TSTP Solution File: SEU160+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU160+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 : n006.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 17:42:54 EDT 2023
% Result : Theorem 3.96s 1.28s
% Output : Proof 4.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU160+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.22/0.36 % DateTime : Wed Aug 23 20:24:08 EDT 2023
% 0.22/0.36 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.19/1.01 Prover 1: Preprocessing ...
% 2.19/1.01 Prover 4: Preprocessing ...
% 2.36/1.06 Prover 2: Preprocessing ...
% 2.36/1.06 Prover 6: Preprocessing ...
% 2.36/1.06 Prover 3: Preprocessing ...
% 2.36/1.06 Prover 0: Preprocessing ...
% 2.36/1.06 Prover 5: Preprocessing ...
% 2.97/1.13 Prover 1: Warning: ignoring some quantifiers
% 2.97/1.14 Prover 3: Warning: ignoring some quantifiers
% 2.97/1.15 Prover 1: Constructing countermodel ...
% 2.97/1.15 Prover 3: Constructing countermodel ...
% 2.97/1.16 Prover 0: Proving ...
% 2.97/1.16 Prover 6: Proving ...
% 2.97/1.16 Prover 2: Proving ...
% 2.97/1.16 Prover 5: Proving ...
% 2.97/1.16 Prover 4: Constructing countermodel ...
% 3.96/1.28 Prover 3: proved (633ms)
% 3.96/1.28
% 3.96/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.96/1.28
% 3.96/1.28 Prover 5: stopped
% 3.96/1.28 Prover 0: stopped
% 3.96/1.28 Prover 6: stopped
% 3.96/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.96/1.28 Prover 2: stopped
% 3.96/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.96/1.29 Prover 1: Found proof (size 25)
% 3.96/1.29 Prover 1: proved (648ms)
% 3.96/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.96/1.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.96/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.96/1.29 Prover 4: stopped
% 3.96/1.29 Prover 7: Preprocessing ...
% 3.96/1.30 Prover 10: Preprocessing ...
% 3.96/1.30 Prover 8: Preprocessing ...
% 3.96/1.30 Prover 11: Preprocessing ...
% 4.27/1.31 Prover 13: Preprocessing ...
% 4.27/1.33 Prover 10: Warning: ignoring some quantifiers
% 4.27/1.33 Prover 7: Warning: ignoring some quantifiers
% 4.27/1.33 Prover 10: Constructing countermodel ...
% 4.27/1.33 Prover 7: Constructing countermodel ...
% 4.27/1.33 Prover 7: stopped
% 4.27/1.34 Prover 8: Warning: ignoring some quantifiers
% 4.27/1.34 Prover 8: Constructing countermodel ...
% 4.27/1.34 Prover 10: stopped
% 4.27/1.34 Prover 13: Warning: ignoring some quantifiers
% 4.27/1.35 Prover 8: stopped
% 4.27/1.35 Prover 13: Constructing countermodel ...
% 4.27/1.35 Prover 11: Constructing countermodel ...
% 4.27/1.35 Prover 13: stopped
% 4.27/1.35 Prover 11: stopped
% 4.27/1.35
% 4.27/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.27/1.35
% 4.27/1.36 % SZS output start Proof for theBenchmark
% 4.27/1.36 Assumptions after simplification:
% 4.27/1.36 ---------------------------------
% 4.27/1.36
% 4.27/1.36 (l4_zfmisc_1)
% 4.27/1.39 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 4.27/1.39 0 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~
% 4.27/1.39 $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) & ! [v0: $i] : ! [v1: $i] :
% 4.27/1.39 ! [v2: $i] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~
% 4.27/1.39 (subset(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 4.27/1.39
% 4.27/1.39 (t39_zfmisc_1)
% 4.27/1.40 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 4.27/1.40 (singleton(v1) = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 =
% 4.27/1.40 0 & ~ (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 =
% 4.27/1.40 empty_set))))
% 4.27/1.40
% 4.27/1.40 Further assumptions not needed in the proof:
% 4.27/1.40 --------------------------------------------
% 4.27/1.40 dt_k1_tarski, dt_k1_xboole_0, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 4.27/1.40 reflexivity_r1_tarski
% 4.27/1.40
% 4.27/1.40 Those formulas are unsatisfiable:
% 4.27/1.40 ---------------------------------
% 4.27/1.40
% 4.27/1.40 Begin of proof
% 4.27/1.40 |
% 4.27/1.40 | ALPHA: (l4_zfmisc_1) implies:
% 4.27/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set |
% 4.27/1.40 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0) | ~ $i(v1) | ~
% 4.27/1.40 | $i(v0))
% 4.27/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.27/1.40 | (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~
% 4.27/1.40 | $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set)))
% 4.27/1.40 |
% 4.27/1.40 | ALPHA: (t39_zfmisc_1) implies:
% 4.27/1.41 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (singleton(v1)
% 4.27/1.41 | = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 = 0 & ~
% 4.27/1.41 | (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 =
% 4.27/1.41 | empty_set))))
% 4.27/1.41 |
% 4.27/1.41 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2,
% 4.27/1.41 | all_11_3 gives:
% 4.27/1.41 | (4) singleton(all_11_2) = all_11_1 & subset(all_11_3, all_11_1) = all_11_0
% 4.27/1.41 | & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) & ((all_11_0 = 0 & ~
% 4.27/1.41 | (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)) | ( ~ (all_11_0
% 4.27/1.41 | = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set)))
% 4.27/1.41 |
% 4.27/1.41 | ALPHA: (4) implies:
% 4.27/1.41 | (5) $i(all_11_3)
% 4.27/1.41 | (6) $i(all_11_2)
% 4.27/1.41 | (7) subset(all_11_3, all_11_1) = all_11_0
% 4.27/1.41 | (8) singleton(all_11_2) = all_11_1
% 4.27/1.41 | (9) (all_11_0 = 0 & ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)) |
% 4.27/1.41 | ( ~ (all_11_0 = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set))
% 4.27/1.41 |
% 4.27/1.41 | GROUND_INST: instantiating (2) with all_11_3, all_11_2, all_11_1, all_11_0,
% 4.27/1.41 | simplifying with (5), (6), (7), (8) gives:
% 4.27/1.41 | (10) all_11_0 = 0 | ( ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set))
% 4.27/1.41 |
% 4.27/1.41 | BETA: splitting (9) gives:
% 4.27/1.41 |
% 4.27/1.41 | Case 1:
% 4.27/1.41 | |
% 4.27/1.42 | | (11) all_11_0 = 0 & ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)
% 4.27/1.42 | |
% 4.27/1.42 | | ALPHA: (11) implies:
% 4.27/1.42 | | (12) all_11_0 = 0
% 4.27/1.42 | | (13) ~ (all_11_3 = empty_set)
% 4.27/1.42 | | (14) ~ (all_11_1 = all_11_3)
% 4.27/1.42 | |
% 4.27/1.42 | | REDUCE: (7), (12) imply:
% 4.27/1.42 | | (15) subset(all_11_3, all_11_1) = 0
% 4.27/1.42 | |
% 4.27/1.42 | | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1,
% 4.27/1.42 | | simplifying with (5), (6), (8), (15) gives:
% 4.27/1.42 | | (16) all_11_1 = all_11_3 | all_11_3 = empty_set
% 4.27/1.42 | |
% 4.27/1.42 | | REF_CLOSE: (13), (14), (16) are inconsistent by sub-proof #1.
% 4.27/1.42 | |
% 4.27/1.42 | Case 2:
% 4.27/1.42 | |
% 4.27/1.42 | | (17) ~ (all_11_0 = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set)
% 4.27/1.42 | |
% 4.27/1.42 | | ALPHA: (17) implies:
% 4.27/1.42 | | (18) ~ (all_11_0 = 0)
% 4.27/1.42 | | (19) all_11_1 = all_11_3 | all_11_3 = empty_set
% 4.27/1.42 | |
% 4.27/1.42 | | BETA: splitting (10) gives:
% 4.27/1.42 | |
% 4.27/1.42 | | Case 1:
% 4.27/1.42 | | |
% 4.27/1.42 | | | (20) all_11_0 = 0
% 4.27/1.42 | | |
% 4.27/1.42 | | | REDUCE: (18), (20) imply:
% 4.27/1.42 | | | (21) $false
% 4.27/1.42 | | |
% 4.27/1.42 | | | CLOSE: (21) is inconsistent.
% 4.27/1.42 | | |
% 4.27/1.42 | | Case 2:
% 4.27/1.42 | | |
% 4.27/1.42 | | | (22) ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)
% 4.27/1.42 | | |
% 4.27/1.42 | | | ALPHA: (22) implies:
% 4.27/1.42 | | | (23) ~ (all_11_3 = empty_set)
% 4.27/1.42 | | | (24) ~ (all_11_1 = all_11_3)
% 4.27/1.42 | | |
% 4.27/1.42 | | | REF_CLOSE: (19), (23), (24) are inconsistent by sub-proof #1.
% 4.27/1.42 | | |
% 4.27/1.42 | | End of split
% 4.27/1.42 | |
% 4.27/1.42 | End of split
% 4.27/1.42 |
% 4.27/1.42 End of proof
% 4.27/1.42
% 4.27/1.42 Sub-proof #1 shows that the following formulas are inconsistent:
% 4.27/1.42 ----------------------------------------------------------------
% 4.27/1.42 (1) all_11_1 = all_11_3 | all_11_3 = empty_set
% 4.27/1.42 (2) ~ (all_11_3 = empty_set)
% 4.27/1.42 (3) ~ (all_11_1 = all_11_3)
% 4.27/1.42
% 4.27/1.42 Begin of proof
% 4.27/1.42 |
% 4.27/1.42 | BETA: splitting (1) gives:
% 4.27/1.42 |
% 4.27/1.42 | Case 1:
% 4.27/1.42 | |
% 4.27/1.42 | | (4) all_11_3 = empty_set
% 4.27/1.42 | |
% 4.27/1.42 | | REDUCE: (2), (4) imply:
% 4.27/1.42 | | (5) $false
% 4.27/1.42 | |
% 4.27/1.42 | | CLOSE: (5) is inconsistent.
% 4.27/1.42 | |
% 4.27/1.42 | Case 2:
% 4.27/1.42 | |
% 4.27/1.42 | | (6) all_11_1 = all_11_3
% 4.27/1.42 | |
% 4.27/1.42 | | REDUCE: (3), (6) imply:
% 4.27/1.42 | | (7) $false
% 4.27/1.42 | |
% 4.27/1.42 | | CLOSE: (7) is inconsistent.
% 4.27/1.42 | |
% 4.27/1.42 | End of split
% 4.27/1.42 |
% 4.27/1.42 End of proof
% 4.27/1.42 % SZS output end Proof for theBenchmark
% 4.27/1.42
% 4.27/1.42 808ms
%------------------------------------------------------------------------------