | | Case 1:
% 4.85/1.41 | | |
% 4.85/1.41 | | | (18) all_16_1 = empty_set
% 4.85/1.41 | | |
% 4.85/1.41 | | | REDUCE: (16), (18) imply:
% 4.85/1.41 | | | (19) $false
% 4.85/1.41 | | |
% 4.85/1.41 | | | CLOSE: (19) is inconsistent.
% 4.85/1.41 | | |
% 4.85/1.41 | | Case 2:
% 4.85/1.41 | | |
% 4.85/1.41 | | | (20) ? [v0: int] : ( ~ (v0 = 0) & subset(all_16_3, all_16_2) = v0)
% 4.85/1.41 | | |
% 4.85/1.41 | | | DELTA: instantiating (20) with fresh symbol all_35_0 gives:
% 4.85/1.41 | | | (21) ~ (all_35_0 = 0) & subset(all_16_3, all_16_2) = all_35_0
% 4.85/1.41 | | |
% 4.85/1.41 | | | ALPHA: (21) implies:
% 4.85/1.41 | | | (22) ~ (all_35_0 = 0)
% 4.85/1.41 | | | (23) subset(all_16_3, all_16_2) = all_35_0
% 4.85/1.41 | | |
% 4.85/1.41 | | | GROUND_INST: instantiating (4) with 0, all_35_0, all_16_2, all_16_3,
% 4.85/1.41 | | | simplifying with (17), (23) gives:
% 4.85/1.41 | | | (24) all_35_0 = 0
% 4.85/1.41 | | |
% 4.85/1.41 | | | REDUCE: (22), (24) imply:
% 4.85/1.41 | | | (25) $false
% 4.85/1.41 | | |
% 4.85/1.41 | | | CLOSE: (25) is inconsistent.
% 4.85/1.41 | | |
% 4.85/1.41 | | End of split
% 4.85/1.41 | |
% 4.85/1.41 | Case 2:
% 4.85/1.41 | |
% 4.85/1.41 | | (26) all_16_1 = empty_set & ~ (all_16_0 = 0)
% 4.85/1.41 | |
% 4.85/1.41 | | ALPHA: (26) implies:
% 4.85/1.41 | | (27) all_16_1 = empty_set
% 4.85/1.41 | | (28) ~ (all_16_0 = 0)
% 4.85/1.41 | |
% 4.85/1.41 | | REDUCE: (10), (27) imply:
% 4.85/1.41 | | (29) set_difference(all_16_3, all_16_2) = empty_set
% 4.85/1.41 | |
% 4.85/1.41 | | BETA: splitting (12) gives:
% 4.85/1.41 | |
% 4.85/1.41 | | Case 1:
% 4.85/1.41 | | |
% 4.85/1.41 | | | (30) all_16_0 = 0
% 4.85/1.41 | | |
% 4.85/1.41 | | | REDUCE: (28), (30) imply:
% 4.85/1.41 | | | (31) $false
% 4.85/1.41 | | |
% 4.85/1.41 | | | CLOSE: (31) is inconsistent.
% 4.85/1.41 | | |
% 4.85/1.41 | | Case 2:
% 4.85/1.41 | | |
% 4.85/1.41 | | | (32) ? [v0: $i] : ( ~ (v0 = empty_set) & set_difference(all_16_3,
% 4.85/1.41 | | | all_16_2) = v0 & $i(v0))
% 4.85/1.41 | | |
% 4.85/1.41 | | | DELTA: instantiating (32) with fresh symbol all_35_0 gives:
% 4.85/1.41 | | | (33) ~ (all_35_0 = empty_set) & set_difference(all_16_3, all_16_2) =
% 4.85/1.41 | | | all_35_0 & $i(all_35_0)
% 4.85/1.41 | | |
% 4.85/1.41 | | | ALPHA: (33) implies:
% 4.85/1.41 | | | (34) ~ (all_35_0 = empty_set)
% 4.85/1.41 | | | (35) set_difference(all_16_3, all_16_2) = all_35_0
% 4.85/1.42 | | |
% 4.85/1.42 | | | GROUND_INST: instantiating (5) with empty_set, all_35_0, all_16_2,
% 4.85/1.42 | | | all_16_3, simplifying with (29), (35) gives:
% 4.85/1.42 | | | (36) all_35_0 = empty_set
% 4.85/1.42 | | |
% 4.85/1.42 | | | REDUCE: (34), (36) imply:
% 4.85/1.42 | | | (37) $false
% 4.85/1.42 | | |
% 4.85/1.42 | | | CLOSE: (37) is inconsistent.
% 4.85/1.42 | | |
% 4.85/1.42 | | End of split
% 4.85/1.42 | |
% 4.85/1.42 | End of split
% 4.85/1.42 |
% 4.85/1.42 End of proof
% 4.85/1.42 % SZS output end Proof for theBenchmark
% 4.85/1.42
% 4.85/1.42 895ms
%------------------------------------------------------------------------------