TSTP Solution File: LCL451+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL451+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 : n012.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 08:11:19 EDT 2023
% Result : Theorem 9.13s 1.92s
% Output : Proof 10.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL451+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n012.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Thu Aug 24 19:43:56 EDT 2023
% 0.16/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.94/1.06 Prover 4: Preprocessing ...
% 2.94/1.07 Prover 1: Preprocessing ...
% 3.22/1.10 Prover 3: Preprocessing ...
% 3.22/1.10 Prover 5: Preprocessing ...
% 3.22/1.10 Prover 2: Preprocessing ...
% 3.22/1.10 Prover 0: Preprocessing ...
% 3.22/1.10 Prover 6: Preprocessing ...
% 7.67/1.74 Prover 6: Constructing countermodel ...
% 7.67/1.75 Prover 1: Constructing countermodel ...
% 7.67/1.75 Prover 5: Proving ...
% 7.67/1.76 Prover 3: Constructing countermodel ...
% 8.30/1.80 Prover 4: Constructing countermodel ...
% 8.30/1.82 Prover 0: Proving ...
% 9.13/1.92 Prover 3: proved (1307ms)
% 9.13/1.92
% 9.13/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.13/1.92
% 9.13/1.93 Prover 6: proved (1304ms)
% 9.13/1.95
% 9.13/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.13/1.95
% 9.13/1.96 Prover 0: stopped
% 9.13/1.96 Prover 5: stopped
% 9.13/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.13/1.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.13/1.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.13/1.98 Prover 2: Proving ...
% 9.13/1.98 Prover 2: stopped
% 9.13/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.13/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.13/1.99 Prover 7: Preprocessing ...
% 9.74/2.01 Prover 1: Found proof (size 19)
% 9.74/2.01 Prover 1: proved (1400ms)
% 9.74/2.01 Prover 4: stopped
% 9.74/2.01 Prover 8: Preprocessing ...
% 9.74/2.03 Prover 10: Preprocessing ...
% 9.74/2.03 Prover 11: Preprocessing ...
% 9.74/2.04 Prover 7: stopped
% 9.74/2.04 Prover 13: Preprocessing ...
% 9.74/2.07 Prover 10: stopped
% 9.74/2.07 Prover 11: stopped
% 9.74/2.08 Prover 13: stopped
% 9.74/2.14 Prover 8: Warning: ignoring some quantifiers
% 9.74/2.16 Prover 8: Constructing countermodel ...
% 9.74/2.16 Prover 8: stopped
% 9.74/2.16
% 9.74/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.74/2.16
% 9.74/2.17 % SZS output start Proof for theBenchmark
% 9.74/2.17 Assumptions after simplification:
% 9.74/2.17 ---------------------------------
% 9.74/2.17
% 9.74/2.17 (cn1)
% 10.83/2.20 (cn1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.83/2.20 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6) | ~
% 10.83/2.20 (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) =
% 10.83/2.20 v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.83/2.20 is_a_theorem(v7) = 0)) | ( ~ cn1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 10.83/2.20 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 10.83/2.20 [v8: int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 &
% 10.83/2.20 implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) = v3 &
% 10.83/2.20 is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 10.83/2.20 $i(v2) & $i(v1) & $i(v0)))
% 10.83/2.20
% 10.83/2.20 (hilbert_implies_3)
% 10.83/2.20 implies_3
% 10.83/2.20
% 10.83/2.20 (implies_3)
% 10.83/2.21 (implies_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 10.83/2.21 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6)
% 10.83/2.21 | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0,
% 10.83/2.21 v2) = v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.83/2.21 $i(v0) | is_a_theorem(v7) = 0)) | ( ~ implies_3 & ? [v0: $i] : ? [v1:
% 10.83/2.21 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 10.83/2.21 : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 &
% 10.83/2.21 implies(v3, v6) = v7 & implies(v1, v2) = v4 & implies(v0, v2) = v5 &
% 10.83/2.21 implies(v0, v1) = v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) &
% 10.83/2.21 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)))
% 10.83/2.21
% 10.83/2.21 (luka_cn1)
% 10.83/2.21 ~ cn1
% 10.83/2.21
% 10.83/2.21 (function-axioms)
% 10.83/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or(v3,
% 10.83/2.21 v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.83/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) =
% 10.83/2.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 10.83/2.21 ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.83/2.21 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~
% 10.83/2.21 (implies(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 10.83/2.21 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.83/2.21 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_a_theorem(v2) = v1)
% 10.83/2.21 | ~ (is_a_theorem(v2) = v0))
% 10.83/2.21
% 10.83/2.21 Further assumptions not needed in the proof:
% 10.83/2.21 --------------------------------------------
% 10.83/2.21 and_1, and_2, and_3, cn2, cn3, equivalence_1, equivalence_2, equivalence_3,
% 10.83/2.21 hilbert_and_1, hilbert_and_2, hilbert_and_3, hilbert_equivalence_1,
% 10.83/2.21 hilbert_equivalence_2, hilbert_equivalence_3, hilbert_implies_1,
% 10.83/2.21 hilbert_implies_2, hilbert_modus_ponens, hilbert_modus_tollens,
% 10.83/2.21 hilbert_op_equiv, hilbert_op_implies_and, hilbert_op_or, hilbert_or_1,
% 10.83/2.21 hilbert_or_2, hilbert_or_3, implies_1, implies_2, kn1, kn2, kn3, luka_op_equiv,
% 10.83/2.21 luka_op_implies, luka_op_or, modus_ponens, modus_tollens, op_and, op_equiv,
% 10.83/2.21 op_implies_and, op_implies_or, op_or, or_1, or_2, or_3, r1, r2, r3, r4, r5,
% 10.83/2.21 substitution_of_equivalents
% 10.83/2.21
% 10.83/2.21 Those formulas are unsatisfiable:
% 10.83/2.21 ---------------------------------
% 10.83/2.21
% 10.83/2.21 Begin of proof
% 10.83/2.21 |
% 10.83/2.21 | ALPHA: (function-axioms) implies:
% 10.83/2.21 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.83/2.21 | (v1 = v0 | ~ (is_a_theorem(v2) = v1) | ~ (is_a_theorem(v2) = v0))
% 10.83/2.21 |
% 10.83/2.21 | BETA: splitting (implies_3) gives:
% 10.83/2.21 |
% 10.83/2.21 | Case 1:
% 10.83/2.21 | |
% 10.83/2.22 | | (2) implies_3 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 10.83/2.22 | | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 10.83/2.22 | | (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~
% 10.83/2.22 | | (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~
% 10.83/2.22 | | (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.83/2.22 | | is_a_theorem(v7) = 0)
% 10.83/2.22 | |
% 10.83/2.22 | | ALPHA: (2) implies:
% 10.83/2.22 | | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.83/2.22 | | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (implies(v4, v5) = v6)
% 10.83/2.22 | | | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~
% 10.83/2.22 | | (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | ~ $i(v2) | ~
% 10.83/2.22 | | $i(v1) | ~ $i(v0) | is_a_theorem(v7) = 0)
% 10.83/2.22 | |
% 10.83/2.22 | | BETA: splitting (cn1) gives:
% 10.83/2.22 | |
% 10.83/2.22 | | Case 1:
% 10.83/2.22 | | |
% 10.83/2.22 | | | (4) cn1 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 10.83/2.22 | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 10.83/2.22 | | | (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~
% 10.83/2.22 | | | (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~
% 10.83/2.22 | | | (implies(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.83/2.22 | | | is_a_theorem(v7) = 0)
% 10.83/2.22 | | |
% 10.83/2.22 | | | ALPHA: (4) implies:
% 10.83/2.22 | | | (5) cn1
% 10.83/2.22 | | |
% 10.83/2.22 | | | PRED_UNIFY: (5), (luka_cn1) imply:
% 10.83/2.22 | | | (6) $false
% 10.83/2.22 | | |
% 10.83/2.22 | | | CLOSE: (6) is inconsistent.
% 10.83/2.22 | | |
% 10.83/2.22 | | Case 2:
% 10.83/2.22 | | |
% 10.83/2.22 | | | (7) ~ cn1 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 10.83/2.22 | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 10.83/2.22 | | | ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 &
% 10.83/2.22 | | | implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) =
% 10.83/2.22 | | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 10.83/2.22 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.83/2.22 | | |
% 10.83/2.22 | | | ALPHA: (7) implies:
% 10.83/2.22 | | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 10.83/2.22 | | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8
% 10.83/2.22 | | | = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7 &
% 10.83/2.22 | | | implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) =
% 10.83/2.22 | | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 10.83/2.22 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.83/2.22 | | |
% 10.83/2.23 | | | DELTA: instantiating (8) with fresh symbols all_77_0, all_77_1, all_77_2,
% 10.83/2.23 | | | all_77_3, all_77_4, all_77_5, all_77_6, all_77_7, all_77_8 gives:
% 10.83/2.23 | | | (9) ~ (all_77_0 = 0) & implies(all_77_4, all_77_3) = all_77_2 &
% 10.83/2.23 | | | implies(all_77_5, all_77_2) = all_77_1 & implies(all_77_7,
% 10.83/2.23 | | | all_77_6) = all_77_4 & implies(all_77_8, all_77_6) = all_77_3 &
% 10.83/2.23 | | | implies(all_77_8, all_77_7) = all_77_5 & is_a_theorem(all_77_1) =
% 10.83/2.23 | | | all_77_0 & $i(all_77_1) & $i(all_77_2) & $i(all_77_3) &
% 10.83/2.23 | | | $i(all_77_4) & $i(all_77_5) & $i(all_77_6) & $i(all_77_7) &
% 10.83/2.23 | | | $i(all_77_8)
% 10.83/2.23 | | |
% 10.83/2.23 | | | ALPHA: (9) implies:
% 10.83/2.23 | | | (10) ~ (all_77_0 = 0)
% 10.83/2.23 | | | (11) $i(all_77_8)
% 10.83/2.23 | | | (12) $i(all_77_7)
% 10.83/2.23 | | | (13) $i(all_77_6)
% 10.83/2.23 | | | (14) is_a_theorem(all_77_1) = all_77_0
% 10.83/2.23 | | | (15) implies(all_77_8, all_77_7) = all_77_5
% 10.83/2.23 | | | (16) implies(all_77_8, all_77_6) = all_77_3
% 10.83/2.23 | | | (17) implies(all_77_7, all_77_6) = all_77_4
% 10.83/2.23 | | | (18) implies(all_77_5, all_77_2) = all_77_1
% 10.83/2.23 | | | (19) implies(all_77_4, all_77_3) = all_77_2
% 10.83/2.23 | | |
% 10.83/2.23 | | | GROUND_INST: instantiating (3) with all_77_8, all_77_7, all_77_6,
% 10.83/2.23 | | | all_77_5, all_77_4, all_77_3, all_77_2, all_77_1, simplifying
% 10.83/2.23 | | | with (11), (12), (13), (15), (16), (17), (18), (19) gives:
% 10.83/2.23 | | | (20) is_a_theorem(all_77_1) = 0
% 10.83/2.23 | | |
% 10.83/2.23 | | | GROUND_INST: instantiating (1) with all_77_0, 0, all_77_1, simplifying
% 10.83/2.23 | | | with (14), (20) gives:
% 10.83/2.23 | | | (21) all_77_0 = 0
% 10.83/2.23 | | |
% 10.83/2.23 | | | REDUCE: (10), (21) imply:
% 10.83/2.23 | | | (22) $false
% 10.83/2.23 | | |
% 10.83/2.23 | | | CLOSE: (22) is inconsistent.
% 10.83/2.23 | | |
% 10.83/2.23 | | End of split
% 10.83/2.23 | |
% 10.83/2.23 | Case 2:
% 10.83/2.23 | |
% 10.83/2.23 | | (23) ~ implies_3 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 10.83/2.23 | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 10.83/2.23 | | int] : ( ~ (v8 = 0) & implies(v4, v5) = v6 & implies(v3, v6) = v7
% 10.83/2.23 | | & implies(v1, v2) = v4 & implies(v0, v2) = v5 & implies(v0, v1) =
% 10.83/2.23 | | v3 & is_a_theorem(v7) = v8 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 10.83/2.23 | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.83/2.23 | |
% 10.83/2.23 | | ALPHA: (23) implies:
% 10.83/2.23 | | (24) ~ implies_3
% 10.83/2.23 | |
% 10.83/2.23 | | PRED_UNIFY: (24), (hilbert_implies_3) imply:
% 10.83/2.23 | | (25) $false
% 10.83/2.23 | |
% 10.83/2.23 | | CLOSE: (25) is inconsistent.
% 10.83/2.23 | |
% 10.83/2.23 | End of split
% 10.83/2.23 |
% 10.83/2.23 End of proof
% 10.83/2.23 % SZS output end Proof for theBenchmark
% 10.83/2.23
% 10.83/2.23 1644ms
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