TSTP Solution File: SEU121+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU121+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 17:42:35 EDT 2023
% Result : Theorem 4.11s 1.15s
% Output : Proof 4.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU121+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.06/0.27 % Computer : n032.cluster.edu
% 0.06/0.27 % Model : x86_64 x86_64
% 0.06/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.27 % Memory : 8042.1875MB
% 0.06/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Wed Aug 23 21:48:41 EDT 2023
% 0.06/0.27 % CPUTime :
% 0.11/0.47 ________ _____
% 0.11/0.47 ___ __ \_________(_)________________________________
% 0.11/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.11/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.11/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.11/0.48
% 0.11/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.11/0.48 (2023-06-19)
% 0.11/0.48
% 0.11/0.48 (c) Philipp Rümmer, 2009-2023
% 0.11/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.11/0.48 Amanda Stjerna.
% 0.11/0.48 Free software under BSD-3-Clause.
% 0.11/0.48
% 0.11/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.11/0.48
% 0.11/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.11/0.49 Running up to 7 provers in parallel.
% 0.11/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.11/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.11/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.11/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.11/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.11/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.11/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.54/0.81 Prover 4: Preprocessing ...
% 1.54/0.81 Prover 1: Preprocessing ...
% 1.97/0.86 Prover 0: Preprocessing ...
% 1.97/0.86 Prover 2: Preprocessing ...
% 1.97/0.86 Prover 5: Preprocessing ...
% 1.97/0.86 Prover 6: Preprocessing ...
% 1.97/0.86 Prover 3: Preprocessing ...
% 2.63/0.97 Prover 5: Proving ...
% 2.63/0.97 Prover 2: Proving ...
% 2.63/0.98 Prover 1: Warning: ignoring some quantifiers
% 2.63/0.99 Prover 3: Warning: ignoring some quantifiers
% 2.63/0.99 Prover 1: Constructing countermodel ...
% 2.63/0.99 Prover 4: Constructing countermodel ...
% 2.63/1.00 Prover 3: Constructing countermodel ...
% 2.63/1.03 Prover 0: Proving ...
% 3.23/1.03 Prover 6: Proving ...
% 3.62/1.15 Prover 3: proved (652ms)
% 4.11/1.15
% 4.11/1.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/1.15
% 4.11/1.16 Prover 2: stopped
% 4.11/1.16 Prover 5: stopped
% 4.11/1.16 Prover 6: stopped
% 4.20/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.20/1.17 Prover 0: proved (665ms)
% 4.20/1.17
% 4.20/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.20/1.17
% 4.20/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.20/1.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.20/1.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.20/1.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.20/1.17 Prover 7: Preprocessing ...
% 4.20/1.18 Prover 8: Preprocessing ...
% 4.20/1.19 Prover 13: Preprocessing ...
% 4.20/1.19 Prover 10: Preprocessing ...
% 4.20/1.20 Prover 11: Preprocessing ...
% 4.20/1.21 Prover 4: Found proof (size 20)
% 4.20/1.21 Prover 4: proved (710ms)
% 4.52/1.21 Prover 7: Warning: ignoring some quantifiers
% 4.52/1.21 Prover 7: Constructing countermodel ...
% 4.52/1.21 Prover 13: Warning: ignoring some quantifiers
% 4.52/1.22 Prover 1: stopped
% 4.52/1.22 Prover 13: Constructing countermodel ...
% 4.52/1.22 Prover 13: stopped
% 4.52/1.22 Prover 7: stopped
% 4.52/1.22 Prover 11: stopped
% 4.52/1.23 Prover 10: Warning: ignoring some quantifiers
% 4.52/1.23 Prover 10: Constructing countermodel ...
% 4.52/1.23 Prover 10: stopped
% 4.52/1.24 Prover 8: Warning: ignoring some quantifiers
% 4.52/1.24 Prover 8: Constructing countermodel ...
% 4.52/1.24 Prover 8: stopped
% 4.52/1.24
% 4.52/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.52/1.24
% 4.52/1.25 % SZS output start Proof for theBenchmark
% 4.52/1.25 Assumptions after simplification:
% 4.52/1.25 ---------------------------------
% 4.52/1.25
% 4.52/1.25 (d3_tarski)
% 4.52/1.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.52/1.28 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.52/1.28 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 4.52/1.28 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 4.52/1.28 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 4.52/1.28 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 4.52/1.28 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 4.52/1.28 $i(v0) | in(v2, v1) = 0)
% 4.52/1.28
% 4.52/1.28 (t1_xboole_1)
% 4.52/1.29 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 4.52/1.29 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) &
% 4.52/1.29 $i(v1) & $i(v0))
% 4.52/1.29
% 4.52/1.29 (function-axioms)
% 4.52/1.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.52/1.29 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.52/1.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 4.52/1.29 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.52/1.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.52/1.29 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.52/1.29
% 4.52/1.29 Further assumptions not needed in the proof:
% 4.52/1.29 --------------------------------------------
% 4.52/1.29 antisymmetry_r2_hidden, dt_k1_xboole_0, fc1_xboole_0, rc1_xboole_0,
% 4.52/1.29 rc2_xboole_0, reflexivity_r1_tarski, t6_boole, t7_boole, t8_boole
% 4.52/1.29
% 4.52/1.29 Those formulas are unsatisfiable:
% 4.52/1.29 ---------------------------------
% 4.52/1.29
% 4.52/1.29 Begin of proof
% 4.52/1.29 |
% 4.52/1.29 | ALPHA: (d3_tarski) implies:
% 4.52/1.29 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 4.52/1.29 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 4.52/1.29 | 0)
% 4.52/1.30 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.52/1.30 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.52/1.30 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 4.52/1.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.52/1.30 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 4.52/1.30 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 4.52/1.30 |
% 4.52/1.30 | ALPHA: (function-axioms) implies:
% 4.52/1.30 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.52/1.30 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.52/1.30 |
% 4.52/1.30 | DELTA: instantiating (t1_xboole_1) with fresh symbols all_14_0, all_14_1,
% 4.52/1.30 | all_14_2, all_14_3 gives:
% 4.52/1.30 | (5) ~ (all_14_0 = 0) & subset(all_14_2, all_14_1) = 0 & subset(all_14_3,
% 4.52/1.30 | all_14_1) = all_14_0 & subset(all_14_3, all_14_2) = 0 & $i(all_14_1)
% 4.52/1.30 | & $i(all_14_2) & $i(all_14_3)
% 4.52/1.30 |
% 4.52/1.30 | ALPHA: (5) implies:
% 4.52/1.30 | (6) ~ (all_14_0 = 0)
% 4.52/1.30 | (7) $i(all_14_3)
% 4.52/1.30 | (8) $i(all_14_2)
% 4.52/1.30 | (9) $i(all_14_1)
% 4.52/1.30 | (10) subset(all_14_3, all_14_2) = 0
% 4.52/1.30 | (11) subset(all_14_3, all_14_1) = all_14_0
% 4.52/1.30 | (12) subset(all_14_2, all_14_1) = 0
% 4.52/1.30 |
% 4.52/1.31 | GROUND_INST: instantiating (2) with all_14_3, all_14_1, all_14_0, simplifying
% 4.52/1.31 | with (7), (9), (11) gives:
% 4.52/1.31 | (13) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 4.52/1.31 | all_14_1) = v1 & in(v0, all_14_3) = 0 & $i(v0))
% 4.52/1.31 |
% 4.52/1.31 | BETA: splitting (13) gives:
% 4.52/1.31 |
% 4.52/1.31 | Case 1:
% 4.52/1.31 | |
% 4.52/1.31 | | (14) all_14_0 = 0
% 4.52/1.31 | |
% 4.52/1.31 | | REDUCE: (6), (14) imply:
% 4.52/1.31 | | (15) $false
% 4.52/1.31 | |
% 4.52/1.31 | | CLOSE: (15) is inconsistent.
% 4.52/1.31 | |
% 4.52/1.31 | Case 2:
% 4.52/1.31 | |
% 4.52/1.31 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 &
% 4.52/1.31 | | in(v0, all_14_3) = 0 & $i(v0))
% 4.52/1.31 | |
% 4.52/1.31 | | DELTA: instantiating (16) with fresh symbols all_26_0, all_26_1 gives:
% 4.52/1.31 | | (17) ~ (all_26_0 = 0) & in(all_26_1, all_14_1) = all_26_0 & in(all_26_1,
% 4.52/1.31 | | all_14_3) = 0 & $i(all_26_1)
% 4.52/1.31 | |
% 4.52/1.31 | | ALPHA: (17) implies:
% 4.52/1.31 | | (18) ~ (all_26_0 = 0)
% 4.52/1.31 | | (19) $i(all_26_1)
% 4.52/1.31 | | (20) in(all_26_1, all_14_3) = 0
% 4.52/1.31 | | (21) in(all_26_1, all_14_1) = all_26_0
% 4.52/1.31 | |
% 4.52/1.31 | | GROUND_INST: instantiating (1) with all_14_3, all_14_2, all_26_1,
% 4.52/1.31 | | simplifying with (7), (8), (10), (19), (20) gives:
% 4.52/1.32 | | (22) in(all_26_1, all_14_2) = 0
% 4.52/1.32 | |
% 4.52/1.32 | | GROUND_INST: instantiating (3) with all_14_2, all_14_1, all_26_1, all_26_0,
% 4.52/1.32 | | simplifying with (8), (9), (12), (19), (21) gives:
% 4.52/1.32 | | (23) all_26_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_26_1, all_14_2)
% 4.52/1.32 | | = v0)
% 4.52/1.32 | |
% 4.52/1.32 | | BETA: splitting (23) gives:
% 4.52/1.32 | |
% 4.52/1.32 | | Case 1:
% 4.52/1.32 | | |
% 4.52/1.32 | | | (24) all_26_0 = 0
% 4.52/1.32 | | |
% 4.52/1.32 | | | REDUCE: (18), (24) imply:
% 4.52/1.32 | | | (25) $false
% 4.52/1.32 | | |
% 4.52/1.32 | | | CLOSE: (25) is inconsistent.
% 4.52/1.32 | | |
% 4.52/1.32 | | Case 2:
% 4.52/1.32 | | |
% 4.52/1.32 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & in(all_26_1, all_14_2) = v0)
% 4.52/1.32 | | |
% 4.52/1.32 | | | DELTA: instantiating (26) with fresh symbol all_42_0 gives:
% 4.52/1.32 | | | (27) ~ (all_42_0 = 0) & in(all_26_1, all_14_2) = all_42_0
% 4.52/1.32 | | |
% 4.52/1.32 | | | ALPHA: (27) implies:
% 4.52/1.32 | | | (28) ~ (all_42_0 = 0)
% 4.52/1.32 | | | (29) in(all_26_1, all_14_2) = all_42_0
% 4.52/1.32 | | |
% 4.52/1.32 | | | GROUND_INST: instantiating (4) with 0, all_42_0, all_14_2, all_26_1,
% 4.52/1.32 | | | simplifying with (22), (29) gives:
% 4.52/1.32 | | | (30) all_42_0 = 0
% 4.52/1.32 | | |
% 4.52/1.32 | | | REDUCE: (28), (30) imply:
% 4.52/1.32 | | | (31) $false
% 4.52/1.32 | | |
% 4.52/1.32 | | | CLOSE: (31) is inconsistent.
% 4.52/1.32 | | |
% 4.52/1.32 | | End of split
% 4.52/1.32 | |
% 4.52/1.32 | End of split
% 4.52/1.32 |
% 4.52/1.32 End of proof
% 4.52/1.32 % SZS output end Proof for theBenchmark
% 4.52/1.32
% 4.52/1.32 845ms
%------------------------------------------------------------------------------