TSTP Solution File: LCL460+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL460+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 : n027.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 08:11:22 EDT 2023
% Result : Theorem 9.54s 2.04s
% Output : Proof 11.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL460+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 03:53:18 EDT 2023
% 0.13/0.34 % 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
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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 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 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
% 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
% 2.96/1.13 Prover 4: Preprocessing ...
% 2.96/1.14 Prover 1: Preprocessing ...
% 3.58/1.20 Prover 0: Preprocessing ...
% 3.58/1.20 Prover 2: Preprocessing ...
% 3.58/1.20 Prover 6: Preprocessing ...
% 3.58/1.20 Prover 5: Preprocessing ...
% 3.58/1.21 Prover 3: Preprocessing ...
% 8.65/1.89 Prover 1: Constructing countermodel ...
% 8.65/1.90 Prover 6: Constructing countermodel ...
% 8.65/1.90 Prover 5: Proving ...
% 8.90/1.92 Prover 3: Constructing countermodel ...
% 8.99/1.97 Prover 4: Constructing countermodel ...
% 8.99/1.99 Prover 0: Proving ...
% 9.54/2.04 Prover 6: proved (1403ms)
% 9.54/2.04
% 9.54/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.54/2.04
% 9.54/2.05 Prover 5: stopped
% 9.54/2.06 Prover 3: stopped
% 9.54/2.06 Prover 0: stopped
% 9.54/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.54/2.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.54/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.98/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.98/2.12 Prover 8: Preprocessing ...
% 9.98/2.13 Prover 7: Preprocessing ...
% 9.98/2.13 Prover 2: Proving ...
% 9.98/2.14 Prover 10: Preprocessing ...
% 9.98/2.14 Prover 2: stopped
% 9.98/2.15 Prover 11: Preprocessing ...
% 9.98/2.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.98/2.17 Prover 1: Found proof (size 19)
% 9.98/2.18 Prover 1: proved (1544ms)
% 9.98/2.18 Prover 4: stopped
% 9.98/2.19 Prover 13: Preprocessing ...
% 9.98/2.20 Prover 10: stopped
% 9.98/2.21 Prover 7: stopped
% 9.98/2.23 Prover 11: stopped
% 9.98/2.24 Prover 13: stopped
% 11.21/2.30 Prover 8: Warning: ignoring some quantifiers
% 11.45/2.31 Prover 8: Constructing countermodel ...
% 11.45/2.31 Prover 8: stopped
% 11.45/2.31
% 11.45/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.45/2.32
% 11.45/2.32 % SZS output start Proof for theBenchmark
% 11.45/2.33 Assumptions after simplification:
% 11.45/2.33 ---------------------------------
% 11.45/2.33
% 11.45/2.33 (and_1)
% 11.61/2.36 (and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0,
% 11.61/2.36 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 11.61/2.37 is_a_theorem(v3) = 0)) | ( ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 11.61/2.37 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 &
% 11.61/2.37 implies(v2, v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 11.61/2.37 $i(v0)))
% 11.61/2.37
% 11.61/2.37 (hilbert_and_1)
% 11.61/2.37 and_1
% 11.61/2.37
% 11.61/2.37 (kn2)
% 11.61/2.37 (kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0,
% 11.61/2.37 v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 11.61/2.37 is_a_theorem(v3) = 0)) | ( ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 11.61/2.37 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2,
% 11.61/2.37 v0) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)))
% 11.61/2.37
% 11.61/2.37 (rosser_kn2)
% 11.61/2.37 ~ kn2
% 11.61/2.37
% 11.61/2.37 (function-axioms)
% 11.61/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 11.61/2.38 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.61/2.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 11.61/2.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 11.61/2.38 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.61/2.38 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 11.61/2.38 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.61/2.38 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.61/2.38 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1)
% 11.61/2.38 | ~ (is_a_theorem(v2) = v0))
% 11.61/2.38
% 11.61/2.38 Further assumptions not needed in the proof:
% 11.61/2.38 --------------------------------------------
% 11.61/2.38 and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3,
% 11.61/2.38 hilbert_and_2, hilbert_and_3, hilbert_equivalence_1, hilbert_equivalence_2,
% 11.61/2.38 hilbert_equivalence_3, hilbert_implies_1, hilbert_implies_2, hilbert_implies_3,
% 11.61/2.38 hilbert_modus_ponens, hilbert_modus_tollens, hilbert_op_equiv,
% 11.61/2.38 hilbert_op_implies_and, hilbert_op_or, hilbert_or_1, hilbert_or_2, hilbert_or_3,
% 11.61/2.38 implies_1, implies_2, implies_3, kn1, kn3, modus_ponens, modus_tollens, op_and,
% 11.61/2.38 op_equiv, op_implies_and, op_implies_or, op_or, or_1, or_2, or_3, r1, r2, r3,
% 11.61/2.38 r4, r5, rosser_op_equiv, rosser_op_implies_and, rosser_op_or,
% 11.61/2.38 substitution_of_equivalents
% 11.61/2.38
% 11.61/2.38 Those formulas are unsatisfiable:
% 11.61/2.38 ---------------------------------
% 11.61/2.38
% 11.61/2.38 Begin of proof
% 11.61/2.38 |
% 11.61/2.38 | ALPHA: (function-axioms) implies:
% 11.61/2.38 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.61/2.38 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 11.61/2.38 |
% 11.61/2.38 | BETA: splitting (and_1) gives:
% 11.61/2.38 |
% 11.61/2.38 | Case 1:
% 11.61/2.38 | |
% 11.61/2.38 | | (2) and_1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.61/2.38 | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~
% 11.61/2.38 | | $i(v0) | is_a_theorem(v3) = 0)
% 11.61/2.38 | |
% 11.61/2.38 | | ALPHA: (2) implies:
% 11.61/2.38 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (and(v0,
% 11.61/2.38 | | v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 11.61/2.38 | | is_a_theorem(v3) = 0)
% 11.61/2.38 | |
% 11.61/2.38 | | BETA: splitting (kn2) gives:
% 11.61/2.38 | |
% 11.61/2.38 | | Case 1:
% 11.61/2.38 | | |
% 11.61/2.38 | | | (4) kn2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.61/2.38 | | | (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | ~ $i(v1) | ~
% 11.61/2.38 | | | $i(v0) | is_a_theorem(v3) = 0)
% 11.61/2.38 | | |
% 11.61/2.38 | | | ALPHA: (4) implies:
% 11.61/2.39 | | | (5) kn2
% 11.61/2.39 | | |
% 11.61/2.39 | | | PRED_UNIFY: (5), (rosser_kn2) imply:
% 11.61/2.39 | | | (6) $false
% 11.61/2.39 | | |
% 11.61/2.39 | | | CLOSE: (6) is inconsistent.
% 11.61/2.39 | | |
% 11.61/2.39 | | Case 2:
% 11.61/2.39 | | |
% 11.61/2.39 | | | (7) ~ kn2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 11.61/2.39 | | | [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3
% 11.61/2.39 | | | & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.61/2.39 | | |
% 11.61/2.39 | | | ALPHA: (7) implies:
% 11.61/2.39 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 11.61/2.39 | | | int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3 &
% 11.61/2.39 | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.61/2.39 | | |
% 11.61/2.39 | | | DELTA: instantiating (8) with fresh symbols all_77_0, all_77_1, all_77_2,
% 11.61/2.39 | | | all_77_3, all_77_4 gives:
% 11.61/2.39 | | | (9) ~ (all_77_0 = 0) & and(all_77_4, all_77_3) = all_77_2 &
% 11.61/2.39 | | | implies(all_77_2, all_77_4) = all_77_1 & is_a_theorem(all_77_1) =
% 11.61/2.39 | | | all_77_0 & $i(all_77_1) & $i(all_77_2) & $i(all_77_3) &
% 11.61/2.39 | | | $i(all_77_4)
% 11.61/2.39 | | |
% 11.61/2.39 | | | ALPHA: (9) implies:
% 11.61/2.39 | | | (10) ~ (all_77_0 = 0)
% 11.61/2.39 | | | (11) $i(all_77_4)
% 11.61/2.39 | | | (12) $i(all_77_3)
% 11.61/2.39 | | | (13) is_a_theorem(all_77_1) = all_77_0
% 11.61/2.39 | | | (14) implies(all_77_2, all_77_4) = all_77_1
% 11.61/2.39 | | | (15) and(all_77_4, all_77_3) = all_77_2
% 11.61/2.39 | | |
% 11.61/2.39 | | | GROUND_INST: instantiating (3) with all_77_4, all_77_3, all_77_2,
% 11.61/2.39 | | | all_77_1, simplifying with (11), (12), (14), (15) gives:
% 11.61/2.39 | | | (16) is_a_theorem(all_77_1) = 0
% 11.61/2.39 | | |
% 11.61/2.39 | | | GROUND_INST: instantiating (1) with all_77_0, 0, all_77_1, simplifying
% 11.61/2.39 | | | with (13), (16) gives:
% 11.61/2.39 | | | (17) all_77_0 = 0
% 11.61/2.39 | | |
% 11.61/2.39 | | | REDUCE: (10), (17) imply:
% 11.61/2.39 | | | (18) $false
% 11.61/2.39 | | |
% 11.61/2.39 | | | CLOSE: (18) is inconsistent.
% 11.61/2.39 | | |
% 11.61/2.39 | | End of split
% 11.61/2.39 | |
% 11.61/2.39 | Case 2:
% 11.61/2.39 | |
% 11.61/2.39 | | (19) ~ and_1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 11.61/2.39 | | ? [v4: int] : ( ~ (v4 = 0) & and(v0, v1) = v2 & implies(v2, v0) = v3
% 11.61/2.39 | | & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.61/2.39 | |
% 11.61/2.39 | | ALPHA: (19) implies:
% 11.61/2.39 | | (20) ~ and_1
% 11.61/2.39 | |
% 11.61/2.39 | | PRED_UNIFY: (20), (hilbert_and_1) imply:
% 11.61/2.39 | | (21) $false
% 11.61/2.39 | |
% 11.61/2.39 | | CLOSE: (21) is inconsistent.
% 11.61/2.39 | |
% 11.61/2.39 | End of split
% 11.61/2.39 |
% 11.61/2.39 End of proof
% 11.61/2.39 % SZS output end Proof for theBenchmark
% 11.61/2.39
% 11.61/2.39 1781ms
%------------------------------------------------------------------------------