TSTP Solution File: LCL491+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL491+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 : n010.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 08:11:27 EDT 2023
% Result : Theorem 8.09s 1.89s
% Output : Proof 10.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL491+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.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 : Thu Aug 24 18:35:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 ________ _____
% 0.21/0.57 ___ __ \_________(_)________________________________
% 0.21/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.57
% 0.21/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.57 (2023-06-19)
% 0.21/0.57
% 0.21/0.57 (c) Philipp Rümmer, 2009-2023
% 0.21/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.57 Amanda Stjerna.
% 0.21/0.57 Free software under BSD-3-Clause.
% 0.21/0.57
% 0.21/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.57
% 0.21/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.59 Running up to 7 provers in parallel.
% 0.21/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 3.24/1.15 Prover 1: Preprocessing ...
% 3.24/1.15 Prover 4: Preprocessing ...
% 3.24/1.19 Prover 2: Preprocessing ...
% 3.24/1.19 Prover 3: Preprocessing ...
% 3.24/1.19 Prover 6: Preprocessing ...
% 3.24/1.19 Prover 5: Preprocessing ...
% 3.24/1.19 Prover 0: Preprocessing ...
% 7.33/1.70 Prover 5: Proving ...
% 7.33/1.71 Prover 6: Constructing countermodel ...
% 7.33/1.74 Prover 1: Constructing countermodel ...
% 8.02/1.80 Prover 4: Constructing countermodel ...
% 8.09/1.81 Prover 3: Constructing countermodel ...
% 8.09/1.82 Prover 0: Proving ...
% 8.09/1.89 Prover 6: proved (1283ms)
% 8.09/1.89 Prover 3: proved (1280ms)
% 8.09/1.89
% 8.09/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.09/1.89
% 8.09/1.89
% 8.09/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.09/1.89
% 8.09/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.09/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.53/1.91 Prover 5: stopped
% 8.53/1.91 Prover 0: stopped
% 8.53/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.53/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.53/1.96 Prover 2: Proving ...
% 8.53/1.96 Prover 8: Preprocessing ...
% 8.53/1.96 Prover 7: Preprocessing ...
% 8.53/1.96 Prover 2: stopped
% 8.53/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.53/2.00 Prover 1: Found proof (size 19)
% 8.53/2.00 Prover 1: proved (1400ms)
% 8.53/2.00 Prover 11: Preprocessing ...
% 8.53/2.00 Prover 10: Preprocessing ...
% 9.45/2.00 Prover 4: stopped
% 9.45/2.01 Prover 13: Preprocessing ...
% 9.45/2.04 Prover 7: stopped
% 9.45/2.04 Prover 11: stopped
% 9.45/2.04 Prover 10: stopped
% 9.45/2.06 Prover 13: stopped
% 10.02/2.13 Prover 8: Warning: ignoring some quantifiers
% 10.02/2.15 Prover 8: Constructing countermodel ...
% 10.02/2.15 Prover 8: stopped
% 10.02/2.15
% 10.02/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.02/2.15
% 10.02/2.16 % SZS output start Proof for theBenchmark
% 10.02/2.16 Assumptions after simplification:
% 10.02/2.16 ---------------------------------
% 10.02/2.16
% 10.02/2.16 (hilbert_or_2)
% 10.02/2.16 ~ or_2
% 10.02/2.16
% 10.02/2.16 (or_2)
% 10.49/2.19 (or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0,
% 10.49/2.19 v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 10.49/2.19 is_a_theorem(v3) = 0)) | ( ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 10.49/2.19 $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 &
% 10.49/2.19 implies(v1, v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 10.49/2.19 $i(v0)))
% 10.49/2.19
% 10.49/2.19 (principia_r2)
% 10.49/2.19 r2
% 10.49/2.19
% 10.49/2.19 (r2)
% 10.52/2.19 (r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0, v1)
% 10.52/2.19 = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 10.52/2.19 is_a_theorem(v3) = 0)) | ( ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 10.52/2.19 : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1,
% 10.52/2.19 v2) = v3 & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)))
% 10.52/2.19
% 10.52/2.19 (function-axioms)
% 10.52/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 10.52/2.20 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.52/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 10.52/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 10.52/2.20 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.52/2.20 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 10.52/2.20 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 10.52/2.20 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.52/2.20 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1)
% 10.52/2.20 | ~ (is_a_theorem(v2) = v0))
% 10.52/2.20
% 10.52/2.20 Further assumptions not needed in the proof:
% 10.52/2.20 --------------------------------------------
% 10.52/2.20 and_1, and_2, and_3, cn1, cn2, cn3, equivalence_1, equivalence_2, equivalence_3,
% 10.52/2.20 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, implies_1, implies_2,
% 10.52/2.20 implies_3, kn1, kn2, kn3, modus_ponens, modus_tollens, op_and, op_equiv,
% 10.52/2.20 op_implies_and, op_implies_or, op_or, or_1, or_3, principia_modus_ponens,
% 10.52/2.20 principia_op_and, principia_op_equiv, principia_op_implies_or, principia_r1,
% 10.52/2.20 principia_r3, principia_r4, principia_r5, r1, r3, r4, r5,
% 10.52/2.20 substitution_of_equivalents
% 10.52/2.20
% 10.52/2.20 Those formulas are unsatisfiable:
% 10.52/2.20 ---------------------------------
% 10.52/2.20
% 10.52/2.20 Begin of proof
% 10.52/2.20 |
% 10.52/2.20 | ALPHA: (function-axioms) implies:
% 10.52/2.20 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.52/2.20 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 10.52/2.20 |
% 10.52/2.20 | BETA: splitting (r2) gives:
% 10.52/2.20 |
% 10.52/2.20 | Case 1:
% 10.52/2.20 | |
% 10.57/2.20 | | (2) r2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.57/2.20 | | (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~
% 10.57/2.20 | | $i(v0) | is_a_theorem(v3) = 0)
% 10.57/2.20 | |
% 10.57/2.20 | | ALPHA: (2) implies:
% 10.57/2.21 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (or(v0,
% 10.57/2.21 | | v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 10.57/2.21 | | is_a_theorem(v3) = 0)
% 10.57/2.21 | |
% 10.57/2.21 | | BETA: splitting (or_2) gives:
% 10.57/2.21 | |
% 10.57/2.21 | | Case 1:
% 10.57/2.21 | | |
% 10.57/2.21 | | | (4) or_2 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.57/2.21 | | | (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ $i(v1) | ~
% 10.57/2.21 | | | $i(v0) | is_a_theorem(v3) = 0)
% 10.57/2.21 | | |
% 10.57/2.21 | | | ALPHA: (4) implies:
% 10.57/2.21 | | | (5) or_2
% 10.57/2.21 | | |
% 10.58/2.21 | | | PRED_UNIFY: (5), (hilbert_or_2) imply:
% 10.58/2.21 | | | (6) $false
% 10.58/2.21 | | |
% 10.58/2.21 | | | CLOSE: (6) is inconsistent.
% 10.58/2.21 | | |
% 10.58/2.21 | | Case 2:
% 10.58/2.21 | | |
% 10.58/2.21 | | | (7) ~ or_2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.58/2.21 | | | ? [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3
% 10.58/2.21 | | | & is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.58/2.21 | | |
% 10.58/2.21 | | | ALPHA: (7) implies:
% 10.58/2.21 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 10.58/2.21 | | | int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 &
% 10.58/2.21 | | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.58/2.21 | | |
% 10.58/2.21 | | | DELTA: instantiating (8) with fresh symbols all_53_0, all_53_1, all_53_2,
% 10.58/2.21 | | | all_53_3, all_53_4 gives:
% 10.58/2.21 | | | (9) ~ (all_53_0 = 0) & or(all_53_4, all_53_3) = all_53_2 &
% 10.58/2.21 | | | implies(all_53_3, all_53_2) = all_53_1 & is_a_theorem(all_53_1) =
% 10.58/2.21 | | | all_53_0 & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) &
% 10.58/2.21 | | | $i(all_53_4)
% 10.58/2.21 | | |
% 10.58/2.21 | | | ALPHA: (9) implies:
% 10.58/2.21 | | | (10) ~ (all_53_0 = 0)
% 10.58/2.21 | | | (11) $i(all_53_4)
% 10.58/2.21 | | | (12) $i(all_53_3)
% 10.58/2.21 | | | (13) is_a_theorem(all_53_1) = all_53_0
% 10.58/2.21 | | | (14) implies(all_53_3, all_53_2) = all_53_1
% 10.58/2.21 | | | (15) or(all_53_4, all_53_3) = all_53_2
% 10.58/2.21 | | |
% 10.58/2.21 | | | GROUND_INST: instantiating (3) with all_53_4, all_53_3, all_53_2,
% 10.58/2.21 | | | all_53_1, simplifying with (11), (12), (14), (15) gives:
% 10.58/2.22 | | | (16) is_a_theorem(all_53_1) = 0
% 10.58/2.22 | | |
% 10.58/2.22 | | | GROUND_INST: instantiating (1) with all_53_0, 0, all_53_1, simplifying
% 10.58/2.22 | | | with (13), (16) gives:
% 10.58/2.22 | | | (17) all_53_0 = 0
% 10.58/2.22 | | |
% 10.58/2.22 | | | REDUCE: (10), (17) imply:
% 10.58/2.22 | | | (18) $false
% 10.58/2.22 | | |
% 10.58/2.22 | | | CLOSE: (18) is inconsistent.
% 10.58/2.22 | | |
% 10.58/2.22 | | End of split
% 10.58/2.22 | |
% 10.58/2.22 | Case 2:
% 10.58/2.22 | |
% 10.58/2.22 | | (19) ~ r2 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 10.58/2.22 | | [v4: int] : ( ~ (v4 = 0) & or(v0, v1) = v2 & implies(v1, v2) = v3 &
% 10.58/2.22 | | is_a_theorem(v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.58/2.22 | |
% 10.58/2.22 | | ALPHA: (19) implies:
% 10.58/2.22 | | (20) ~ r2
% 10.58/2.22 | |
% 10.58/2.22 | | PRED_UNIFY: (20), (principia_r2) imply:
% 10.58/2.22 | | (21) $false
% 10.58/2.22 | |
% 10.58/2.22 | | CLOSE: (21) is inconsistent.
% 10.58/2.22 | |
% 10.58/2.22 | End of split
% 10.58/2.22 |
% 10.58/2.22 End of proof
% 10.58/2.22 % SZS output end Proof for theBenchmark
% 10.58/2.22
% 10.58/2.22 1647ms
%------------------------------------------------------------------------------