TSTP Solution File: SEU161+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 17:42:55 EDT 2023
% Result : Theorem 12.53s 2.44s
% Output : Proof 14.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.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 : Wed Aug 23 20:03:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.46/1.17 Prover 4: Preprocessing ...
% 3.46/1.17 Prover 1: Preprocessing ...
% 3.75/1.21 Prover 6: Preprocessing ...
% 3.75/1.21 Prover 2: Preprocessing ...
% 3.75/1.21 Prover 3: Preprocessing ...
% 3.75/1.21 Prover 5: Preprocessing ...
% 3.75/1.21 Prover 0: Preprocessing ...
% 10.07/2.13 Prover 1: Warning: ignoring some quantifiers
% 10.07/2.16 Prover 5: Proving ...
% 10.07/2.24 Prover 3: Warning: ignoring some quantifiers
% 10.07/2.26 Prover 1: Constructing countermodel ...
% 10.07/2.27 Prover 3: Constructing countermodel ...
% 10.07/2.28 Prover 4: Warning: ignoring some quantifiers
% 10.07/2.28 Prover 6: Proving ...
% 11.89/2.38 Prover 4: Constructing countermodel ...
% 11.89/2.43 Prover 2: Proving ...
% 12.53/2.44 Prover 3: proved (1815ms)
% 12.53/2.44
% 12.53/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.53/2.44
% 12.53/2.45 Prover 6: stopped
% 12.53/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.53/2.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.53/2.45 Prover 5: proved (1820ms)
% 12.53/2.45
% 12.53/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.53/2.45
% 12.53/2.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.53/2.46 Prover 0: Proving ...
% 12.53/2.47 Prover 2: stopped
% 12.53/2.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.53/2.47 Prover 0: stopped
% 12.80/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.35/2.57 Prover 10: Preprocessing ...
% 13.35/2.59 Prover 8: Preprocessing ...
% 13.35/2.59 Prover 7: Preprocessing ...
% 13.79/2.62 Prover 11: Preprocessing ...
% 13.79/2.63 Prover 13: Preprocessing ...
% 14.14/2.68 Prover 1: Found proof (size 13)
% 14.14/2.68 Prover 1: proved (2054ms)
% 14.14/2.68 Prover 4: stopped
% 14.14/2.68 Prover 10: stopped
% 14.14/2.70 Prover 7: stopped
% 14.72/2.74 Prover 11: stopped
% 14.72/2.74 Prover 13: stopped
% 14.91/2.83 Prover 8: Warning: ignoring some quantifiers
% 14.91/2.86 Prover 8: Constructing countermodel ...
% 14.91/2.88 Prover 8: stopped
% 14.91/2.88
% 14.91/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.91/2.88
% 14.91/2.88 % SZS output start Proof for theBenchmark
% 14.91/2.89 Assumptions after simplification:
% 14.91/2.89 ---------------------------------
% 14.91/2.89
% 14.91/2.89 (l23_zfmisc_1)
% 14.91/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 14.91/2.91 (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0)
% 14.91/2.91 | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 14.91/2.91
% 14.91/2.91 (t46_zfmisc_1)
% 14.91/2.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) &
% 14.91/2.91 singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) = 0 & $i(v3) &
% 14.91/2.91 $i(v2) & $i(v1) & $i(v0))
% 14.91/2.91
% 14.91/2.91 (function-axioms)
% 14.91/2.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.91/2.93 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 14.91/2.93 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 14.91/2.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 14.91/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 14.91/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.91/2.93 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 14.91/2.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 14.91/2.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 14.91/2.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 14.91/2.93 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.91/2.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.91/2.93 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 14.91/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.91/2.93 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 14.91/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.91/2.93 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.91/2.93 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i]
% 14.91/2.93 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 14.91/2.93 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.91/2.93 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 14.91/2.93
% 14.91/2.93 Further assumptions not needed in the proof:
% 14.91/2.93 --------------------------------------------
% 14.91/2.93 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 14.91/2.93 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 14.91/2.93 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski,
% 14.91/2.93 d3_xboole_0, d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0,
% 14.91/2.93 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0,
% 14.91/2.93 dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0,
% 14.91/2.93 fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 14.91/2.93 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l25_zfmisc_1,
% 14.91/2.93 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1,
% 14.91/2.93 l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 14.91/2.93 symmetry_r1_xboole_0, t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1,
% 14.91/2.93 t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 14.91/2.93 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1,
% 14.91/2.93 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_xboole_0,
% 14.91/2.93 t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0,
% 14.91/2.93 t60_xboole_1, t63_xboole_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole,
% 14.91/2.93 t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1
% 14.91/2.93
% 14.91/2.93 Those formulas are unsatisfiable:
% 14.91/2.93 ---------------------------------
% 14.91/2.93
% 14.91/2.93 Begin of proof
% 14.91/2.93 |
% 14.91/2.93 | ALPHA: (function-axioms) implies:
% 14.91/2.93 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.91/2.93 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 14.91/2.93 |
% 14.91/2.93 | DELTA: instantiating (t46_zfmisc_1) with fresh symbols all_90_0, all_90_1,
% 14.91/2.93 | all_90_2, all_90_3 gives:
% 14.91/2.93 | (2) ~ (all_90_0 = all_90_2) & singleton(all_90_3) = all_90_1 &
% 14.91/2.93 | set_union2(all_90_1, all_90_2) = all_90_0 & in(all_90_3, all_90_2) = 0
% 14.91/2.93 | & $i(all_90_0) & $i(all_90_1) & $i(all_90_2) & $i(all_90_3)
% 14.91/2.93 |
% 14.91/2.93 | ALPHA: (2) implies:
% 14.91/2.93 | (3) ~ (all_90_0 = all_90_2)
% 14.91/2.93 | (4) $i(all_90_3)
% 14.91/2.93 | (5) $i(all_90_2)
% 14.91/2.94 | (6) in(all_90_3, all_90_2) = 0
% 14.91/2.94 | (7) set_union2(all_90_1, all_90_2) = all_90_0
% 14.91/2.94 | (8) singleton(all_90_3) = all_90_1
% 14.91/2.94 |
% 14.91/2.94 | GROUND_INST: instantiating (l23_zfmisc_1) with all_90_3, all_90_2, all_90_1,
% 14.91/2.94 | all_90_0, simplifying with (4), (5), (7), (8) gives:
% 14.91/2.94 | (9) all_90_0 = all_90_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_90_3,
% 14.91/2.94 | all_90_2) = v0)
% 14.91/2.94 |
% 14.91/2.94 | BETA: splitting (9) gives:
% 14.91/2.94 |
% 14.91/2.94 | Case 1:
% 14.91/2.94 | |
% 14.91/2.94 | | (10) all_90_0 = all_90_2
% 14.91/2.94 | |
% 14.91/2.94 | | REDUCE: (3), (10) imply:
% 14.91/2.94 | | (11) $false
% 14.91/2.94 | |
% 14.91/2.94 | | CLOSE: (11) is inconsistent.
% 14.91/2.94 | |
% 14.91/2.94 | Case 2:
% 14.91/2.94 | |
% 14.91/2.94 | | (12) ? [v0: int] : ( ~ (v0 = 0) & in(all_90_3, all_90_2) = v0)
% 14.91/2.94 | |
% 14.91/2.94 | | DELTA: instantiating (12) with fresh symbol all_131_0 gives:
% 14.91/2.94 | | (13) ~ (all_131_0 = 0) & in(all_90_3, all_90_2) = all_131_0
% 14.91/2.94 | |
% 14.91/2.94 | | ALPHA: (13) implies:
% 14.91/2.94 | | (14) ~ (all_131_0 = 0)
% 14.91/2.94 | | (15) in(all_90_3, all_90_2) = all_131_0
% 14.91/2.94 | |
% 14.91/2.94 | | GROUND_INST: instantiating (1) with 0, all_131_0, all_90_2, all_90_3,
% 14.91/2.94 | | simplifying with (6), (15) gives:
% 14.91/2.94 | | (16) all_131_0 = 0
% 14.91/2.94 | |
% 14.91/2.94 | | REDUCE: (14), (16) imply:
% 14.91/2.94 | | (17) $false
% 14.91/2.94 | |
% 14.91/2.94 | | CLOSE: (17) is inconsistent.
% 14.91/2.94 | |
% 14.91/2.94 | End of split
% 14.91/2.94 |
% 14.91/2.94 End of proof
% 14.91/2.94 % SZS output end Proof for theBenchmark
% 14.91/2.94
% 14.91/2.94 2335ms
%------------------------------------------------------------------------------