TSTP Solution File: SET873+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 15:26:51 EDT 2023
% Result : Theorem 5.98s 1.61s
% Output : Proof 6.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 08:57:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62 Running up to 7 provers in parallel.
% 0.73/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.73/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.73/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.73/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.73/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.73/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.73/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/1.01 Prover 1: Preprocessing ...
% 2.14/1.01 Prover 4: Preprocessing ...
% 2.14/1.06 Prover 3: Preprocessing ...
% 2.14/1.06 Prover 5: Preprocessing ...
% 2.14/1.06 Prover 6: Preprocessing ...
% 2.14/1.06 Prover 2: Preprocessing ...
% 2.14/1.06 Prover 0: Preprocessing ...
% 3.78/1.25 Prover 1: Warning: ignoring some quantifiers
% 3.78/1.25 Prover 4: Warning: ignoring some quantifiers
% 3.78/1.26 Prover 3: Warning: ignoring some quantifiers
% 3.78/1.27 Prover 1: Constructing countermodel ...
% 3.78/1.27 Prover 4: Constructing countermodel ...
% 3.78/1.27 Prover 2: Proving ...
% 3.78/1.27 Prover 6: Proving ...
% 3.78/1.27 Prover 5: Proving ...
% 3.78/1.28 Prover 3: Constructing countermodel ...
% 3.78/1.28 Prover 0: Proving ...
% 5.71/1.53 Prover 3: gave up
% 5.71/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.98/1.56 Prover 7: Preprocessing ...
% 5.98/1.58 Prover 4: Found proof (size 17)
% 5.98/1.58 Prover 4: proved (948ms)
% 5.98/1.58 Prover 1: stopped
% 5.98/1.58 Prover 5: stopped
% 5.98/1.58 Prover 0: stopped
% 5.98/1.58 Prover 2: stopped
% 5.98/1.58 Prover 6: stopped
% 5.98/1.60 Prover 7: Warning: ignoring some quantifiers
% 5.98/1.61 Prover 7: Constructing countermodel ...
% 5.98/1.61 Prover 7: stopped
% 5.98/1.61
% 5.98/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.98/1.61
% 5.98/1.62 % SZS output start Proof for theBenchmark
% 5.98/1.62 Assumptions after simplification:
% 5.98/1.62 ---------------------------------
% 5.98/1.62
% 5.98/1.62 (commutativity_k2_xboole_0)
% 6.56/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 6.56/1.65 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 6.56/1.65 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 6.56/1.65 | (set_union2(v1, v0) = v2 & $i(v2)))
% 6.56/1.65
% 6.56/1.65 (d1_tarski)
% 6.56/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 6.56/1.66 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 6.56/1.66 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 6.56/1.66 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.56/1.66 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 6.56/1.66 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 =
% 6.56/1.66 0 | v3 = v1)))
% 6.56/1.66
% 6.56/1.66 (l21_zfmisc_1)
% 6.56/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v0) =
% 6.56/1.66 v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 6.56/1.66 : ? [v5: any] : (subset(v3, v1) = v4 & in(v0, v1) = v5 & ( ~ (v4 = 0) | v5
% 6.56/1.66 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0,
% 6.56/1.66 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 6.56/1.66 int] : ( ~ (v5 = 0) & subset(v4, v1) = v5 & singleton(v0) = v3 &
% 6.56/1.66 set_union2(v3, v1) = v4 & $i(v4) & $i(v3)))
% 6.56/1.66
% 6.56/1.66 (reflexivity_r1_tarski)
% 6.56/1.67 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 6.56/1.67
% 6.56/1.67 (t13_zfmisc_1)
% 6.56/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 6.56/1.67 singleton(v1) = v3 & singleton(v0) = v2 & set_union2(v2, v3) = v2 & $i(v3) &
% 6.56/1.67 $i(v2) & $i(v1) & $i(v0))
% 6.56/1.67
% 6.56/1.67 Further assumptions not needed in the proof:
% 6.56/1.67 --------------------------------------------
% 6.56/1.67 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 6.56/1.67 rc1_xboole_0, rc2_xboole_0
% 6.56/1.67
% 6.56/1.67 Those formulas are unsatisfiable:
% 6.56/1.67 ---------------------------------
% 6.56/1.67
% 6.56/1.67 Begin of proof
% 6.56/1.67 |
% 6.56/1.67 | ALPHA: (commutativity_k2_xboole_0) implies:
% 6.56/1.67 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 6.56/1.67 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 6.56/1.67 |
% 6.56/1.67 | ALPHA: (d1_tarski) implies:
% 6.56/1.67 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 6.56/1.67 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 6.56/1.67 |
% 6.56/1.67 | ALPHA: (l21_zfmisc_1) implies:
% 6.56/1.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 6.56/1.68 | (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~
% 6.56/1.68 | $i(v0) | ? [v4: any] : ? [v5: any] : (subset(v3, v1) = v4 & in(v0,
% 6.56/1.68 | v1) = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 6.56/1.68 |
% 6.56/1.68 | DELTA: instantiating (t13_zfmisc_1) with fresh symbols all_15_0, all_15_1,
% 6.56/1.68 | all_15_2, all_15_3 gives:
% 6.56/1.68 | (4) ~ (all_15_2 = all_15_3) & singleton(all_15_2) = all_15_0 &
% 6.56/1.68 | singleton(all_15_3) = all_15_1 & set_union2(all_15_1, all_15_0) =
% 6.56/1.68 | all_15_1 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_3)
% 6.56/1.68 |
% 6.56/1.68 | ALPHA: (4) implies:
% 6.56/1.68 | (5) ~ (all_15_2 = all_15_3)
% 6.56/1.68 | (6) $i(all_15_3)
% 6.56/1.68 | (7) $i(all_15_2)
% 6.56/1.68 | (8) $i(all_15_1)
% 6.56/1.68 | (9) $i(all_15_0)
% 6.56/1.68 | (10) set_union2(all_15_1, all_15_0) = all_15_1
% 6.56/1.68 | (11) singleton(all_15_3) = all_15_1
% 6.56/1.68 | (12) singleton(all_15_2) = all_15_0
% 6.56/1.68 |
% 6.56/1.68 | GROUND_INST: instantiating (1) with all_15_0, all_15_1, all_15_1, simplifying
% 6.56/1.68 | with (8), (9), (10) gives:
% 6.56/1.68 | (13) set_union2(all_15_0, all_15_1) = all_15_1
% 6.56/1.68 |
% 6.56/1.69 | GROUND_INST: instantiating (3) with all_15_2, all_15_1, all_15_0, all_15_1,
% 6.56/1.69 | simplifying with (7), (8), (12), (13) gives:
% 6.56/1.69 | (14) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_1) = v0 &
% 6.56/1.69 | in(all_15_2, all_15_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.56/1.69 |
% 6.56/1.69 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1 gives:
% 6.56/1.69 | (15) subset(all_15_1, all_15_1) = all_42_1 & in(all_15_2, all_15_1) =
% 6.56/1.69 | all_42_0 & ( ~ (all_42_1 = 0) | all_42_0 = 0)
% 6.56/1.69 |
% 6.56/1.69 | ALPHA: (15) implies:
% 6.56/1.69 | (16) in(all_15_2, all_15_1) = all_42_0
% 6.56/1.69 | (17) subset(all_15_1, all_15_1) = all_42_1
% 6.56/1.69 | (18) ~ (all_42_1 = 0) | all_42_0 = 0
% 6.56/1.69 |
% 6.83/1.69 | GROUND_INST: instantiating (reflexivity_r1_tarski) with all_15_1, all_42_1,
% 6.83/1.69 | simplifying with (8), (17) gives:
% 6.83/1.69 | (19) all_42_1 = 0
% 6.83/1.69 |
% 6.83/1.69 | BETA: splitting (18) gives:
% 6.83/1.69 |
% 6.83/1.69 | Case 1:
% 6.83/1.69 | |
% 6.83/1.69 | | (20) ~ (all_42_1 = 0)
% 6.83/1.69 | |
% 6.83/1.69 | | REDUCE: (19), (20) imply:
% 6.83/1.69 | | (21) $false
% 6.83/1.69 | |
% 6.83/1.69 | | CLOSE: (21) is inconsistent.
% 6.83/1.69 | |
% 6.83/1.69 | Case 2:
% 6.83/1.69 | |
% 6.83/1.69 | | (22) all_42_0 = 0
% 6.83/1.69 | |
% 6.83/1.69 | | REDUCE: (16), (22) imply:
% 6.83/1.69 | | (23) in(all_15_2, all_15_1) = 0
% 6.83/1.69 | |
% 6.83/1.69 | | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_2,
% 6.83/1.69 | | simplifying with (6), (7), (8), (11), (23) gives:
% 6.83/1.69 | | (24) all_15_2 = all_15_3
% 6.83/1.69 | |
% 6.83/1.69 | | REDUCE: (5), (24) imply:
% 6.83/1.69 | | (25) $false
% 6.83/1.69 | |
% 6.83/1.69 | | CLOSE: (25) is inconsistent.
% 6.83/1.69 | |
% 6.83/1.69 | End of split
% 6.83/1.69 |
% 6.83/1.69 End of proof
% 6.83/1.69 % SZS output end Proof for theBenchmark
% 6.83/1.69
% 6.83/1.69 1084ms
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