TSTP Solution File: GEO174+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO174+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 23:21:51 EDT 2023
% Result : Theorem 7.64s 2.67s
% Output : Proof 9.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : GEO174+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.38 % Computer : n018.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Tue Aug 29 22:51:18 EDT 2023
% 0.14/0.39 % CPUTime :
% 0.45/0.69 ________ _____
% 0.45/0.69 ___ __ \_________(_)________________________________
% 0.45/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.45/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.45/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.45/0.69
% 0.45/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.45/0.69 (2023-06-19)
% 0.45/0.69
% 0.45/0.69 (c) Philipp Rümmer, 2009-2023
% 0.45/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.45/0.69 Amanda Stjerna.
% 0.45/0.69 Free software under BSD-3-Clause.
% 0.45/0.69
% 0.45/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.45/0.69
% 0.45/0.69 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.45/0.70 Running up to 7 provers in parallel.
% 0.68/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.41 Prover 4: Preprocessing ...
% 2.40/1.41 Prover 1: Preprocessing ...
% 2.70/1.53 Prover 2: Preprocessing ...
% 2.70/1.53 Prover 3: Preprocessing ...
% 2.70/1.53 Prover 6: Preprocessing ...
% 2.70/1.53 Prover 0: Preprocessing ...
% 2.70/1.53 Prover 5: Preprocessing ...
% 5.43/2.16 Prover 2: Proving ...
% 5.43/2.18 Prover 5: Proving ...
% 5.89/2.29 Prover 6: Constructing countermodel ...
% 6.15/2.34 Prover 1: Constructing countermodel ...
% 6.15/2.35 Prover 3: Constructing countermodel ...
% 7.34/2.66 Prover 6: proved (1913ms)
% 7.64/2.67
% 7.64/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.64/2.67
% 7.64/2.68 Prover 3: proved (1935ms)
% 7.64/2.68
% 7.64/2.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.64/2.68
% 7.64/2.69 Prover 2: stopped
% 7.64/2.69 Prover 5: stopped
% 7.83/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.83/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.83/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.83/2.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.95/2.81 Prover 7: Preprocessing ...
% 8.26/2.83 Prover 8: Preprocessing ...
% 8.26/2.83 Prover 10: Preprocessing ...
% 8.26/2.84 Prover 4: Constructing countermodel ...
% 8.26/2.85 Prover 11: Preprocessing ...
% 8.44/2.89 Prover 1: Found proof (size 33)
% 8.44/2.89 Prover 1: proved (2182ms)
% 8.44/2.91 Prover 0: Proving ...
% 8.44/2.91 Prover 7: Warning: ignoring some quantifiers
% 8.44/2.92 Prover 4: stopped
% 8.44/2.92 Prover 10: Warning: ignoring some quantifiers
% 8.78/2.94 Prover 7: Constructing countermodel ...
% 8.78/2.94 Prover 0: stopped
% 8.78/2.95 Prover 7: stopped
% 8.78/2.95 Prover 10: Constructing countermodel ...
% 8.78/2.96 Prover 10: stopped
% 8.91/3.00 Prover 8: Warning: ignoring some quantifiers
% 8.91/3.01 Prover 11: stopped
% 8.91/3.01 Prover 8: Constructing countermodel ...
% 8.91/3.02 Prover 8: stopped
% 8.91/3.02
% 8.91/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.91/3.02
% 9.14/3.03 % SZS output start Proof for theBenchmark
% 9.14/3.03 Assumptions after simplification:
% 9.14/3.04 ---------------------------------
% 9.14/3.04
% 9.14/3.04 (ceq2)
% 9.47/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 9.47/3.15 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~
% 9.47/3.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0)
% 9.47/3.15
% 9.47/3.15 (ci1)
% 9.47/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.47/3.16 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 9.47/3.16 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 9.47/3.16
% 9.47/3.16 (ci2)
% 9.47/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.47/3.16 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 9.47/3.16 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 9.47/3.16
% 9.47/3.16 (con)
% 9.47/3.17 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 9.47/3.17 any] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & line_connecting(v0, v1) =
% 9.47/3.17 v6 & apart_point_and_line(v1, v2) = v5 & apart_point_and_line(v0, v2) = v4 &
% 9.47/3.17 convergent_lines(v2, v3) = 0 & distinct_lines(v2, v6) = v7 &
% 9.47/3.17 distinct_points(v0, v1) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 9.47/3.17 (v5 = 0 | v4 = 0))
% 9.47/3.17
% 9.47/3.17 (con1)
% 9.47/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.47/3.19 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 9.47/3.19 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 9.47/3.19 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 9.47/3.19 v6 = 0)))
% 9.47/3.19
% 9.47/3.19 (function-axioms)
% 9.47/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.47/3.21 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 9.47/3.21 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.47/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/3.21 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 9.47/3.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.47/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 9.47/3.21 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.47/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/3.21 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 9.47/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.47/3.21 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 9.47/3.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/3.21 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.47/3.21 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.47/3.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 9.47/3.21 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.47/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.47/3.21 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.47/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.47/3.21 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.47/3.21 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.47/3.21 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.47/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/3.21 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.47/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.47/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.47/3.21 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.47/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.47/3.21 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.47/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.47/3.21 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.47/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.47/3.21 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.47/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.47/3.21 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.47/3.21
% 9.47/3.21 Further assumptions not needed in the proof:
% 9.47/3.21 --------------------------------------------
% 9.47/3.21 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq3,
% 9.47/3.21 ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cu1, cup1, int1, oac1, occu1, ooc1,
% 9.47/3.21 ooc2, orth1, ouo1, p1, par1
% 9.47/3.21
% 9.47/3.21 Those formulas are unsatisfiable:
% 9.47/3.21 ---------------------------------
% 9.47/3.21
% 9.47/3.21 Begin of proof
% 9.47/3.21 |
% 9.47/3.21 | ALPHA: (function-axioms) implies:
% 9.47/3.21 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.47/3.21 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 9.47/3.21 | (distinct_points(v3, v2) = v0))
% 9.47/3.21 |
% 9.47/3.21 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 9.47/3.21 | all_38_3, all_38_4, all_38_5, all_38_6, all_38_7 gives:
% 9.47/3.21 | (2) ~ (all_38_0 = 0) & line_connecting(all_38_7, all_38_6) = all_38_1 &
% 9.47/3.21 | apart_point_and_line(all_38_6, all_38_5) = all_38_2 &
% 9.47/3.21 | apart_point_and_line(all_38_7, all_38_5) = all_38_3 &
% 9.47/3.21 | convergent_lines(all_38_5, all_38_4) = 0 & distinct_lines(all_38_5,
% 9.47/3.21 | all_38_1) = all_38_0 & distinct_points(all_38_7, all_38_6) = 0 &
% 9.47/3.21 | $i(all_38_1) & $i(all_38_4) & $i(all_38_5) & $i(all_38_6) &
% 9.47/3.21 | $i(all_38_7) & (all_38_2 = 0 | all_38_3 = 0)
% 9.47/3.21 |
% 9.47/3.21 | ALPHA: (2) implies:
% 9.47/3.21 | (3) ~ (all_38_0 = 0)
% 9.47/3.22 | (4) $i(all_38_7)
% 9.47/3.22 | (5) $i(all_38_6)
% 9.47/3.22 | (6) $i(all_38_5)
% 9.47/3.22 | (7) $i(all_38_1)
% 9.47/3.22 | (8) distinct_points(all_38_7, all_38_6) = 0
% 9.47/3.22 | (9) distinct_lines(all_38_5, all_38_1) = all_38_0
% 9.47/3.22 | (10) apart_point_and_line(all_38_7, all_38_5) = all_38_3
% 9.47/3.22 | (11) apart_point_and_line(all_38_6, all_38_5) = all_38_2
% 9.47/3.22 | (12) line_connecting(all_38_7, all_38_6) = all_38_1
% 9.47/3.22 | (13) all_38_2 = 0 | all_38_3 = 0
% 9.47/3.22 |
% 9.47/3.22 | GROUND_INST: instantiating (con1) with all_38_7, all_38_6, all_38_1,
% 9.47/3.22 | simplifying with (4), (5), (12) gives:
% 9.47/3.22 | (14) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 9.47/3.22 | (point(all_38_6) = v1 & point(all_38_7) = v0 & line(all_38_1) = v3 &
% 9.47/3.22 | distinct_points(all_38_7, all_38_6) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 9.47/3.22 | 0) | ~ (v0 = 0) | v3 = 0))
% 9.47/3.22 |
% 9.47/3.22 | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2,
% 9.47/3.22 | all_45_3 gives:
% 9.47/3.22 | (15) point(all_38_6) = all_45_2 & point(all_38_7) = all_45_3 &
% 9.47/3.22 | line(all_38_1) = all_45_0 & distinct_points(all_38_7, all_38_6) =
% 9.47/3.22 | all_45_1 & ( ~ (all_45_1 = 0) | ~ (all_45_2 = 0) | ~ (all_45_3 = 0)
% 9.47/3.22 | | all_45_0 = 0)
% 9.47/3.22 |
% 9.47/3.22 | ALPHA: (15) implies:
% 9.47/3.22 | (16) distinct_points(all_38_7, all_38_6) = all_45_1
% 9.47/3.22 |
% 9.47/3.22 | GROUND_INST: instantiating (1) with 0, all_45_1, all_38_6, all_38_7,
% 9.47/3.22 | simplifying with (8), (16) gives:
% 9.47/3.22 | (17) all_45_1 = 0
% 9.47/3.22 |
% 9.47/3.22 | BETA: splitting (13) gives:
% 9.47/3.22 |
% 9.47/3.22 | Case 1:
% 9.47/3.22 | |
% 9.47/3.22 | | (18) all_38_2 = 0
% 9.47/3.22 | |
% 9.47/3.22 | | REDUCE: (11), (18) imply:
% 9.47/3.22 | | (19) apart_point_and_line(all_38_6, all_38_5) = 0
% 9.47/3.22 | |
% 9.47/3.22 | | GROUND_INST: instantiating (ceq2) with all_38_6, all_38_5, all_38_1,
% 9.47/3.22 | | all_38_0, simplifying with (5), (6), (7), (9), (19) gives:
% 9.47/3.22 | | (20) all_38_0 = 0 | apart_point_and_line(all_38_6, all_38_1) = 0
% 9.47/3.22 | |
% 9.47/3.22 | | BETA: splitting (20) gives:
% 9.47/3.22 | |
% 9.47/3.22 | | Case 1:
% 9.47/3.22 | | |
% 9.47/3.22 | | | (21) apart_point_and_line(all_38_6, all_38_1) = 0
% 9.47/3.22 | | |
% 9.47/3.22 | | | GROUND_INST: instantiating (ci2) with all_38_7, all_38_6, all_38_1,
% 9.47/3.22 | | | simplifying with (4), (5), (12), (21) gives:
% 9.47/3.22 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_7, all_38_6)
% 9.47/3.22 | | | = v0)
% 9.47/3.22 | | |
% 9.47/3.22 | | | DELTA: instantiating (22) with fresh symbol all_74_0 gives:
% 9.47/3.22 | | | (23) ~ (all_74_0 = 0) & distinct_points(all_38_7, all_38_6) = all_74_0
% 9.47/3.22 | | |
% 9.47/3.23 | | | ALPHA: (23) implies:
% 9.47/3.23 | | | (24) ~ (all_74_0 = 0)
% 9.47/3.23 | | | (25) distinct_points(all_38_7, all_38_6) = all_74_0
% 9.47/3.23 | | |
% 9.47/3.23 | | | GROUND_INST: instantiating (1) with 0, all_74_0, all_38_6, all_38_7,
% 9.47/3.23 | | | simplifying with (8), (25) gives:
% 9.47/3.23 | | | (26) all_74_0 = 0
% 9.47/3.23 | | |
% 9.47/3.23 | | | REDUCE: (24), (26) imply:
% 9.47/3.23 | | | (27) $false
% 9.47/3.23 | | |
% 9.47/3.23 | | | CLOSE: (27) is inconsistent.
% 9.47/3.23 | | |
% 9.47/3.23 | | Case 2:
% 9.47/3.23 | | |
% 9.47/3.23 | | | (28) all_38_0 = 0
% 9.47/3.23 | | |
% 9.47/3.23 | | | REDUCE: (3), (28) imply:
% 9.47/3.23 | | | (29) $false
% 9.47/3.23 | | |
% 9.47/3.23 | | | CLOSE: (29) is inconsistent.
% 9.47/3.23 | | |
% 9.47/3.23 | | End of split
% 9.47/3.23 | |
% 9.47/3.23 | Case 2:
% 9.47/3.23 | |
% 9.47/3.23 | | (30) all_38_3 = 0
% 9.47/3.23 | |
% 9.47/3.23 | | REDUCE: (10), (30) imply:
% 9.47/3.23 | | (31) apart_point_and_line(all_38_7, all_38_5) = 0
% 9.47/3.23 | |
% 9.47/3.23 | | GROUND_INST: instantiating (ceq2) with all_38_7, all_38_5, all_38_1,
% 9.47/3.23 | | all_38_0, simplifying with (4), (6), (7), (9), (31) gives:
% 9.47/3.24 | | (32) all_38_0 = 0 | apart_point_and_line(all_38_7, all_38_1) = 0
% 9.47/3.24 | |
% 9.47/3.24 | | BETA: splitting (32) gives:
% 9.47/3.24 | |
% 9.47/3.24 | | Case 1:
% 9.47/3.24 | | |
% 9.47/3.24 | | | (33) apart_point_and_line(all_38_7, all_38_1) = 0
% 9.47/3.24 | | |
% 9.47/3.24 | | | GROUND_INST: instantiating (ci1) with all_38_7, all_38_6, all_38_1,
% 9.47/3.24 | | | simplifying with (4), (5), (12), (33) gives:
% 9.47/3.24 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_7, all_38_6)
% 9.47/3.24 | | | = v0)
% 9.47/3.24 | | |
% 9.47/3.24 | | | DELTA: instantiating (34) with fresh symbol all_74_0 gives:
% 9.47/3.24 | | | (35) ~ (all_74_0 = 0) & distinct_points(all_38_7, all_38_6) = all_74_0
% 9.47/3.24 | | |
% 9.47/3.24 | | | ALPHA: (35) implies:
% 9.47/3.24 | | | (36) ~ (all_74_0 = 0)
% 9.47/3.24 | | | (37) distinct_points(all_38_7, all_38_6) = all_74_0
% 9.47/3.24 | | |
% 9.47/3.24 | | | GROUND_INST: instantiating (1) with 0, all_74_0, all_38_6, all_38_7,
% 9.47/3.24 | | | simplifying with (8), (37) gives:
% 9.47/3.24 | | | (38) all_74_0 = 0
% 9.47/3.24 | | |
% 9.47/3.24 | | | REDUCE: (36), (38) imply:
% 9.47/3.24 | | | (39) $false
% 9.47/3.24 | | |
% 9.47/3.24 | | | CLOSE: (39) is inconsistent.
% 9.47/3.24 | | |
% 9.47/3.24 | | Case 2:
% 9.47/3.24 | | |
% 9.65/3.24 | | | (40) all_38_0 = 0
% 9.65/3.24 | | |
% 9.65/3.24 | | | REDUCE: (3), (40) imply:
% 9.65/3.24 | | | (41) $false
% 9.65/3.24 | | |
% 9.65/3.24 | | | CLOSE: (41) is inconsistent.
% 9.65/3.24 | | |
% 9.65/3.24 | | End of split
% 9.65/3.24 | |
% 9.65/3.24 | End of split
% 9.65/3.24 |
% 9.65/3.24 End of proof
% 9.65/3.24 % SZS output end Proof for theBenchmark
% 9.65/3.24
% 9.65/3.24 2550ms
%------------------------------------------------------------------------------