TSTP Solution File: GEO176+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO176+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 23:21:52 EDT 2023
% Result : Theorem 6.11s 1.71s
% Output : Proof 8.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO176+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 20:57:46 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.60 ________ _____
% 0.17/0.60 ___ __ \_________(_)________________________________
% 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.60
% 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.60 (2023-06-19)
% 0.17/0.60
% 0.17/0.60 (c) Philipp Rümmer, 2009-2023
% 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.60 Amanda Stjerna.
% 0.17/0.60 Free software under BSD-3-Clause.
% 0.17/0.60
% 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.60
% 0.17/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.62 Running up to 7 provers in parallel.
% 0.17/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.36/1.13 Prover 4: Preprocessing ...
% 2.71/1.15 Prover 1: Preprocessing ...
% 2.78/1.19 Prover 3: Preprocessing ...
% 2.78/1.19 Prover 5: Preprocessing ...
% 2.78/1.19 Prover 6: Preprocessing ...
% 2.78/1.19 Prover 0: Preprocessing ...
% 2.78/1.19 Prover 2: Preprocessing ...
% 5.05/1.49 Prover 5: Proving ...
% 5.05/1.50 Prover 2: Proving ...
% 5.05/1.52 Prover 1: Constructing countermodel ...
% 5.05/1.54 Prover 3: Constructing countermodel ...
% 5.52/1.57 Prover 6: Constructing countermodel ...
% 6.11/1.70 Prover 4: Constructing countermodel ...
% 6.11/1.71 Prover 6: proved (1075ms)
% 6.11/1.71
% 6.11/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.11/1.71
% 6.11/1.71 Prover 3: stopped
% 6.11/1.72 Prover 5: stopped
% 6.11/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.11/1.73 Prover 2: stopped
% 6.73/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.73/1.75 Prover 0: Proving ...
% 6.73/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.73/1.75 Prover 0: stopped
% 6.73/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.73/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.73/1.77 Prover 7: Preprocessing ...
% 7.07/1.81 Prover 10: Preprocessing ...
% 7.07/1.81 Prover 8: Preprocessing ...
% 7.07/1.81 Prover 11: Preprocessing ...
% 7.07/1.84 Prover 7: Warning: ignoring some quantifiers
% 7.07/1.84 Prover 13: Preprocessing ...
% 7.51/1.85 Prover 7: Constructing countermodel ...
% 7.51/1.86 Prover 1: Found proof (size 35)
% 7.51/1.86 Prover 1: proved (1238ms)
% 7.51/1.87 Prover 13: stopped
% 7.51/1.87 Prover 7: stopped
% 7.51/1.87 Prover 4: stopped
% 7.51/1.88 Prover 10: Warning: ignoring some quantifiers
% 7.51/1.88 Prover 11: stopped
% 7.51/1.89 Prover 10: Constructing countermodel ...
% 7.51/1.89 Prover 10: stopped
% 7.51/1.94 Prover 8: Warning: ignoring some quantifiers
% 8.05/1.95 Prover 8: Constructing countermodel ...
% 8.05/1.96 Prover 8: stopped
% 8.05/1.96
% 8.05/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.05/1.96
% 8.05/1.96 % SZS output start Proof for theBenchmark
% 8.05/1.97 Assumptions after simplification:
% 8.05/1.97 ---------------------------------
% 8.05/1.97
% 8.05/1.97 (con)
% 8.30/2.01 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 8.30/2.01 any] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & intersection_point(v2,
% 8.30/2.01 v3) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0,
% 8.30/2.01 v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = v7 &
% 8.30/2.01 distinct_points(v0, v1) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 8.30/2.01 (v5 = 0 | v4 = 0))
% 8.30/2.01
% 8.30/2.01 (con2)
% 8.30/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.30/2.01 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) |
% 8.30/2.01 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 8.30/2.01 any] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) =
% 8.30/2.01 v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6
% 8.30/2.01 = 0)))))
% 8.30/2.01
% 8.30/2.01 (function-axioms)
% 8.30/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/2.02 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 8.30/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/2.02 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 8.30/2.02 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.30/2.02 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 8.30/2.02 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.30/2.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.30/2.02 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 8.30/2.02 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.30/2.02 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 8.30/2.02 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.30/2.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.30/2.02 (distinct_points(v3, v2) = v0))
% 8.30/2.02
% 8.30/2.02 Further assumptions not needed in the proof:
% 8.30/2.02 --------------------------------------------
% 8.30/2.02 apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con1, cu1
% 8.30/2.02
% 8.30/2.02 Those formulas are unsatisfiable:
% 8.30/2.02 ---------------------------------
% 8.30/2.02
% 8.30/2.02 Begin of proof
% 8.30/2.02 |
% 8.30/2.02 | ALPHA: (function-axioms) implies:
% 8.30/2.02 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.30/2.02 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 8.30/2.02 | (convergent_lines(v3, v2) = v0))
% 8.30/2.03 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.30/2.03 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 8.30/2.03 | (apart_point_and_line(v3, v2) = v0))
% 8.30/2.03 |
% 8.30/2.03 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.30/2.03 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 8.30/2.03 | (3) ~ (all_15_0 = 0) & intersection_point(all_15_5, all_15_4) = all_15_1 &
% 8.30/2.03 | apart_point_and_line(all_15_7, all_15_4) = all_15_2 &
% 8.30/2.03 | apart_point_and_line(all_15_7, all_15_5) = all_15_3 &
% 8.30/2.03 | convergent_lines(all_15_5, all_15_4) = 0 & distinct_points(all_15_7,
% 8.30/2.03 | all_15_1) = all_15_0 & distinct_points(all_15_7, all_15_6) = 0 &
% 8.30/2.03 | $i(all_15_1) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) &
% 8.30/2.03 | $i(all_15_7) & (all_15_2 = 0 | all_15_3 = 0)
% 8.30/2.03 |
% 8.30/2.03 | ALPHA: (3) implies:
% 8.30/2.03 | (4) ~ (all_15_0 = 0)
% 8.30/2.03 | (5) $i(all_15_7)
% 8.48/2.03 | (6) $i(all_15_5)
% 8.48/2.03 | (7) $i(all_15_4)
% 8.48/2.03 | (8) distinct_points(all_15_7, all_15_1) = all_15_0
% 8.48/2.03 | (9) convergent_lines(all_15_5, all_15_4) = 0
% 8.48/2.03 | (10) apart_point_and_line(all_15_7, all_15_5) = all_15_3
% 8.48/2.03 | (11) apart_point_and_line(all_15_7, all_15_4) = all_15_2
% 8.48/2.03 | (12) intersection_point(all_15_5, all_15_4) = all_15_1
% 8.48/2.03 | (13) all_15_2 = 0 | all_15_3 = 0
% 8.50/2.03 |
% 8.50/2.04 | GROUND_INST: instantiating (con2) with all_15_5, all_15_4, all_15_7, all_15_1,
% 8.50/2.04 | all_15_0, simplifying with (5), (6), (7), (8), (12) gives:
% 8.50/2.04 | (14) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.50/2.04 | (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 8.50/2.04 | apart_point_and_line(all_15_7, all_15_5) = v1 &
% 8.50/2.04 | convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~ (v2 =
% 8.50/2.04 | 0) & ~ (v1 = 0))))
% 8.50/2.04 |
% 8.50/2.04 | BETA: splitting (13) gives:
% 8.50/2.04 |
% 8.50/2.04 | Case 1:
% 8.50/2.04 | |
% 8.50/2.04 | | (15) all_15_2 = 0
% 8.50/2.04 | |
% 8.50/2.04 | | REDUCE: (11), (15) imply:
% 8.50/2.04 | | (16) apart_point_and_line(all_15_7, all_15_4) = 0
% 8.50/2.04 | |
% 8.50/2.04 | | BETA: splitting (14) gives:
% 8.50/2.04 | |
% 8.50/2.04 | | Case 1:
% 8.50/2.04 | | |
% 8.50/2.04 | | | (17) all_15_0 = 0
% 8.50/2.04 | | |
% 8.50/2.04 | | | REDUCE: (4), (17) imply:
% 8.50/2.04 | | | (18) $false
% 8.50/2.04 | | |
% 8.50/2.04 | | | CLOSE: (18) is inconsistent.
% 8.50/2.04 | | |
% 8.50/2.04 | | Case 2:
% 8.50/2.04 | | |
% 8.50/2.04 | | | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.50/2.04 | | | (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 8.50/2.04 | | | apart_point_and_line(all_15_7, all_15_5) = v1 &
% 8.50/2.04 | | | convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~
% 8.50/2.04 | | | (v2 = 0) & ~ (v1 = 0))))
% 8.50/2.04 | | |
% 8.50/2.04 | | | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 8.50/2.04 | | | gives:
% 8.50/2.04 | | | (20) apart_point_and_line(all_15_7, all_15_4) = all_32_0 &
% 8.50/2.04 | | | apart_point_and_line(all_15_7, all_15_5) = all_32_1 &
% 8.50/2.04 | | | convergent_lines(all_15_5, all_15_4) = all_32_2 & ( ~ (all_32_2 =
% 8.50/2.04 | | | 0) | ( ~ (all_32_0 = 0) & ~ (all_32_1 = 0)))
% 8.50/2.04 | | |
% 8.50/2.04 | | | ALPHA: (20) implies:
% 8.50/2.05 | | | (21) convergent_lines(all_15_5, all_15_4) = all_32_2
% 8.50/2.05 | | | (22) apart_point_and_line(all_15_7, all_15_4) = all_32_0
% 8.50/2.05 | | | (23) ~ (all_32_2 = 0) | ( ~ (all_32_0 = 0) & ~ (all_32_1 = 0))
% 8.50/2.05 | | |
% 8.50/2.05 | | | GROUND_INST: instantiating (1) with 0, all_32_2, all_15_4, all_15_5,
% 8.50/2.05 | | | simplifying with (9), (21) gives:
% 8.50/2.05 | | | (24) all_32_2 = 0
% 8.50/2.05 | | |
% 8.50/2.05 | | | GROUND_INST: instantiating (2) with 0, all_32_0, all_15_4, all_15_7,
% 8.50/2.05 | | | simplifying with (16), (22) gives:
% 8.50/2.05 | | | (25) all_32_0 = 0
% 8.50/2.05 | | |
% 8.50/2.05 | | | BETA: splitting (23) gives:
% 8.50/2.05 | | |
% 8.50/2.05 | | | Case 1:
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | (26) ~ (all_32_2 = 0)
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | REDUCE: (24), (26) imply:
% 8.50/2.05 | | | | (27) $false
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | CLOSE: (27) is inconsistent.
% 8.50/2.05 | | | |
% 8.50/2.05 | | | Case 2:
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | (28) ~ (all_32_0 = 0) & ~ (all_32_1 = 0)
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | ALPHA: (28) implies:
% 8.50/2.05 | | | | (29) ~ (all_32_0 = 0)
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | REDUCE: (25), (29) imply:
% 8.50/2.05 | | | | (30) $false
% 8.50/2.05 | | | |
% 8.50/2.05 | | | | CLOSE: (30) is inconsistent.
% 8.50/2.05 | | | |
% 8.50/2.05 | | | End of split
% 8.50/2.05 | | |
% 8.50/2.05 | | End of split
% 8.50/2.05 | |
% 8.50/2.05 | Case 2:
% 8.50/2.05 | |
% 8.50/2.05 | | (31) all_15_3 = 0
% 8.50/2.05 | |
% 8.50/2.05 | | REDUCE: (10), (31) imply:
% 8.50/2.05 | | (32) apart_point_and_line(all_15_7, all_15_5) = 0
% 8.50/2.05 | |
% 8.50/2.05 | | BETA: splitting (14) gives:
% 8.50/2.05 | |
% 8.50/2.05 | | Case 1:
% 8.50/2.05 | | |
% 8.50/2.05 | | | (33) all_15_0 = 0
% 8.50/2.05 | | |
% 8.50/2.05 | | | REDUCE: (4), (33) imply:
% 8.50/2.05 | | | (34) $false
% 8.50/2.05 | | |
% 8.50/2.05 | | | CLOSE: (34) is inconsistent.
% 8.50/2.05 | | |
% 8.50/2.05 | | Case 2:
% 8.50/2.05 | | |
% 8.50/2.05 | | | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.50/2.05 | | | (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 8.50/2.05 | | | apart_point_and_line(all_15_7, all_15_5) = v1 &
% 8.50/2.05 | | | convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~
% 8.50/2.05 | | | (v2 = 0) & ~ (v1 = 0))))
% 8.50/2.05 | | |
% 8.50/2.05 | | | DELTA: instantiating (35) with fresh symbols all_32_0, all_32_1, all_32_2
% 8.50/2.05 | | | gives:
% 8.50/2.05 | | | (36) apart_point_and_line(all_15_7, all_15_4) = all_32_0 &
% 8.50/2.05 | | | apart_point_and_line(all_15_7, all_15_5) = all_32_1 &
% 8.50/2.05 | | | convergent_lines(all_15_5, all_15_4) = all_32_2 & ( ~ (all_32_2 =
% 8.50/2.05 | | | 0) | ( ~ (all_32_0 = 0) & ~ (all_32_1 = 0)))
% 8.50/2.05 | | |
% 8.50/2.05 | | | ALPHA: (36) implies:
% 8.50/2.05 | | | (37) convergent_lines(all_15_5, all_15_4) = all_32_2
% 8.50/2.05 | | | (38) apart_point_and_line(all_15_7, all_15_5) = all_32_1
% 8.50/2.05 | | | (39) ~ (all_32_2 = 0) | ( ~ (all_32_0 = 0) & ~ (all_32_1 = 0))
% 8.50/2.05 | | |
% 8.50/2.06 | | | GROUND_INST: instantiating (1) with 0, all_32_2, all_15_4, all_15_5,
% 8.50/2.06 | | | simplifying with (9), (37) gives:
% 8.50/2.06 | | | (40) all_32_2 = 0
% 8.50/2.06 | | |
% 8.50/2.06 | | | GROUND_INST: instantiating (2) with 0, all_32_1, all_15_5, all_15_7,
% 8.50/2.06 | | | simplifying with (32), (38) gives:
% 8.50/2.06 | | | (41) all_32_1 = 0
% 8.50/2.06 | | |
% 8.50/2.06 | | | BETA: splitting (39) gives:
% 8.50/2.06 | | |
% 8.50/2.06 | | | Case 1:
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | (42) ~ (all_32_2 = 0)
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | REDUCE: (40), (42) imply:
% 8.50/2.06 | | | | (43) $false
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | CLOSE: (43) is inconsistent.
% 8.50/2.06 | | | |
% 8.50/2.06 | | | Case 2:
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | (44) ~ (all_32_0 = 0) & ~ (all_32_1 = 0)
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | ALPHA: (44) implies:
% 8.50/2.06 | | | | (45) ~ (all_32_1 = 0)
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | REDUCE: (41), (45) imply:
% 8.50/2.06 | | | | (46) $false
% 8.50/2.06 | | | |
% 8.50/2.06 | | | | CLOSE: (46) is inconsistent.
% 8.50/2.06 | | | |
% 8.50/2.06 | | | End of split
% 8.50/2.06 | | |
% 8.50/2.06 | | End of split
% 8.50/2.06 | |
% 8.50/2.06 | End of split
% 8.50/2.06 |
% 8.50/2.06 End of proof
% 8.50/2.06 % SZS output end Proof for theBenchmark
% 8.50/2.06
% 8.50/2.06 1458ms
%------------------------------------------------------------------------------