TSTP Solution File: GEO206+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO206+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 : n029.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 23:22:18 EDT 2023
% Result : Theorem 5.57s 1.49s
% Output : Proof 7.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO206+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 21:17:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.66/0.63 ________ _____
% 0.66/0.63 ___ __ \_________(_)________________________________
% 0.66/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.66/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.66/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.66/0.63
% 0.66/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.63 (2023-06-19)
% 0.66/0.63
% 0.66/0.63 (c) Philipp Rümmer, 2009-2023
% 0.66/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.63 Amanda Stjerna.
% 0.66/0.63 Free software under BSD-3-Clause.
% 0.66/0.63
% 0.66/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.64 Running up to 7 provers in parallel.
% 0.66/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.62/1.05 Prover 4: Preprocessing ...
% 2.62/1.06 Prover 1: Preprocessing ...
% 2.62/1.09 Prover 5: Preprocessing ...
% 2.62/1.09 Prover 2: Preprocessing ...
% 2.62/1.09 Prover 0: Preprocessing ...
% 2.62/1.09 Prover 6: Preprocessing ...
% 2.62/1.10 Prover 3: Preprocessing ...
% 4.40/1.33 Prover 2: Proving ...
% 4.40/1.33 Prover 5: Proving ...
% 4.40/1.36 Prover 3: Constructing countermodel ...
% 4.40/1.36 Prover 1: Constructing countermodel ...
% 4.40/1.36 Prover 6: Constructing countermodel ...
% 5.57/1.49 Prover 3: proved (836ms)
% 5.57/1.49
% 5.57/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.57/1.49
% 5.57/1.49 Prover 6: proved (835ms)
% 5.57/1.49
% 5.57/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.57/1.49
% 5.57/1.49 Prover 5: stopped
% 5.57/1.49 Prover 2: stopped
% 5.57/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.57/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.57/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.57/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.57/1.50 Prover 4: Constructing countermodel ...
% 5.57/1.52 Prover 0: Proving ...
% 6.23/1.53 Prover 0: stopped
% 6.23/1.53 Prover 7: Preprocessing ...
% 6.23/1.53 Prover 8: Preprocessing ...
% 6.23/1.54 Prover 11: Preprocessing ...
% 6.23/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.23/1.55 Prover 10: Preprocessing ...
% 6.23/1.56 Prover 13: Preprocessing ...
% 6.23/1.56 Prover 1: Found proof (size 19)
% 6.23/1.56 Prover 1: proved (913ms)
% 6.23/1.56 Prover 7: stopped
% 6.23/1.57 Prover 10: stopped
% 6.23/1.57 Prover 4: stopped
% 6.23/1.58 Prover 13: stopped
% 6.72/1.59 Prover 11: stopped
% 6.72/1.61 Prover 8: Warning: ignoring some quantifiers
% 6.72/1.62 Prover 8: Constructing countermodel ...
% 6.72/1.62 Prover 8: stopped
% 6.72/1.62
% 6.72/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.62
% 6.72/1.63 % SZS output start Proof for theBenchmark
% 6.72/1.63 Assumptions after simplification:
% 6.72/1.63 ---------------------------------
% 6.72/1.63
% 6.72/1.63 (ax6)
% 6.72/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.72/1.66 (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ~
% 6.72/1.66 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 6.72/1.66
% 6.72/1.66 (con)
% 6.72/1.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ?
% 6.72/1.66 [v5: $i] : ( ~ (v4 = 0) & ~ (v3 = 0) & parallel_through_point(v2, v0) = v5 &
% 6.72/1.66 apart_point_and_line(v0, v1) = v3 & convergent_lines(v1, v2) = v4 &
% 6.72/1.66 distinct_lines(v1, v5) = 0 & $i(v5) & $i(v2) & $i(v1) & $i(v0))
% 6.72/1.66
% 6.72/1.66 (cp1)
% 6.72/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0)
% 6.72/1.66 = v2) | ~ (convergent_lines(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 6.72/1.66
% 6.72/1.66 (cp2)
% 7.10/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0)
% 7.10/1.66 = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 7.10/1.66
% 7.10/1.66 (cup1)
% 7.10/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.10/1.67 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~
% 7.10/1.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.10/1.67 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0
% 7.10/1.67 | v4 = 0)))
% 7.10/1.67
% 7.10/1.67 Further assumptions not needed in the proof:
% 7.10/1.67 --------------------------------------------
% 7.10/1.67 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, ci1, ci2, ci3, ci4,
% 7.10/1.67 cu1
% 7.10/1.67
% 7.10/1.67 Those formulas are unsatisfiable:
% 7.10/1.67 ---------------------------------
% 7.10/1.67
% 7.10/1.67 Begin of proof
% 7.10/1.67 |
% 7.10/1.67 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 7.10/1.67 | all_20_3, all_20_4, all_20_5 gives:
% 7.10/1.67 | (1) ~ (all_20_1 = 0) & ~ (all_20_2 = 0) &
% 7.10/1.67 | parallel_through_point(all_20_3, all_20_5) = all_20_0 &
% 7.10/1.67 | apart_point_and_line(all_20_5, all_20_4) = all_20_2 &
% 7.10/1.67 | convergent_lines(all_20_4, all_20_3) = all_20_1 &
% 7.10/1.67 | distinct_lines(all_20_4, all_20_0) = 0 & $i(all_20_0) & $i(all_20_3) &
% 7.10/1.67 | $i(all_20_4) & $i(all_20_5)
% 7.10/1.67 |
% 7.10/1.67 | ALPHA: (1) implies:
% 7.10/1.67 | (2) ~ (all_20_2 = 0)
% 7.10/1.67 | (3) ~ (all_20_1 = 0)
% 7.10/1.68 | (4) $i(all_20_5)
% 7.16/1.68 | (5) $i(all_20_4)
% 7.16/1.68 | (6) $i(all_20_3)
% 7.16/1.68 | (7) $i(all_20_0)
% 7.16/1.68 | (8) distinct_lines(all_20_4, all_20_0) = 0
% 7.16/1.68 | (9) convergent_lines(all_20_4, all_20_3) = all_20_1
% 7.16/1.68 | (10) apart_point_and_line(all_20_5, all_20_4) = all_20_2
% 7.16/1.68 | (11) parallel_through_point(all_20_3, all_20_5) = all_20_0
% 7.16/1.68 |
% 7.16/1.68 | GROUND_INST: instantiating (cup1) with all_20_5, all_20_4, all_20_0, all_20_2,
% 7.16/1.68 | simplifying with (4), (5), (7), (8), (10) gives:
% 7.16/1.68 | (12) all_20_2 = 0 | ? [v0: any] : ? [v1: any] :
% 7.16/1.68 | (apart_point_and_line(all_20_5, all_20_0) = v0 &
% 7.16/1.68 | convergent_lines(all_20_4, all_20_0) = v1 & (v1 = 0 | v0 = 0))
% 7.16/1.68 |
% 7.16/1.68 | BETA: splitting (12) gives:
% 7.16/1.68 |
% 7.16/1.68 | Case 1:
% 7.16/1.68 | |
% 7.16/1.68 | | (13) all_20_2 = 0
% 7.16/1.68 | |
% 7.16/1.68 | | REDUCE: (2), (13) imply:
% 7.16/1.68 | | (14) $false
% 7.16/1.68 | |
% 7.16/1.68 | | CLOSE: (14) is inconsistent.
% 7.16/1.68 | |
% 7.16/1.68 | Case 2:
% 7.16/1.68 | |
% 7.16/1.68 | | (15) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_20_5,
% 7.16/1.68 | | all_20_0) = v0 & convergent_lines(all_20_4, all_20_0) = v1 & (v1
% 7.16/1.68 | | = 0 | v0 = 0))
% 7.16/1.68 | |
% 7.16/1.68 | | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1 gives:
% 7.16/1.69 | | (16) apart_point_and_line(all_20_5, all_20_0) = all_29_1 &
% 7.16/1.69 | | convergent_lines(all_20_4, all_20_0) = all_29_0 & (all_29_0 = 0 |
% 7.16/1.69 | | all_29_1 = 0)
% 7.16/1.69 | |
% 7.16/1.69 | | ALPHA: (16) implies:
% 7.16/1.69 | | (17) convergent_lines(all_20_4, all_20_0) = all_29_0
% 7.16/1.69 | | (18) apart_point_and_line(all_20_5, all_20_0) = all_29_1
% 7.16/1.69 | | (19) all_29_0 = 0 | all_29_1 = 0
% 7.16/1.69 | |
% 7.16/1.69 | | BETA: splitting (19) gives:
% 7.16/1.69 | |
% 7.16/1.69 | | Case 1:
% 7.16/1.69 | | |
% 7.16/1.69 | | | (20) all_29_0 = 0
% 7.16/1.69 | | |
% 7.16/1.69 | | | REDUCE: (17), (20) imply:
% 7.16/1.69 | | | (21) convergent_lines(all_20_4, all_20_0) = 0
% 7.16/1.69 | | |
% 7.16/1.69 | | | GROUND_INST: instantiating (ax6) with all_20_4, all_20_0, all_20_3,
% 7.16/1.69 | | | all_20_1, simplifying with (5), (6), (7), (9), (21) gives:
% 7.16/1.69 | | | (22) all_20_1 = 0 | convergent_lines(all_20_0, all_20_3) = 0
% 7.16/1.69 | | |
% 7.16/1.69 | | | BETA: splitting (22) gives:
% 7.16/1.69 | | |
% 7.16/1.69 | | | Case 1:
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | (23) convergent_lines(all_20_0, all_20_3) = 0
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | GROUND_INST: instantiating (cp1) with all_20_5, all_20_3, all_20_0,
% 7.16/1.69 | | | | simplifying with (4), (6), (11), (23) gives:
% 7.16/1.69 | | | | (24) $false
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | CLOSE: (24) is inconsistent.
% 7.16/1.69 | | | |
% 7.16/1.69 | | | Case 2:
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | (25) all_20_1 = 0
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | REDUCE: (3), (25) imply:
% 7.16/1.69 | | | | (26) $false
% 7.16/1.69 | | | |
% 7.16/1.69 | | | | CLOSE: (26) is inconsistent.
% 7.16/1.69 | | | |
% 7.16/1.69 | | | End of split
% 7.16/1.69 | | |
% 7.16/1.69 | | Case 2:
% 7.16/1.69 | | |
% 7.16/1.69 | | | (27) all_29_1 = 0
% 7.16/1.69 | | |
% 7.16/1.69 | | | REDUCE: (18), (27) imply:
% 7.16/1.69 | | | (28) apart_point_and_line(all_20_5, all_20_0) = 0
% 7.16/1.69 | | |
% 7.16/1.69 | | | GROUND_INST: instantiating (cp2) with all_20_5, all_20_3, all_20_0,
% 7.16/1.69 | | | simplifying with (4), (6), (11), (28) gives:
% 7.16/1.69 | | | (29) $false
% 7.16/1.69 | | |
% 7.16/1.69 | | | CLOSE: (29) is inconsistent.
% 7.16/1.69 | | |
% 7.16/1.69 | | End of split
% 7.16/1.69 | |
% 7.16/1.69 | End of split
% 7.16/1.69 |
% 7.16/1.69 End of proof
% 7.16/1.69 % SZS output end Proof for theBenchmark
% 7.16/1.69
% 7.16/1.69 1062ms
%------------------------------------------------------------------------------