TSTP Solution File: GEO232+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO232+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 : Wed Aug 30 23:22:36 EDT 2023
% Result : Theorem 7.66s 1.86s
% Output : Proof 11.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO232+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 22:56:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.15 Prover 4: Preprocessing ...
% 2.88/1.15 Prover 1: Preprocessing ...
% 3.13/1.19 Prover 3: Preprocessing ...
% 3.13/1.19 Prover 6: Preprocessing ...
% 3.13/1.19 Prover 5: Preprocessing ...
% 3.13/1.19 Prover 2: Preprocessing ...
% 3.13/1.19 Prover 0: Preprocessing ...
% 6.92/1.66 Prover 5: Proving ...
% 7.40/1.75 Prover 2: Proving ...
% 7.40/1.76 Prover 1: Constructing countermodel ...
% 7.40/1.76 Prover 3: Constructing countermodel ...
% 7.40/1.78 Prover 6: Constructing countermodel ...
% 7.66/1.86 Prover 5: proved (1221ms)
% 7.66/1.86
% 7.66/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.66/1.86
% 7.66/1.86 Prover 3: stopped
% 7.66/1.86 Prover 6: stopped
% 7.66/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.66/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.66/1.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.66/1.87 Prover 2: stopped
% 8.48/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.92/1.95 Prover 8: Preprocessing ...
% 8.92/1.95 Prover 7: Preprocessing ...
% 8.92/1.95 Prover 11: Preprocessing ...
% 8.92/1.96 Prover 10: Preprocessing ...
% 9.78/2.06 Prover 1: Found proof (size 30)
% 9.78/2.06 Prover 1: proved (1430ms)
% 9.78/2.07 Prover 11: stopped
% 9.78/2.08 Prover 7: Warning: ignoring some quantifiers
% 9.78/2.08 Prover 10: Warning: ignoring some quantifiers
% 9.78/2.11 Prover 7: Constructing countermodel ...
% 9.78/2.12 Prover 10: Constructing countermodel ...
% 9.78/2.13 Prover 7: stopped
% 9.78/2.13 Prover 10: stopped
% 10.34/2.15 Prover 8: Warning: ignoring some quantifiers
% 10.34/2.16 Prover 8: Constructing countermodel ...
% 10.34/2.17 Prover 8: stopped
% 10.34/2.17 Prover 4: Constructing countermodel ...
% 10.59/2.18 Prover 0: Proving ...
% 10.59/2.18 Prover 4: stopped
% 10.59/2.19 Prover 0: stopped
% 10.59/2.19
% 10.59/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.59/2.19
% 10.59/2.19 % SZS output start Proof for theBenchmark
% 10.59/2.20 Assumptions after simplification:
% 10.59/2.20 ---------------------------------
% 10.59/2.20
% 10.59/2.20 (con)
% 10.59/2.22 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & line(v0) = 0 &
% 10.59/2.22 unequally_directed_lines(v0, v1) = v2 & reverse_line(v0) = v1 & $i(v1) &
% 10.59/2.22 $i(v0))
% 10.59/2.22
% 10.59/2.22 (con_def)
% 10.59/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.59/2.22 (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 10.59/2.23 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (convergent_lines(v0, v1)
% 10.59/2.23 = v4 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3
% 10.59/2.23 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.59/2.23 (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ~
% 10.59/2.23 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (convergent_lines(v0, v1)
% 10.59/2.23 = v4 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.59/2.23
% 10.59/2.23 (oag5)
% 10.59/2.23 ! [v0: $i] : ( ~ (unequally_directed_lines(v0, v0) = 0) | ~ $i(v0))
% 10.59/2.23
% 10.59/2.23 (oag8)
% 10.59/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.59/2.23 (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 10.59/2.23 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (line(v1)
% 10.59/2.23 = v5 & line(v0) = v4 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v5 =
% 10.59/2.23 0) | ~ (v4 = 0) | v6 = 0)))
% 10.59/2.23
% 10.59/2.23 (function-axioms)
% 10.92/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.92/2.24 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 10.92/2.24 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 10.92/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.92/2.24 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 10.92/2.24 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.92/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 10.92/2.24 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 10.92/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.92/2.24 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 10.92/2.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 10.92/2.24 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 10.92/2.24 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.92/2.24 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 10.92/2.24 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.92/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.92/2.24 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 10.92/2.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.92/2.24 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 10.92/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.92/2.24 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3,
% 10.92/2.24 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.92/2.24 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 10.92/2.24 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.92/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.92/2.24 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3,
% 10.92/2.24 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.92/2.24 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) |
% 10.92/2.24 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.92/2.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.92/2.24 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & !
% 10.92/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 10.92/2.24 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] :
% 10.92/2.24 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 10.92/2.24 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.92/2.24 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 10.92/2.24
% 10.92/2.24 Further assumptions not needed in the proof:
% 10.92/2.24 --------------------------------------------
% 10.92/2.24 apt_def, bet_def, bf_def, div_def, oag1, oag10, oag11, oag2, oag3, oag4, oag6,
% 10.92/2.24 oag7, oag9, oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, oagco7,
% 10.92/2.24 oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2
% 10.92/2.24
% 10.92/2.24 Those formulas are unsatisfiable:
% 10.92/2.24 ---------------------------------
% 10.92/2.24
% 10.92/2.24 Begin of proof
% 10.92/2.25 |
% 10.92/2.25 | ALPHA: (con_def) implies:
% 10.92/2.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.92/2.25 | (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2)
% 10.92/2.25 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 10.92/2.25 | (convergent_lines(v0, v1) = v4 & unequally_directed_lines(v0, v1) =
% 10.92/2.25 | v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 10.92/2.25 |
% 10.92/2.25 | ALPHA: (function-axioms) implies:
% 10.92/2.25 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.92/2.25 | (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 10.92/2.25 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.92/2.25 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) |
% 10.92/2.25 | ~ (unequally_directed_lines(v3, v2) = v0))
% 10.92/2.25 |
% 10.92/2.25 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2
% 10.92/2.25 | gives:
% 10.92/2.25 | (4) ~ (all_34_0 = 0) & line(all_34_2) = 0 &
% 10.92/2.25 | unequally_directed_lines(all_34_2, all_34_1) = all_34_0 &
% 10.92/2.25 | reverse_line(all_34_2) = all_34_1 & $i(all_34_1) & $i(all_34_2)
% 10.92/2.25 |
% 10.92/2.25 | ALPHA: (4) implies:
% 10.92/2.25 | (5) ~ (all_34_0 = 0)
% 10.92/2.25 | (6) $i(all_34_2)
% 10.92/2.25 | (7) reverse_line(all_34_2) = all_34_1
% 10.92/2.25 | (8) unequally_directed_lines(all_34_2, all_34_1) = all_34_0
% 10.92/2.25 | (9) line(all_34_2) = 0
% 10.92/2.25 |
% 10.92/2.25 | GROUND_INST: instantiating (oag8) with all_34_2, all_34_2, all_34_1, all_34_0,
% 10.92/2.25 | simplifying with (6), (7), (8) gives:
% 10.92/2.26 | (10) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 10.92/2.26 | (line(all_34_2) = v1 & line(all_34_2) = v0 &
% 10.92/2.26 | unequally_directed_lines(all_34_2, all_34_2) = v2 & ( ~ (v1 = 0) |
% 10.92/2.26 | ~ (v0 = 0) | v2 = 0))
% 10.92/2.26 |
% 10.92/2.26 | GROUND_INST: instantiating (1) with all_34_2, all_34_2, all_34_1, all_34_0,
% 10.92/2.26 | simplifying with (6), (7), (8) gives:
% 10.92/2.26 | (11) ? [v0: any] : ? [v1: any] : (convergent_lines(all_34_2, all_34_2) =
% 10.92/2.26 | v0 & unequally_directed_lines(all_34_2, all_34_2) = v1 & ( ~ (v0 =
% 10.92/2.26 | 0) | (v1 = 0 & all_34_0 = 0)))
% 10.92/2.26 |
% 10.92/2.26 | DELTA: instantiating (11) with fresh symbols all_43_0, all_43_1 gives:
% 10.92/2.26 | (12) convergent_lines(all_34_2, all_34_2) = all_43_1 &
% 10.92/2.26 | unequally_directed_lines(all_34_2, all_34_2) = all_43_0 & ( ~
% 10.92/2.26 | (all_43_1 = 0) | (all_43_0 = 0 & all_34_0 = 0))
% 10.92/2.26 |
% 10.92/2.26 | ALPHA: (12) implies:
% 10.92/2.26 | (13) unequally_directed_lines(all_34_2, all_34_2) = all_43_0
% 10.92/2.26 |
% 10.92/2.26 | BETA: splitting (10) gives:
% 10.92/2.26 |
% 10.92/2.26 | Case 1:
% 10.92/2.26 | |
% 10.92/2.26 | | (14) all_34_0 = 0
% 10.92/2.26 | |
% 10.92/2.26 | | REDUCE: (5), (14) imply:
% 10.92/2.26 | | (15) $false
% 10.92/2.26 | |
% 10.92/2.26 | | CLOSE: (15) is inconsistent.
% 10.92/2.26 | |
% 10.92/2.26 | Case 2:
% 10.92/2.26 | |
% 10.92/2.26 | | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : (line(all_34_2) = v1 &
% 10.92/2.26 | | line(all_34_2) = v0 & unequally_directed_lines(all_34_2, all_34_2)
% 10.92/2.26 | | = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 10.92/2.26 | |
% 10.92/2.26 | | DELTA: instantiating (16) with fresh symbols all_53_0, all_53_1, all_53_2
% 10.92/2.26 | | gives:
% 11.04/2.26 | | (17) line(all_34_2) = all_53_1 & line(all_34_2) = all_53_2 &
% 11.04/2.26 | | unequally_directed_lines(all_34_2, all_34_2) = all_53_0 & ( ~
% 11.04/2.26 | | (all_53_1 = 0) | ~ (all_53_2 = 0) | all_53_0 = 0)
% 11.04/2.26 | |
% 11.04/2.26 | | ALPHA: (17) implies:
% 11.04/2.26 | | (18) unequally_directed_lines(all_34_2, all_34_2) = all_53_0
% 11.04/2.26 | | (19) line(all_34_2) = all_53_2
% 11.04/2.26 | | (20) line(all_34_2) = all_53_1
% 11.04/2.26 | | (21) ~ (all_53_1 = 0) | ~ (all_53_2 = 0) | all_53_0 = 0
% 11.04/2.26 | |
% 11.04/2.26 | | GROUND_INST: instantiating (3) with all_43_0, all_53_0, all_34_2, all_34_2,
% 11.04/2.26 | | simplifying with (13), (18) gives:
% 11.04/2.26 | | (22) all_53_0 = all_43_0
% 11.04/2.26 | |
% 11.04/2.26 | | GROUND_INST: instantiating (2) with 0, all_53_1, all_34_2, simplifying with
% 11.04/2.26 | | (9), (20) gives:
% 11.04/2.26 | | (23) all_53_1 = 0
% 11.04/2.26 | |
% 11.04/2.26 | | GROUND_INST: instantiating (2) with all_53_2, all_53_1, all_34_2,
% 11.04/2.26 | | simplifying with (19), (20) gives:
% 11.04/2.26 | | (24) all_53_1 = all_53_2
% 11.04/2.26 | |
% 11.04/2.26 | | COMBINE_EQS: (23), (24) imply:
% 11.04/2.26 | | (25) all_53_2 = 0
% 11.04/2.26 | |
% 11.04/2.26 | | BETA: splitting (21) gives:
% 11.04/2.26 | |
% 11.04/2.26 | | Case 1:
% 11.04/2.26 | | |
% 11.04/2.26 | | | (26) ~ (all_53_1 = 0)
% 11.04/2.26 | | |
% 11.04/2.26 | | | REDUCE: (23), (26) imply:
% 11.04/2.26 | | | (27) $false
% 11.04/2.26 | | |
% 11.04/2.26 | | | CLOSE: (27) is inconsistent.
% 11.04/2.26 | | |
% 11.04/2.26 | | Case 2:
% 11.04/2.26 | | |
% 11.04/2.26 | | | (28) ~ (all_53_2 = 0) | all_53_0 = 0
% 11.04/2.26 | | |
% 11.04/2.26 | | | BETA: splitting (28) gives:
% 11.04/2.26 | | |
% 11.04/2.26 | | | Case 1:
% 11.04/2.26 | | | |
% 11.04/2.26 | | | | (29) ~ (all_53_2 = 0)
% 11.04/2.26 | | | |
% 11.04/2.26 | | | | REDUCE: (25), (29) imply:
% 11.04/2.26 | | | | (30) $false
% 11.04/2.26 | | | |
% 11.04/2.26 | | | | CLOSE: (30) is inconsistent.
% 11.04/2.26 | | | |
% 11.04/2.26 | | | Case 2:
% 11.04/2.26 | | | |
% 11.04/2.26 | | | | (31) all_53_0 = 0
% 11.04/2.26 | | | |
% 11.04/2.27 | | | | COMBINE_EQS: (22), (31) imply:
% 11.04/2.27 | | | | (32) all_43_0 = 0
% 11.04/2.27 | | | |
% 11.04/2.27 | | | | REDUCE: (13), (32) imply:
% 11.04/2.27 | | | | (33) unequally_directed_lines(all_34_2, all_34_2) = 0
% 11.04/2.27 | | | |
% 11.04/2.27 | | | | GROUND_INST: instantiating (oag5) with all_34_2, simplifying with (6),
% 11.04/2.27 | | | | (33) gives:
% 11.04/2.27 | | | | (34) $false
% 11.04/2.27 | | | |
% 11.04/2.27 | | | | CLOSE: (34) is inconsistent.
% 11.04/2.27 | | | |
% 11.04/2.27 | | | End of split
% 11.04/2.27 | | |
% 11.04/2.27 | | End of split
% 11.04/2.27 | |
% 11.04/2.27 | End of split
% 11.04/2.27 |
% 11.04/2.27 End of proof
% 11.04/2.27 % SZS output end Proof for theBenchmark
% 11.04/2.27
% 11.04/2.27 1665ms
%------------------------------------------------------------------------------