TSTP Solution File: GRP194+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 01:11:35 EDT 2023
% Result : Theorem 5.78s 1.54s
% Output : Proof 7.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 : Mon Aug 28 21:09:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.46/0.61 ________ _____
% 0.46/0.61 ___ __ \_________(_)________________________________
% 0.46/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.46/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.46/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.46/0.61
% 0.46/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.46/0.61 (2023-06-19)
% 0.46/0.61
% 0.46/0.61 (c) Philipp Rümmer, 2009-2023
% 0.46/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.46/0.61 Amanda Stjerna.
% 0.46/0.61 Free software under BSD-3-Clause.
% 0.46/0.61
% 0.46/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.46/0.61
% 0.46/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.46/0.62 Running up to 7 provers in parallel.
% 0.46/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.46/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.46/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.46/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.46/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.46/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.46/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/1.03 Prover 4: Preprocessing ...
% 2.14/1.03 Prover 1: Preprocessing ...
% 2.63/1.07 Prover 6: Preprocessing ...
% 2.63/1.07 Prover 5: Preprocessing ...
% 2.63/1.07 Prover 0: Preprocessing ...
% 2.63/1.07 Prover 2: Preprocessing ...
% 2.63/1.07 Prover 3: Preprocessing ...
% 3.97/1.34 Prover 1: Constructing countermodel ...
% 3.97/1.34 Prover 5: Constructing countermodel ...
% 3.97/1.34 Prover 6: Proving ...
% 3.97/1.34 Prover 3: Constructing countermodel ...
% 4.39/1.35 Prover 2: Proving ...
% 4.48/1.36 Prover 4: Constructing countermodel ...
% 4.48/1.41 Prover 0: Proving ...
% 5.12/1.53 Prover 3: proved (903ms)
% 5.12/1.53
% 5.78/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.78/1.54
% 5.78/1.54 Prover 5: stopped
% 5.78/1.54 Prover 2: stopped
% 5.78/1.54 Prover 6: stopped
% 5.78/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.78/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.78/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.78/1.54 Prover 0: stopped
% 5.78/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.78/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.78/1.57 Prover 10: Preprocessing ...
% 5.78/1.58 Prover 8: Preprocessing ...
% 5.78/1.58 Prover 11: Preprocessing ...
% 6.10/1.58 Prover 7: Preprocessing ...
% 6.10/1.59 Prover 13: Preprocessing ...
% 6.10/1.64 Prover 7: Constructing countermodel ...
% 6.10/1.64 Prover 10: Constructing countermodel ...
% 6.10/1.65 Prover 8: Warning: ignoring some quantifiers
% 6.66/1.66 Prover 8: Constructing countermodel ...
% 6.66/1.67 Prover 13: Constructing countermodel ...
% 6.77/1.69 Prover 1: Found proof (size 67)
% 6.77/1.69 Prover 1: proved (1065ms)
% 6.77/1.69 Prover 4: stopped
% 6.77/1.69 Prover 10: stopped
% 6.77/1.70 Prover 7: stopped
% 6.77/1.70 Prover 8: stopped
% 6.77/1.70 Prover 11: Constructing countermodel ...
% 6.77/1.70 Prover 13: stopped
% 6.77/1.71 Prover 11: stopped
% 6.77/1.71
% 6.77/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/1.71
% 7.09/1.72 % SZS output start Proof for theBenchmark
% 7.09/1.73 Assumptions after simplification:
% 7.09/1.73 ---------------------------------
% 7.09/1.73
% 7.09/1.73 (homomorphism1)
% 7.22/1.75 $i(h) & $i(f) & ! [v0: $i] : ( ~ (group_member(v0, f) = 0) | ~ $i(v0) | ?
% 7.22/1.75 [v1: $i] : (phi(v0) = v1 & group_member(v1, h) = 0 & $i(v1)))
% 7.22/1.75
% 7.22/1.75 (homomorphism2)
% 7.22/1.76 $i(h) & $i(f) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 7.22/1.76 [v4: $i] : ( ~ (phi(v1) = v3) | ~ (phi(v0) = v2) | ~ (multiply(h, v2, v3) =
% 7.22/1.76 v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 7.22/1.76 ? [v8: $i] : (phi(v7) = v8 & multiply(f, v0, v1) = v7 & group_member(v1, f)
% 7.22/1.76 = v6 & group_member(v0, f) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 7.22/1.76 = 0) | v8 = v4)))
% 7.22/1.76
% 7.22/1.76 (left_zero)
% 7.22/1.76 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (left_zero(v0, v1) =
% 7.22/1.76 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v1) &
% 7.22/1.76 multiply(v0, v1, v3) = v4 & group_member(v3, v0) = 0 & $i(v4) & $i(v3)) |
% 7.22/1.76 ? [v3: int] : ( ~ (v3 = 0) & group_member(v1, v0) = v3)) & ! [v0: $i] : !
% 7.22/1.76 [v1: $i] : ( ~ (left_zero(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.22/1.76 (group_member(v1, v0) = 0 & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 7.22/1.76 (multiply(v0, v1, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 7.22/1.76 group_member(v2, v0) = v4))))
% 7.22/1.76
% 7.22/1.76 (left_zero_for_f)
% 7.22/1.77 left_zero(f, f_left_zero) = 0 & $i(f_left_zero) & $i(f)
% 7.22/1.77
% 7.22/1.77 (prove_left_zero_h)
% 7.22/1.77 $i(f_left_zero) & $i(h) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 7.22/1.77 left_zero(h, v0) = v1 & phi(f_left_zero) = v0 & $i(v0))
% 7.22/1.77
% 7.22/1.77 (surjective)
% 7.22/1.77 $i(h) & $i(f) & ! [v0: $i] : ( ~ (group_member(v0, h) = 0) | ~ $i(v0) | ?
% 7.22/1.77 [v1: $i] : (phi(v1) = v0 & group_member(v1, f) = 0 & $i(v1)))
% 7.22/1.77
% 7.22/1.77 (function-axioms)
% 7.22/1.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 7.22/1.77 | ~ (multiply(v4, v3, v2) = v1) | ~ (multiply(v4, v3, v2) = v0)) & ! [v0:
% 7.22/1.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.22/1.77 : (v1 = v0 | ~ (left_zero(v3, v2) = v1) | ~ (left_zero(v3, v2) = v0)) & !
% 7.22/1.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.22/1.77 $i] : (v1 = v0 | ~ (group_member(v3, v2) = v1) | ~ (group_member(v3, v2) =
% 7.22/1.77 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (phi(v2) =
% 7.22/1.77 v1) | ~ (phi(v2) = v0))
% 7.22/1.77
% 7.22/1.77 Further assumptions not needed in the proof:
% 7.22/1.77 --------------------------------------------
% 7.22/1.77 associativity, total_function
% 7.22/1.77
% 7.22/1.77 Those formulas are unsatisfiable:
% 7.22/1.77 ---------------------------------
% 7.22/1.77
% 7.22/1.77 Begin of proof
% 7.22/1.77 |
% 7.22/1.77 | ALPHA: (homomorphism1) implies:
% 7.22/1.78 | (1) ! [v0: $i] : ( ~ (group_member(v0, f) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.22/1.78 | (phi(v0) = v1 & group_member(v1, h) = 0 & $i(v1)))
% 7.22/1.78 |
% 7.22/1.78 | ALPHA: (homomorphism2) implies:
% 7.22/1.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 7.22/1.78 | ~ (phi(v1) = v3) | ~ (phi(v0) = v2) | ~ (multiply(h, v2, v3) = v4)
% 7.22/1.78 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 7.22/1.78 | ? [v8: $i] : (phi(v7) = v8 & multiply(f, v0, v1) = v7 &
% 7.22/1.78 | group_member(v1, f) = v6 & group_member(v0, f) = v5 & $i(v8) &
% 7.22/1.78 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))
% 7.22/1.78 |
% 7.22/1.78 | ALPHA: (surjective) implies:
% 7.22/1.78 | (3) ! [v0: $i] : ( ~ (group_member(v0, h) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.22/1.78 | (phi(v1) = v0 & group_member(v1, f) = 0 & $i(v1)))
% 7.22/1.78 |
% 7.22/1.78 | ALPHA: (left_zero) implies:
% 7.22/1.79 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (left_zero(v0, v1) = 0) | ~ $i(v1) |
% 7.22/1.79 | ~ $i(v0) | (group_member(v1, v0) = 0 & ! [v2: $i] : ! [v3: $i] :
% 7.22/1.79 | (v3 = v1 | ~ (multiply(v0, v1, v2) = v3) | ~ $i(v2) | ? [v4:
% 7.22/1.79 | int] : ( ~ (v4 = 0) & group_member(v2, v0) = v4))))
% 7.22/1.79 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (left_zero(v0,
% 7.22/1.79 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (
% 7.22/1.79 | ~ (v4 = v1) & multiply(v0, v1, v3) = v4 & group_member(v3, v0) = 0
% 7.22/1.79 | & $i(v4) & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & group_member(v1,
% 7.22/1.79 | v0) = v3))
% 7.22/1.79 |
% 7.22/1.79 | ALPHA: (left_zero_for_f) implies:
% 7.22/1.79 | (6) $i(f)
% 7.22/1.79 | (7) left_zero(f, f_left_zero) = 0
% 7.22/1.79 |
% 7.22/1.79 | ALPHA: (prove_left_zero_h) implies:
% 7.22/1.79 | (8) $i(h)
% 7.22/1.79 | (9) $i(f_left_zero)
% 7.22/1.79 | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & left_zero(h, v0) = v1 &
% 7.22/1.79 | phi(f_left_zero) = v0 & $i(v0))
% 7.22/1.79 |
% 7.22/1.79 | ALPHA: (function-axioms) implies:
% 7.22/1.79 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (phi(v2) = v1)
% 7.22/1.79 | | ~ (phi(v2) = v0))
% 7.22/1.79 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.22/1.79 | : ! [v3: $i] : (v1 = v0 | ~ (group_member(v3, v2) = v1) | ~
% 7.22/1.79 | (group_member(v3, v2) = v0))
% 7.22/1.79 |
% 7.22/1.79 | DELTA: instantiating (10) with fresh symbols all_10_0, all_10_1 gives:
% 7.22/1.79 | (13) ~ (all_10_0 = 0) & left_zero(h, all_10_1) = all_10_0 &
% 7.22/1.79 | phi(f_left_zero) = all_10_1 & $i(all_10_1)
% 7.22/1.79 |
% 7.22/1.79 | ALPHA: (13) implies:
% 7.22/1.79 | (14) ~ (all_10_0 = 0)
% 7.22/1.79 | (15) $i(all_10_1)
% 7.22/1.79 | (16) phi(f_left_zero) = all_10_1
% 7.22/1.79 | (17) left_zero(h, all_10_1) = all_10_0
% 7.22/1.80 |
% 7.22/1.80 | GROUND_INST: instantiating (4) with f, f_left_zero, simplifying with (6), (7),
% 7.22/1.80 | (9) gives:
% 7.22/1.80 | (18) group_member(f_left_zero, f) = 0 & ! [v0: $i] : ! [v1: $i] : (v1 =
% 7.22/1.80 | f_left_zero | ~ (multiply(f, f_left_zero, v0) = v1) | ~ $i(v0) |
% 7.22/1.80 | ? [v2: int] : ( ~ (v2 = 0) & group_member(v0, f) = v2))
% 7.22/1.80 |
% 7.22/1.80 | ALPHA: (18) implies:
% 7.22/1.80 | (19) group_member(f_left_zero, f) = 0
% 7.22/1.80 | (20) ! [v0: $i] : ! [v1: $i] : (v1 = f_left_zero | ~ (multiply(f,
% 7.22/1.80 | f_left_zero, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 7.22/1.80 | & group_member(v0, f) = v2))
% 7.22/1.80 |
% 7.22/1.80 | GROUND_INST: instantiating (5) with h, all_10_1, all_10_0, simplifying with
% 7.22/1.80 | (8), (15), (17) gives:
% 7.22/1.80 | (21) all_10_0 = 0 | ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_10_1) &
% 7.22/1.80 | multiply(h, all_10_1, v0) = v1 & group_member(v0, h) = 0 & $i(v1) &
% 7.22/1.80 | $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) & group_member(all_10_1, h) =
% 7.22/1.80 | v0)
% 7.22/1.80 |
% 7.22/1.80 | GROUND_INST: instantiating (1) with f_left_zero, simplifying with (9), (19)
% 7.22/1.80 | gives:
% 7.22/1.80 | (22) ? [v0: $i] : (phi(f_left_zero) = v0 & group_member(v0, h) = 0 &
% 7.22/1.80 | $i(v0))
% 7.22/1.80 |
% 7.22/1.80 | DELTA: instantiating (22) with fresh symbol all_24_0 gives:
% 7.22/1.80 | (23) phi(f_left_zero) = all_24_0 & group_member(all_24_0, h) = 0 &
% 7.22/1.80 | $i(all_24_0)
% 7.22/1.80 |
% 7.22/1.80 | ALPHA: (23) implies:
% 7.22/1.80 | (24) $i(all_24_0)
% 7.22/1.80 | (25) group_member(all_24_0, h) = 0
% 7.22/1.80 | (26) phi(f_left_zero) = all_24_0
% 7.22/1.80 |
% 7.22/1.80 | GROUND_INST: instantiating (11) with all_10_1, all_24_0, f_left_zero,
% 7.22/1.80 | simplifying with (16), (26) gives:
% 7.22/1.80 | (27) all_24_0 = all_10_1
% 7.22/1.80 |
% 7.22/1.80 | REDUCE: (25), (27) imply:
% 7.22/1.80 | (28) group_member(all_10_1, h) = 0
% 7.22/1.80 |
% 7.22/1.80 | BETA: splitting (21) gives:
% 7.22/1.80 |
% 7.22/1.80 | Case 1:
% 7.22/1.80 | |
% 7.22/1.80 | | (29) all_10_0 = 0
% 7.22/1.80 | |
% 7.22/1.80 | | REDUCE: (14), (29) imply:
% 7.22/1.80 | | (30) $false
% 7.22/1.81 | |
% 7.22/1.81 | | CLOSE: (30) is inconsistent.
% 7.22/1.81 | |
% 7.22/1.81 | Case 2:
% 7.22/1.81 | |
% 7.22/1.81 | | (31) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_10_1) & multiply(h,
% 7.22/1.81 | | all_10_1, v0) = v1 & group_member(v0, h) = 0 & $i(v1) & $i(v0))
% 7.22/1.81 | | | ? [v0: int] : ( ~ (v0 = 0) & group_member(all_10_1, h) = v0)
% 7.22/1.81 | |
% 7.22/1.81 | | BETA: splitting (31) gives:
% 7.22/1.81 | |
% 7.22/1.81 | | Case 1:
% 7.22/1.81 | | |
% 7.22/1.81 | | | (32) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_10_1) & multiply(h,
% 7.22/1.81 | | | all_10_1, v0) = v1 & group_member(v0, h) = 0 & $i(v1) &
% 7.22/1.81 | | | $i(v0))
% 7.22/1.81 | | |
% 7.22/1.81 | | | DELTA: instantiating (32) with fresh symbols all_37_0, all_37_1 gives:
% 7.22/1.81 | | | (33) ~ (all_37_0 = all_10_1) & multiply(h, all_10_1, all_37_1) =
% 7.22/1.81 | | | all_37_0 & group_member(all_37_1, h) = 0 & $i(all_37_0) &
% 7.22/1.81 | | | $i(all_37_1)
% 7.22/1.81 | | |
% 7.22/1.81 | | | ALPHA: (33) implies:
% 7.22/1.81 | | | (34) ~ (all_37_0 = all_10_1)
% 7.22/1.81 | | | (35) $i(all_37_1)
% 7.22/1.81 | | | (36) group_member(all_37_1, h) = 0
% 7.22/1.81 | | | (37) multiply(h, all_10_1, all_37_1) = all_37_0
% 7.22/1.81 | | |
% 7.22/1.81 | | | GROUND_INST: instantiating (3) with all_10_1, simplifying with (15), (28)
% 7.22/1.81 | | | gives:
% 7.22/1.81 | | | (38) ? [v0: $i] : (phi(v0) = all_10_1 & group_member(v0, f) = 0 &
% 7.22/1.81 | | | $i(v0))
% 7.22/1.81 | | |
% 7.22/1.81 | | | GROUND_INST: instantiating (3) with all_37_1, simplifying with (35), (36)
% 7.22/1.81 | | | gives:
% 7.22/1.81 | | | (39) ? [v0: $i] : (phi(v0) = all_37_1 & group_member(v0, f) = 0 &
% 7.22/1.81 | | | $i(v0))
% 7.22/1.81 | | |
% 7.22/1.81 | | | DELTA: instantiating (39) with fresh symbol all_44_0 gives:
% 7.22/1.81 | | | (40) phi(all_44_0) = all_37_1 & group_member(all_44_0, f) = 0 &
% 7.22/1.81 | | | $i(all_44_0)
% 7.22/1.81 | | |
% 7.22/1.81 | | | ALPHA: (40) implies:
% 7.22/1.81 | | | (41) $i(all_44_0)
% 7.22/1.81 | | | (42) group_member(all_44_0, f) = 0
% 7.22/1.81 | | | (43) phi(all_44_0) = all_37_1
% 7.22/1.81 | | |
% 7.22/1.81 | | | DELTA: instantiating (38) with fresh symbol all_46_0 gives:
% 7.22/1.81 | | | (44) phi(all_46_0) = all_10_1 & group_member(all_46_0, f) = 0 &
% 7.22/1.81 | | | $i(all_46_0)
% 7.22/1.81 | | |
% 7.22/1.81 | | | ALPHA: (44) implies:
% 7.22/1.81 | | | (45) $i(all_46_0)
% 7.22/1.81 | | | (46) phi(all_46_0) = all_10_1
% 7.22/1.81 | | |
% 7.22/1.82 | | | GROUND_INST: instantiating (2) with f_left_zero, all_44_0, all_10_1,
% 7.22/1.82 | | | all_37_1, all_37_0, simplifying with (9), (16), (37), (41),
% 7.22/1.82 | | | (43) gives:
% 7.22/1.82 | | | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (phi(v2)
% 7.22/1.82 | | | = v3 & multiply(f, f_left_zero, all_44_0) = v2 &
% 7.22/1.82 | | | group_member(all_44_0, f) = v1 & group_member(f_left_zero, f) =
% 7.22/1.82 | | | v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 =
% 7.22/1.82 | | | all_37_0))
% 7.22/1.82 | | |
% 7.22/1.82 | | | GROUND_INST: instantiating (2) with all_46_0, all_44_0, all_10_1,
% 7.22/1.82 | | | all_37_1, all_37_0, simplifying with (37), (41), (43), (45),
% 7.22/1.82 | | | (46) gives:
% 7.22/1.82 | | | (48) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (phi(v2)
% 7.22/1.82 | | | = v3 & multiply(f, all_46_0, all_44_0) = v2 &
% 7.22/1.82 | | | group_member(all_46_0, f) = v0 & group_member(all_44_0, f) = v1
% 7.22/1.82 | | | & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_37_0))
% 7.22/1.82 | | |
% 7.22/1.82 | | | DELTA: instantiating (48) with fresh symbols all_53_0, all_53_1, all_53_2,
% 7.22/1.82 | | | all_53_3 gives:
% 7.22/1.82 | | | (49) phi(all_53_1) = all_53_0 & multiply(f, all_46_0, all_44_0) =
% 7.22/1.82 | | | all_53_1 & group_member(all_46_0, f) = all_53_3 &
% 7.22/1.82 | | | group_member(all_44_0, f) = all_53_2 & $i(all_53_0) & $i(all_53_1)
% 7.22/1.82 | | | & ( ~ (all_53_2 = 0) | ~ (all_53_3 = 0) | all_53_0 = all_37_0)
% 7.22/1.82 | | |
% 7.22/1.82 | | | ALPHA: (49) implies:
% 7.22/1.82 | | | (50) group_member(all_44_0, f) = all_53_2
% 7.22/1.82 | | |
% 7.22/1.82 | | | DELTA: instantiating (47) with fresh symbols all_55_0, all_55_1, all_55_2,
% 7.22/1.82 | | | all_55_3 gives:
% 7.22/1.82 | | | (51) phi(all_55_1) = all_55_0 & multiply(f, f_left_zero, all_44_0) =
% 7.22/1.82 | | | all_55_1 & group_member(all_44_0, f) = all_55_2 &
% 7.22/1.82 | | | group_member(f_left_zero, f) = all_55_3 & $i(all_55_0) &
% 7.22/1.82 | | | $i(all_55_1) & ( ~ (all_55_2 = 0) | ~ (all_55_3 = 0) | all_55_0 =
% 7.22/1.82 | | | all_37_0)
% 7.22/1.82 | | |
% 7.22/1.82 | | | ALPHA: (51) implies:
% 7.22/1.82 | | | (52) group_member(f_left_zero, f) = all_55_3
% 7.22/1.82 | | | (53) group_member(all_44_0, f) = all_55_2
% 7.59/1.82 | | | (54) multiply(f, f_left_zero, all_44_0) = all_55_1
% 7.59/1.82 | | | (55) phi(all_55_1) = all_55_0
% 7.59/1.82 | | | (56) ~ (all_55_2 = 0) | ~ (all_55_3 = 0) | all_55_0 = all_37_0
% 7.59/1.82 | | |
% 7.59/1.82 | | | GROUND_INST: instantiating (12) with 0, all_55_3, f, f_left_zero,
% 7.59/1.82 | | | simplifying with (19), (52) gives:
% 7.59/1.82 | | | (57) all_55_3 = 0
% 7.59/1.82 | | |
% 7.59/1.82 | | | GROUND_INST: instantiating (12) with 0, all_55_2, f, all_44_0, simplifying
% 7.59/1.82 | | | with (42), (53) gives:
% 7.59/1.82 | | | (58) all_55_2 = 0
% 7.59/1.82 | | |
% 7.59/1.83 | | | GROUND_INST: instantiating (12) with all_53_2, all_55_2, f, all_44_0,
% 7.59/1.83 | | | simplifying with (50), (53) gives:
% 7.59/1.83 | | | (59) all_55_2 = all_53_2
% 7.59/1.83 | | |
% 7.59/1.83 | | | COMBINE_EQS: (58), (59) imply:
% 7.59/1.83 | | | (60) all_53_2 = 0
% 7.59/1.83 | | |
% 7.59/1.83 | | | BETA: splitting (56) gives:
% 7.59/1.83 | | |
% 7.59/1.83 | | | Case 1:
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | (61) ~ (all_55_2 = 0)
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | REDUCE: (58), (61) imply:
% 7.59/1.83 | | | | (62) $false
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | CLOSE: (62) is inconsistent.
% 7.59/1.83 | | | |
% 7.59/1.83 | | | Case 2:
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | (63) ~ (all_55_3 = 0) | all_55_0 = all_37_0
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | BETA: splitting (63) gives:
% 7.59/1.83 | | | |
% 7.59/1.83 | | | | Case 1:
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | (64) ~ (all_55_3 = 0)
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | REDUCE: (57), (64) imply:
% 7.59/1.83 | | | | | (65) $false
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | CLOSE: (65) is inconsistent.
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | Case 2:
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | (66) all_55_0 = all_37_0
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | REDUCE: (55), (66) imply:
% 7.59/1.83 | | | | | (67) phi(all_55_1) = all_37_0
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | GROUND_INST: instantiating (20) with all_44_0, all_55_1, simplifying
% 7.59/1.83 | | | | | with (41), (54) gives:
% 7.59/1.83 | | | | | (68) all_55_1 = f_left_zero | ? [v0: int] : ( ~ (v0 = 0) &
% 7.59/1.83 | | | | | group_member(all_44_0, f) = v0)
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | BETA: splitting (68) gives:
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | | Case 1:
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | (69) all_55_1 = f_left_zero
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | REDUCE: (67), (69) imply:
% 7.59/1.83 | | | | | | (70) phi(f_left_zero) = all_37_0
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | GROUND_INST: instantiating (11) with all_10_1, all_37_0,
% 7.59/1.83 | | | | | | f_left_zero, simplifying with (16), (70) gives:
% 7.59/1.83 | | | | | | (71) all_37_0 = all_10_1
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | REDUCE: (34), (71) imply:
% 7.59/1.83 | | | | | | (72) $false
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | CLOSE: (72) is inconsistent.
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | Case 2:
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & group_member(all_44_0, f) =
% 7.59/1.83 | | | | | | v0)
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | DELTA: instantiating (73) with fresh symbol all_84_0 gives:
% 7.59/1.83 | | | | | | (74) ~ (all_84_0 = 0) & group_member(all_44_0, f) = all_84_0
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | ALPHA: (74) implies:
% 7.59/1.83 | | | | | | (75) ~ (all_84_0 = 0)
% 7.59/1.83 | | | | | | (76) group_member(all_44_0, f) = all_84_0
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | GROUND_INST: instantiating (12) with 0, all_84_0, f, all_44_0,
% 7.59/1.83 | | | | | | simplifying with (42), (76) gives:
% 7.59/1.83 | | | | | | (77) all_84_0 = 0
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | REDUCE: (75), (77) imply:
% 7.59/1.83 | | | | | | (78) $false
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | | CLOSE: (78) is inconsistent.
% 7.59/1.83 | | | | | |
% 7.59/1.83 | | | | | End of split
% 7.59/1.83 | | | | |
% 7.59/1.83 | | | | End of split
% 7.59/1.83 | | | |
% 7.59/1.83 | | | End of split
% 7.59/1.83 | | |
% 7.59/1.83 | | Case 2:
% 7.59/1.83 | | |
% 7.59/1.83 | | | (79) ? [v0: int] : ( ~ (v0 = 0) & group_member(all_10_1, h) = v0)
% 7.59/1.83 | | |
% 7.59/1.83 | | | DELTA: instantiating (79) with fresh symbol all_37_0 gives:
% 7.59/1.83 | | | (80) ~ (all_37_0 = 0) & group_member(all_10_1, h) = all_37_0
% 7.59/1.83 | | |
% 7.59/1.83 | | | ALPHA: (80) implies:
% 7.59/1.83 | | | (81) ~ (all_37_0 = 0)
% 7.59/1.83 | | | (82) group_member(all_10_1, h) = all_37_0
% 7.59/1.83 | | |
% 7.59/1.84 | | | GROUND_INST: instantiating (12) with 0, all_37_0, h, all_10_1, simplifying
% 7.59/1.84 | | | with (28), (82) gives:
% 7.59/1.84 | | | (83) all_37_0 = 0
% 7.59/1.84 | | |
% 7.59/1.84 | | | REDUCE: (81), (83) imply:
% 7.59/1.84 | | | (84) $false
% 7.59/1.84 | | |
% 7.59/1.84 | | | CLOSE: (84) is inconsistent.
% 7.59/1.84 | | |
% 7.59/1.84 | | End of split
% 7.59/1.84 | |
% 7.59/1.84 | End of split
% 7.59/1.84 |
% 7.59/1.84 End of proof
% 7.59/1.84 % SZS output end Proof for theBenchmark
% 7.59/1.84
% 7.59/1.84 1227ms
%------------------------------------------------------------------------------