TSTP Solution File: GEO210+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO210+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 : n008.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 23:22:21 EDT 2023
% Result : Theorem 7.79s 1.83s
% Output : Proof 9.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n008.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 21:43:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.13 Prover 4: Preprocessing ...
% 2.63/1.13 Prover 1: Preprocessing ...
% 3.23/1.17 Prover 0: Preprocessing ...
% 3.23/1.17 Prover 2: Preprocessing ...
% 3.23/1.17 Prover 3: Preprocessing ...
% 3.23/1.17 Prover 6: Preprocessing ...
% 3.23/1.17 Prover 5: Preprocessing ...
% 4.74/1.47 Prover 5: Proving ...
% 4.74/1.51 Prover 2: Proving ...
% 4.74/1.59 Prover 3: Constructing countermodel ...
% 4.74/1.59 Prover 1: Constructing countermodel ...
% 4.74/1.60 Prover 6: Constructing countermodel ...
% 7.79/1.83 Prover 6: proved (1142ms)
% 7.79/1.83
% 7.79/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.79/1.83
% 7.79/1.83 Prover 3: proved (1159ms)
% 7.79/1.84
% 7.79/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.79/1.84
% 7.79/1.84 Prover 5: stopped
% 7.79/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.79/1.85 Prover 2: stopped
% 7.79/1.85 Prover 4: Constructing countermodel ...
% 7.79/1.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.79/1.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.79/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.79/1.88 Prover 0: Proving ...
% 8.30/1.92 Prover 7: Preprocessing ...
% 8.30/1.92 Prover 8: Preprocessing ...
% 8.30/1.92 Prover 10: Preprocessing ...
% 8.30/1.92 Prover 0: stopped
% 8.30/1.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.30/1.93 Prover 11: Preprocessing ...
% 8.30/1.94 Prover 1: Found proof (size 31)
% 8.30/1.94 Prover 1: proved (1261ms)
% 8.30/1.94 Prover 7: stopped
% 8.30/1.95 Prover 4: stopped
% 8.30/1.95 Prover 10: stopped
% 8.30/1.95 Prover 13: Preprocessing ...
% 8.79/1.97 Prover 13: stopped
% 8.79/1.99 Prover 11: stopped
% 8.79/2.01 Prover 8: Warning: ignoring some quantifiers
% 8.79/2.02 Prover 8: Constructing countermodel ...
% 8.79/2.03 Prover 8: stopped
% 8.79/2.03
% 8.79/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.79/2.03
% 8.79/2.03 % SZS output start Proof for theBenchmark
% 8.79/2.04 Assumptions after simplification:
% 8.79/2.04 ---------------------------------
% 8.79/2.04
% 8.79/2.04 (con)
% 8.79/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ?
% 8.79/2.07 [v5: $i] : ( ~ (v4 = 0) & ~ (v3 = 0) & orthogonal_through_point(v2, v0) = v5
% 8.79/2.07 & unorthogonal_lines(v1, v2) = v4 & apart_point_and_line(v0, v1) = v3 &
% 8.79/2.07 distinct_lines(v1, v5) = 0 & $i(v5) & $i(v2) & $i(v1) & $i(v0))
% 8.79/2.07
% 8.79/2.07 (cup1)
% 9.31/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.31/2.07 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~
% 9.31/2.07 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 9.31/2.07 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0
% 9.31/2.07 | v4 = 0)))
% 9.31/2.07
% 9.31/2.07 (ooc1)
% 9.31/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 9.31/2.07 v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 9.31/2.07
% 9.31/2.07 (ooc2)
% 9.31/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 9.31/2.07 v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~
% 9.31/2.07 $i(v0))
% 9.31/2.07
% 9.31/2.07 (ouo1)
% 9.31/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 9.31/2.08 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 9.31/2.08 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 9.31/2.08 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 9.31/2.08 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 =
% 9.31/2.08 0 | v6 = 0)))
% 9.31/2.08
% 9.31/2.08 (function-axioms)
% 9.31/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.31/2.08 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.31/2.08 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.31/2.08 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 9.31/2.08 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.31/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.31/2.08 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.31/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.31/2.08 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.31/2.09 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.31/2.09 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.31/2.09 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.31/2.09 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.31/2.09 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.31/2.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.31/2.09 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.31/2.09 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.31/2.09 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.31/2.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.31/2.09 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.31/2.09 v0))
% 9.31/2.09
% 9.31/2.09 Further assumptions not needed in the proof:
% 9.31/2.09 --------------------------------------------
% 9.31/2.09 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci1, ci2, ci3,
% 9.31/2.09 ci4, cp1, cp2, cu1, oac1, occu1
% 9.31/2.09
% 9.31/2.09 Those formulas are unsatisfiable:
% 9.31/2.09 ---------------------------------
% 9.31/2.09
% 9.31/2.09 Begin of proof
% 9.31/2.09 |
% 9.31/2.09 | ALPHA: (function-axioms) implies:
% 9.31/2.09 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.31/2.09 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 9.31/2.09 | (apart_point_and_line(v3, v2) = v0))
% 9.31/2.09 |
% 9.31/2.09 | DELTA: instantiating (con) with fresh symbols all_25_0, all_25_1, all_25_2,
% 9.31/2.09 | all_25_3, all_25_4, all_25_5 gives:
% 9.31/2.09 | (2) ~ (all_25_1 = 0) & ~ (all_25_2 = 0) &
% 9.31/2.09 | orthogonal_through_point(all_25_3, all_25_5) = all_25_0 &
% 9.31/2.09 | unorthogonal_lines(all_25_4, all_25_3) = all_25_1 &
% 9.31/2.09 | apart_point_and_line(all_25_5, all_25_4) = all_25_2 &
% 9.31/2.09 | distinct_lines(all_25_4, all_25_0) = 0 & $i(all_25_0) & $i(all_25_3) &
% 9.31/2.09 | $i(all_25_4) & $i(all_25_5)
% 9.31/2.09 |
% 9.31/2.09 | ALPHA: (2) implies:
% 9.31/2.09 | (3) ~ (all_25_2 = 0)
% 9.31/2.09 | (4) ~ (all_25_1 = 0)
% 9.31/2.09 | (5) $i(all_25_5)
% 9.31/2.09 | (6) $i(all_25_4)
% 9.31/2.09 | (7) $i(all_25_3)
% 9.31/2.09 | (8) $i(all_25_0)
% 9.43/2.10 | (9) distinct_lines(all_25_4, all_25_0) = 0
% 9.43/2.10 | (10) apart_point_and_line(all_25_5, all_25_4) = all_25_2
% 9.43/2.10 | (11) unorthogonal_lines(all_25_4, all_25_3) = all_25_1
% 9.43/2.10 | (12) orthogonal_through_point(all_25_3, all_25_5) = all_25_0
% 9.43/2.10 |
% 9.43/2.10 | GROUND_INST: instantiating (cup1) with all_25_5, all_25_4, all_25_0, all_25_2,
% 9.43/2.10 | simplifying with (5), (6), (8), (9), (10) gives:
% 9.43/2.10 | (13) all_25_2 = 0 | ? [v0: any] : ? [v1: any] :
% 9.43/2.10 | (apart_point_and_line(all_25_5, all_25_0) = v0 &
% 9.43/2.10 | convergent_lines(all_25_4, all_25_0) = v1 & (v1 = 0 | v0 = 0))
% 9.43/2.10 |
% 9.43/2.10 | GROUND_INST: instantiating (ouo1) with all_25_5, all_25_4, all_25_0, all_25_3,
% 9.43/2.10 | all_25_2, all_25_1, simplifying with (5), (6), (7), (8), (9),
% 9.43/2.10 | (10), (11) gives:
% 9.43/2.10 | (14) all_25_1 = 0 | all_25_2 = 0 | ? [v0: any] : ? [v1: any] :
% 9.43/2.10 | (unorthogonal_lines(all_25_0, all_25_3) = v1 &
% 9.43/2.10 | apart_point_and_line(all_25_5, all_25_0) = v0 & (v1 = 0 | v0 = 0))
% 9.43/2.10 |
% 9.43/2.10 | BETA: splitting (13) gives:
% 9.43/2.10 |
% 9.43/2.10 | Case 1:
% 9.43/2.10 | |
% 9.43/2.10 | | (15) all_25_2 = 0
% 9.43/2.10 | |
% 9.43/2.10 | | REDUCE: (3), (15) imply:
% 9.43/2.10 | | (16) $false
% 9.43/2.10 | |
% 9.43/2.10 | | CLOSE: (16) is inconsistent.
% 9.43/2.10 | |
% 9.43/2.10 | Case 2:
% 9.43/2.10 | |
% 9.43/2.10 | | (17) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_25_5,
% 9.43/2.10 | | all_25_0) = v0 & convergent_lines(all_25_4, all_25_0) = v1 & (v1
% 9.43/2.10 | | = 0 | v0 = 0))
% 9.43/2.10 | |
% 9.43/2.10 | | DELTA: instantiating (17) with fresh symbols all_38_0, all_38_1 gives:
% 9.43/2.11 | | (18) apart_point_and_line(all_25_5, all_25_0) = all_38_1 &
% 9.43/2.11 | | convergent_lines(all_25_4, all_25_0) = all_38_0 & (all_38_0 = 0 |
% 9.43/2.11 | | all_38_1 = 0)
% 9.43/2.11 | |
% 9.43/2.11 | | ALPHA: (18) implies:
% 9.43/2.11 | | (19) apart_point_and_line(all_25_5, all_25_0) = all_38_1
% 9.43/2.11 | |
% 9.43/2.11 | | BETA: splitting (14) gives:
% 9.43/2.11 | |
% 9.43/2.11 | | Case 1:
% 9.43/2.11 | | |
% 9.43/2.11 | | | (20) all_25_1 = 0
% 9.43/2.11 | | |
% 9.43/2.11 | | | REDUCE: (4), (20) imply:
% 9.43/2.11 | | | (21) $false
% 9.43/2.11 | | |
% 9.43/2.11 | | | CLOSE: (21) is inconsistent.
% 9.43/2.11 | | |
% 9.43/2.11 | | Case 2:
% 9.43/2.11 | | |
% 9.43/2.11 | | | (22) all_25_2 = 0 | ? [v0: any] : ? [v1: any] :
% 9.43/2.11 | | | (unorthogonal_lines(all_25_0, all_25_3) = v1 &
% 9.43/2.11 | | | apart_point_and_line(all_25_5, all_25_0) = v0 & (v1 = 0 | v0 =
% 9.43/2.11 | | | 0))
% 9.43/2.11 | | |
% 9.43/2.11 | | | BETA: splitting (22) gives:
% 9.43/2.11 | | |
% 9.43/2.11 | | | Case 1:
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | (23) all_25_2 = 0
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | REDUCE: (3), (23) imply:
% 9.43/2.11 | | | | (24) $false
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | CLOSE: (24) is inconsistent.
% 9.43/2.11 | | | |
% 9.43/2.11 | | | Case 2:
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | (25) ? [v0: any] : ? [v1: any] : (unorthogonal_lines(all_25_0,
% 9.43/2.11 | | | | all_25_3) = v1 & apart_point_and_line(all_25_5, all_25_0) =
% 9.43/2.11 | | | | v0 & (v1 = 0 | v0 = 0))
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | DELTA: instantiating (25) with fresh symbols all_47_0, all_47_1 gives:
% 9.43/2.11 | | | | (26) unorthogonal_lines(all_25_0, all_25_3) = all_47_0 &
% 9.43/2.11 | | | | apart_point_and_line(all_25_5, all_25_0) = all_47_1 & (all_47_0
% 9.43/2.11 | | | | = 0 | all_47_1 = 0)
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | ALPHA: (26) implies:
% 9.43/2.11 | | | | (27) apart_point_and_line(all_25_5, all_25_0) = all_47_1
% 9.43/2.11 | | | | (28) unorthogonal_lines(all_25_0, all_25_3) = all_47_0
% 9.43/2.11 | | | | (29) all_47_0 = 0 | all_47_1 = 0
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | GROUND_INST: instantiating (1) with all_38_1, all_47_1, all_25_0,
% 9.43/2.11 | | | | all_25_5, simplifying with (19), (27) gives:
% 9.43/2.11 | | | | (30) all_47_1 = all_38_1
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | BETA: splitting (29) gives:
% 9.43/2.11 | | | |
% 9.43/2.11 | | | | Case 1:
% 9.43/2.11 | | | | |
% 9.43/2.11 | | | | | (31) all_47_0 = 0
% 9.43/2.11 | | | | |
% 9.43/2.11 | | | | | REDUCE: (28), (31) imply:
% 9.43/2.11 | | | | | (32) unorthogonal_lines(all_25_0, all_25_3) = 0
% 9.43/2.11 | | | | |
% 9.43/2.11 | | | | | GROUND_INST: instantiating (ooc1) with all_25_5, all_25_3, all_25_0,
% 9.43/2.11 | | | | | simplifying with (5), (7), (12), (32) gives:
% 9.43/2.11 | | | | | (33) $false
% 9.43/2.11 | | | | |
% 9.43/2.11 | | | | | CLOSE: (33) is inconsistent.
% 9.43/2.11 | | | | |
% 9.43/2.11 | | | | Case 2:
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | | (34) all_47_1 = 0
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | | COMBINE_EQS: (30), (34) imply:
% 9.43/2.12 | | | | | (35) all_38_1 = 0
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | | REDUCE: (19), (35) imply:
% 9.43/2.12 | | | | | (36) apart_point_and_line(all_25_5, all_25_0) = 0
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | | GROUND_INST: instantiating (ooc2) with all_25_5, all_25_3, all_25_0,
% 9.43/2.12 | | | | | simplifying with (5), (7), (12), (36) gives:
% 9.43/2.12 | | | | | (37) $false
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | | CLOSE: (37) is inconsistent.
% 9.43/2.12 | | | | |
% 9.43/2.12 | | | | End of split
% 9.43/2.12 | | | |
% 9.43/2.12 | | | End of split
% 9.43/2.12 | | |
% 9.43/2.12 | | End of split
% 9.43/2.12 | |
% 9.43/2.12 | End of split
% 9.43/2.12 |
% 9.43/2.12 End of proof
% 9.43/2.12 % SZS output end Proof for theBenchmark
% 9.43/2.12
% 9.43/2.12 1466ms
%------------------------------------------------------------------------------