TSTP Solution File: SEU121+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU121+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 : n020.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 17:42:35 EDT 2023
% Result : Theorem 6.34s 1.70s
% Output : Proof 7.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU121+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 16:19:45 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 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 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 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 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
% 2.31/1.02 Prover 1: Preprocessing ...
% 2.31/1.02 Prover 4: Preprocessing ...
% 2.31/1.05 Prover 0: Preprocessing ...
% 2.31/1.05 Prover 6: Preprocessing ...
% 2.31/1.05 Prover 5: Preprocessing ...
% 2.31/1.05 Prover 2: Preprocessing ...
% 2.31/1.05 Prover 3: Preprocessing ...
% 4.14/1.43 Prover 5: Proving ...
% 4.14/1.44 Prover 1: Warning: ignoring some quantifiers
% 5.04/1.49 Prover 3: Warning: ignoring some quantifiers
% 5.04/1.50 Prover 4: Warning: ignoring some quantifiers
% 5.04/1.50 Prover 1: Constructing countermodel ...
% 5.04/1.50 Prover 3: Constructing countermodel ...
% 5.04/1.51 Prover 2: Proving ...
% 5.04/1.51 Prover 6: Proving ...
% 5.04/1.52 Prover 4: Constructing countermodel ...
% 6.34/1.66 Prover 0: Proving ...
% 6.34/1.68 Prover 3: proved (1042ms)
% 6.34/1.68
% 6.34/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.34/1.70
% 6.34/1.70 Prover 2: stopped
% 6.34/1.70 Prover 5: stopped
% 6.34/1.70 Prover 6: stopped
% 6.34/1.70 Prover 0: stopped
% 6.65/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.65/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.65/1.71 Prover 1: Found proof (size 17)
% 6.65/1.71 Prover 1: proved (1088ms)
% 6.65/1.71 Prover 4: Found proof (size 20)
% 6.65/1.71 Prover 4: proved (1078ms)
% 6.65/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.65/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.65/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.65/1.73 Prover 7: Preprocessing ...
% 6.65/1.74 Prover 8: Preprocessing ...
% 6.65/1.75 Prover 11: Preprocessing ...
% 6.65/1.75 Prover 10: Preprocessing ...
% 6.94/1.75 Prover 13: Preprocessing ...
% 6.94/1.76 Prover 10: stopped
% 6.94/1.76 Prover 7: stopped
% 6.94/1.78 Prover 11: stopped
% 6.94/1.79 Prover 13: stopped
% 6.94/1.83 Prover 8: Warning: ignoring some quantifiers
% 7.44/1.85 Prover 8: Constructing countermodel ...
% 7.44/1.85 Prover 8: stopped
% 7.44/1.85
% 7.44/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.44/1.85
% 7.44/1.86 % SZS output start Proof for theBenchmark
% 7.44/1.86 Assumptions after simplification:
% 7.44/1.86 ---------------------------------
% 7.44/1.86
% 7.44/1.86 (d3_tarski)
% 7.66/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.66/1.90 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 7.66/1.90 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 7.66/1.90 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 7.66/1.90 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 7.66/1.90
% 7.66/1.90 (t1_xboole_1)
% 7.66/1.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.66/1.90 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) &
% 7.66/1.90 $i(v1) & $i(v0))
% 7.66/1.90
% 7.66/1.90 (function-axioms)
% 7.66/1.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.66/1.91 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 7.66/1.91 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.66/1.91 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.66/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.66/1.91 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.66/1.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.66/1.91 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.66/1.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.66/1.91 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.66/1.91
% 7.66/1.91 Further assumptions not needed in the proof:
% 7.66/1.91 --------------------------------------------
% 7.66/1.91 antisymmetry_r2_hidden, commutativity_k3_xboole_0, d1_xboole_0, d3_xboole_0,
% 7.66/1.91 d7_xboole_0, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 7.66/1.91 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 7.66/1.91 symmetry_r1_xboole_0, t3_xboole_0, t4_xboole_0, t6_boole, t7_boole, t8_boole
% 7.66/1.91
% 7.66/1.91 Those formulas are unsatisfiable:
% 7.66/1.91 ---------------------------------
% 7.66/1.91
% 7.66/1.91 Begin of proof
% 7.66/1.91 |
% 7.66/1.91 | ALPHA: (d3_tarski) implies:
% 7.66/1.91 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 7.66/1.91 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1)
% 7.66/1.91 | = 0))
% 7.66/1.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.66/1.92 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.66/1.92 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 7.66/1.92 |
% 7.66/1.92 | ALPHA: (function-axioms) implies:
% 7.66/1.92 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.66/1.92 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.66/1.92 |
% 7.66/1.92 | DELTA: instantiating (t1_xboole_1) with fresh symbols all_25_0, all_25_1,
% 7.66/1.92 | all_25_2, all_25_3 gives:
% 7.66/1.92 | (4) ~ (all_25_0 = 0) & subset(all_25_2, all_25_1) = 0 & subset(all_25_3,
% 7.66/1.92 | all_25_1) = all_25_0 & subset(all_25_3, all_25_2) = 0 & $i(all_25_1)
% 7.66/1.92 | & $i(all_25_2) & $i(all_25_3)
% 7.66/1.92 |
% 7.66/1.92 | ALPHA: (4) implies:
% 7.66/1.92 | (5) ~ (all_25_0 = 0)
% 7.66/1.92 | (6) $i(all_25_3)
% 7.66/1.92 | (7) $i(all_25_2)
% 7.66/1.92 | (8) $i(all_25_1)
% 7.66/1.92 | (9) subset(all_25_3, all_25_2) = 0
% 7.66/1.92 | (10) subset(all_25_3, all_25_1) = all_25_0
% 7.66/1.92 | (11) subset(all_25_2, all_25_1) = 0
% 7.66/1.92 |
% 7.66/1.92 | GROUND_INST: instantiating (1) with all_25_3, all_25_2, simplifying with (6),
% 7.66/1.92 | (7), (9) gives:
% 7.66/1.92 | (12) ! [v0: $i] : ( ~ (in(v0, all_25_3) = 0) | ~ $i(v0) | in(v0,
% 7.66/1.92 | all_25_2) = 0)
% 7.66/1.92 |
% 7.66/1.92 | GROUND_INST: instantiating (2) with all_25_3, all_25_1, all_25_0, simplifying
% 7.66/1.92 | with (6), (8), (10) gives:
% 7.66/1.93 | (13) all_25_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 7.66/1.93 | all_25_1) = v1 & in(v0, all_25_3) = 0 & $i(v0))
% 7.66/1.93 |
% 7.66/1.93 | GROUND_INST: instantiating (1) with all_25_2, all_25_1, simplifying with (7),
% 7.66/1.93 | (8), (11) gives:
% 7.66/1.93 | (14) ! [v0: $i] : ( ~ (in(v0, all_25_2) = 0) | ~ $i(v0) | in(v0,
% 7.66/1.93 | all_25_1) = 0)
% 7.66/1.93 |
% 7.66/1.93 | BETA: splitting (13) gives:
% 7.66/1.93 |
% 7.66/1.93 | Case 1:
% 7.66/1.93 | |
% 7.66/1.93 | | (15) all_25_0 = 0
% 7.66/1.93 | |
% 7.66/1.93 | | REDUCE: (5), (15) imply:
% 7.66/1.93 | | (16) $false
% 7.66/1.93 | |
% 7.66/1.93 | | CLOSE: (16) is inconsistent.
% 7.66/1.93 | |
% 7.66/1.93 | Case 2:
% 7.66/1.93 | |
% 7.66/1.93 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_25_1) = v1 &
% 7.66/1.93 | | in(v0, all_25_3) = 0 & $i(v0))
% 7.66/1.93 | |
% 7.66/1.93 | | DELTA: instantiating (17) with fresh symbols all_41_0, all_41_1 gives:
% 7.66/1.93 | | (18) ~ (all_41_0 = 0) & in(all_41_1, all_25_1) = all_41_0 & in(all_41_1,
% 7.66/1.93 | | all_25_3) = 0 & $i(all_41_1)
% 7.66/1.93 | |
% 7.66/1.93 | | ALPHA: (18) implies:
% 7.66/1.93 | | (19) ~ (all_41_0 = 0)
% 7.66/1.93 | | (20) $i(all_41_1)
% 7.66/1.93 | | (21) in(all_41_1, all_25_3) = 0
% 7.66/1.93 | | (22) in(all_41_1, all_25_1) = all_41_0
% 7.66/1.93 | |
% 7.66/1.93 | | GROUND_INST: instantiating (12) with all_41_1, simplifying with (20), (21)
% 7.66/1.93 | | gives:
% 7.66/1.93 | | (23) in(all_41_1, all_25_2) = 0
% 7.66/1.93 | |
% 7.66/1.93 | | GROUND_INST: instantiating (14) with all_41_1, simplifying with (20), (23)
% 7.66/1.93 | | gives:
% 7.66/1.93 | | (24) in(all_41_1, all_25_1) = 0
% 7.66/1.93 | |
% 7.66/1.93 | | GROUND_INST: instantiating (3) with all_41_0, 0, all_25_1, all_41_1,
% 7.66/1.93 | | simplifying with (22), (24) gives:
% 7.66/1.93 | | (25) all_41_0 = 0
% 7.66/1.93 | |
% 7.66/1.93 | | REDUCE: (19), (25) imply:
% 7.66/1.93 | | (26) $false
% 7.66/1.93 | |
% 7.66/1.93 | | CLOSE: (26) is inconsistent.
% 7.66/1.93 | |
% 7.66/1.93 | End of split
% 7.66/1.93 |
% 7.66/1.93 End of proof
% 7.66/1.93 % SZS output end Proof for theBenchmark
% 7.66/1.93
% 7.66/1.93 1340ms
%------------------------------------------------------------------------------