TSTP Solution File: SEU122+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU122+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 : n028.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 17:42:36 EDT 2023
% Result : Theorem 3.90s 1.33s
% Output : Proof 5.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU122+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 21:04:04 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.88/1.01 Prover 1: Preprocessing ...
% 1.88/1.01 Prover 4: Preprocessing ...
% 2.51/1.05 Prover 3: Preprocessing ...
% 2.51/1.05 Prover 2: Preprocessing ...
% 2.51/1.05 Prover 6: Preprocessing ...
% 2.51/1.05 Prover 0: Preprocessing ...
% 2.51/1.05 Prover 5: Preprocessing ...
% 3.23/1.19 Prover 2: Proving ...
% 3.57/1.20 Prover 1: Warning: ignoring some quantifiers
% 3.57/1.20 Prover 5: Proving ...
% 3.57/1.20 Prover 0: Proving ...
% 3.57/1.21 Prover 1: Constructing countermodel ...
% 3.57/1.21 Prover 3: Warning: ignoring some quantifiers
% 3.57/1.21 Prover 3: Constructing countermodel ...
% 3.57/1.22 Prover 6: Proving ...
% 3.57/1.22 Prover 4: Constructing countermodel ...
% 3.90/1.33 Prover 3: proved (695ms)
% 3.90/1.33
% 3.90/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/1.33
% 3.90/1.33 Prover 5: stopped
% 3.90/1.33 Prover 2: stopped
% 3.90/1.34 Prover 0: proved (700ms)
% 3.90/1.34
% 3.90/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/1.34
% 3.90/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.90/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.90/1.34 Prover 6: proved (699ms)
% 3.90/1.34
% 3.90/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/1.34
% 4.57/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.57/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.57/1.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.57/1.36 Prover 10: Preprocessing ...
% 4.57/1.37 Prover 7: Preprocessing ...
% 4.57/1.37 Prover 8: Preprocessing ...
% 4.57/1.37 Prover 11: Preprocessing ...
% 4.57/1.37 Prover 13: Preprocessing ...
% 4.57/1.38 Prover 1: Found proof (size 23)
% 4.57/1.38 Prover 1: proved (743ms)
% 4.57/1.38 Prover 4: Found proof (size 23)
% 4.57/1.38 Prover 4: proved (742ms)
% 4.57/1.38 Prover 10: Warning: ignoring some quantifiers
% 4.57/1.39 Prover 10: Constructing countermodel ...
% 4.57/1.39 Prover 10: stopped
% 4.57/1.39 Prover 11: stopped
% 4.57/1.39 Prover 7: Warning: ignoring some quantifiers
% 4.57/1.39 Prover 13: Warning: ignoring some quantifiers
% 4.57/1.40 Prover 7: Constructing countermodel ...
% 4.57/1.40 Prover 13: Constructing countermodel ...
% 4.57/1.40 Prover 7: stopped
% 4.57/1.40 Prover 13: stopped
% 4.57/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.57/1.42 Prover 8: Constructing countermodel ...
% 4.57/1.43 Prover 8: stopped
% 4.57/1.43
% 4.57/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/1.43
% 4.57/1.43 % SZS output start Proof for theBenchmark
% 4.57/1.44 Assumptions after simplification:
% 4.57/1.44 ---------------------------------
% 4.57/1.44
% 4.57/1.44 (d3_tarski)
% 4.57/1.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 4.57/1.46 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 4.57/1.46 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 4.57/1.46 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 4.57/1.47 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 4.57/1.47
% 4.57/1.47 (rc1_xboole_0)
% 4.57/1.47 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 4.57/1.47
% 4.57/1.47 (t2_xboole_1)
% 4.57/1.47 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set,
% 4.57/1.47 v0) = v1 & $i(v0))
% 4.57/1.47
% 4.57/1.47 (t6_boole)
% 4.57/1.47 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 4.57/1.47 $i(v0))
% 4.57/1.47
% 4.57/1.47 (t7_boole)
% 4.57/1.47 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 4.57/1.47 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 4.57/1.47
% 4.57/1.47 (function-axioms)
% 4.57/1.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.57/1.47 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.57/1.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 4.57/1.47 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.57/1.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.57/1.47 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.57/1.47
% 4.57/1.47 Further assumptions not needed in the proof:
% 4.57/1.47 --------------------------------------------
% 4.57/1.47 antisymmetry_r2_hidden, dt_k1_xboole_0, fc1_xboole_0, rc2_xboole_0,
% 4.57/1.47 reflexivity_r1_tarski, t8_boole
% 4.57/1.47
% 4.57/1.47 Those formulas are unsatisfiable:
% 4.57/1.47 ---------------------------------
% 4.57/1.47
% 4.57/1.47 Begin of proof
% 4.57/1.47 |
% 4.57/1.48 | ALPHA: (d3_tarski) implies:
% 4.57/1.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.57/1.48 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.57/1.48 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 4.57/1.48 |
% 4.57/1.48 | ALPHA: (t6_boole) implies:
% 4.57/1.48 | (2) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 4.57/1.48 |
% 4.57/1.48 | ALPHA: (t2_xboole_1) implies:
% 4.57/1.48 | (3) $i(empty_set)
% 4.57/1.48 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set, v0) = v1
% 4.57/1.48 | & $i(v0))
% 4.57/1.48 |
% 4.57/1.48 | ALPHA: (function-axioms) implies:
% 4.57/1.48 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.57/1.48 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.57/1.48 |
% 4.57/1.48 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_9_0 gives:
% 4.57/1.48 | (6) empty(all_9_0) = 0 & $i(all_9_0)
% 4.57/1.48 |
% 4.57/1.48 | ALPHA: (6) implies:
% 4.57/1.48 | (7) $i(all_9_0)
% 4.57/1.48 | (8) empty(all_9_0) = 0
% 4.57/1.48 |
% 4.57/1.48 | DELTA: instantiating (4) with fresh symbols all_13_0, all_13_1 gives:
% 4.57/1.48 | (9) ~ (all_13_0 = 0) & subset(empty_set, all_13_1) = all_13_0 &
% 4.57/1.48 | $i(all_13_1)
% 4.57/1.48 |
% 4.57/1.48 | ALPHA: (9) implies:
% 4.57/1.48 | (10) ~ (all_13_0 = 0)
% 4.57/1.48 | (11) $i(all_13_1)
% 4.57/1.49 | (12) subset(empty_set, all_13_1) = all_13_0
% 4.57/1.49 |
% 4.57/1.49 | GROUND_INST: instantiating (1) with empty_set, all_13_1, all_13_0, simplifying
% 4.57/1.49 | with (3), (11), (12) gives:
% 4.57/1.49 | (13) all_13_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 4.57/1.49 | all_13_1) = v1 & in(v0, empty_set) = 0 & $i(v0))
% 4.57/1.49 |
% 4.57/1.49 | GROUND_INST: instantiating (2) with all_9_0, simplifying with (7), (8) gives:
% 4.57/1.49 | (14) all_9_0 = empty_set
% 4.57/1.49 |
% 4.57/1.49 | REDUCE: (8), (14) imply:
% 4.57/1.49 | (15) empty(empty_set) = 0
% 4.57/1.49 |
% 4.57/1.49 | BETA: splitting (13) gives:
% 4.57/1.49 |
% 5.34/1.49 | Case 1:
% 5.34/1.49 | |
% 5.34/1.49 | | (16) all_13_0 = 0
% 5.34/1.49 | |
% 5.34/1.49 | | REDUCE: (10), (16) imply:
% 5.34/1.49 | | (17) $false
% 5.34/1.49 | |
% 5.34/1.49 | | CLOSE: (17) is inconsistent.
% 5.34/1.49 | |
% 5.34/1.49 | Case 2:
% 5.34/1.49 | |
% 5.34/1.49 | | (18) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_13_1) = v1 &
% 5.34/1.49 | | in(v0, empty_set) = 0 & $i(v0))
% 5.34/1.49 | |
% 5.34/1.49 | | DELTA: instantiating (18) with fresh symbols all_27_0, all_27_1 gives:
% 5.34/1.49 | | (19) ~ (all_27_0 = 0) & in(all_27_1, all_13_1) = all_27_0 & in(all_27_1,
% 5.34/1.49 | | empty_set) = 0 & $i(all_27_1)
% 5.34/1.49 | |
% 5.34/1.49 | | ALPHA: (19) implies:
% 5.34/1.49 | | (20) $i(all_27_1)
% 5.34/1.49 | | (21) in(all_27_1, empty_set) = 0
% 5.34/1.49 | |
% 5.34/1.49 | | GROUND_INST: instantiating (t7_boole) with all_27_1, empty_set, simplifying
% 5.34/1.49 | | with (3), (20), (21) gives:
% 5.34/1.49 | | (22) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 5.34/1.49 | |
% 5.34/1.49 | | DELTA: instantiating (22) with fresh symbol all_36_0 gives:
% 5.34/1.49 | | (23) ~ (all_36_0 = 0) & empty(empty_set) = all_36_0
% 5.34/1.49 | |
% 5.34/1.49 | | ALPHA: (23) implies:
% 5.34/1.49 | | (24) ~ (all_36_0 = 0)
% 5.34/1.49 | | (25) empty(empty_set) = all_36_0
% 5.34/1.49 | |
% 5.34/1.49 | | GROUND_INST: instantiating (5) with 0, all_36_0, empty_set, simplifying with
% 5.34/1.49 | | (15), (25) gives:
% 5.34/1.49 | | (26) all_36_0 = 0
% 5.34/1.49 | |
% 5.34/1.50 | | REDUCE: (24), (26) imply:
% 5.34/1.50 | | (27) $false
% 5.34/1.50 | |
% 5.34/1.50 | | CLOSE: (27) is inconsistent.
% 5.34/1.50 | |
% 5.34/1.50 | End of split
% 5.34/1.50 |
% 5.34/1.50 End of proof
% 5.34/1.50 % SZS output end Proof for theBenchmark
% 5.34/1.50
% 5.34/1.50 880ms
%------------------------------------------------------------------------------