TSTP Solution File: GEO216+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO216+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 : n002.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 23:22:25 EDT 2023
% Result : Theorem 4.99s 1.43s
% Output : Proof 6.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO216+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 19:35:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.04 Prover 1: Preprocessing ...
% 2.40/1.04 Prover 4: Preprocessing ...
% 2.94/1.08 Prover 5: Preprocessing ...
% 2.94/1.08 Prover 0: Preprocessing ...
% 2.94/1.09 Prover 2: Preprocessing ...
% 2.94/1.09 Prover 6: Preprocessing ...
% 2.94/1.09 Prover 3: Preprocessing ...
% 4.20/1.30 Prover 5: Proving ...
% 4.20/1.31 Prover 2: Proving ...
% 4.20/1.33 Prover 3: Constructing countermodel ...
% 4.20/1.33 Prover 6: Constructing countermodel ...
% 4.99/1.39 Prover 1: Constructing countermodel ...
% 4.99/1.43 Prover 6: proved (775ms)
% 4.99/1.43
% 4.99/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.99/1.43
% 4.99/1.43 Prover 3: stopped
% 4.99/1.44 Prover 5: stopped
% 5.65/1.44 Prover 2: stopped
% 5.68/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.68/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.68/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.68/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.68/1.47 Prover 8: Preprocessing ...
% 5.68/1.48 Prover 7: Preprocessing ...
% 5.68/1.50 Prover 11: Preprocessing ...
% 5.68/1.50 Prover 10: Preprocessing ...
% 6.12/1.51 Prover 7: Warning: ignoring some quantifiers
% 6.12/1.52 Prover 7: Constructing countermodel ...
% 6.12/1.53 Prover 10: Warning: ignoring some quantifiers
% 6.12/1.54 Prover 10: Constructing countermodel ...
% 6.12/1.55 Prover 4: Constructing countermodel ...
% 6.52/1.56 Prover 1: Found proof (size 16)
% 6.52/1.56 Prover 1: proved (908ms)
% 6.52/1.56 Prover 10: stopped
% 6.52/1.56 Prover 7: stopped
% 6.52/1.57 Prover 4: stopped
% 6.52/1.57 Prover 0: Proving ...
% 6.52/1.57 Prover 11: stopped
% 6.52/1.58 Prover 0: stopped
% 6.52/1.58 Prover 8: Warning: ignoring some quantifiers
% 6.52/1.59 Prover 8: Constructing countermodel ...
% 6.52/1.59 Prover 8: stopped
% 6.52/1.59
% 6.52/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.52/1.59
% 6.52/1.60 % SZS output start Proof for theBenchmark
% 6.52/1.60 Assumptions after simplification:
% 6.52/1.60 ---------------------------------
% 6.52/1.60
% 6.52/1.60 (coipo1)
% 6.52/1.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 6.52/1.62 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 6.52/1.62 convergent_lines(v0, v1) = 0)
% 6.52/1.62
% 6.52/1.62 (con)
% 6.52/1.63 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & unorthogonal_lines(v0, v0) = v1 &
% 6.52/1.63 $i(v0))
% 6.52/1.63
% 6.52/1.63 (couo1)
% 6.52/1.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 6.52/1.63 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 6.52/1.63 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 6.52/1.63 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 6.52/1.63
% 6.52/1.63 (function-axioms)
% 6.52/1.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.52/1.63 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 6.52/1.63 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 6.52/1.63 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 6.52/1.63 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 6.52/1.64 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 6.52/1.64 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.52/1.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.52/1.64 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 6.52/1.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.52/1.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 6.52/1.64 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.52/1.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.52/1.64 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 6.52/1.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.52/1.64 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 6.52/1.64 v0))
% 6.52/1.64
% 6.52/1.64 Further assumptions not needed in the proof:
% 6.52/1.64 --------------------------------------------
% 6.52/1.64 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci1, ci2, ci3,
% 6.52/1.64 ci4, cotno1, cu1
% 6.52/1.64
% 6.52/1.64 Those formulas are unsatisfiable:
% 6.52/1.64 ---------------------------------
% 6.52/1.64
% 6.52/1.64 Begin of proof
% 6.52/1.64 |
% 6.52/1.64 | ALPHA: (function-axioms) implies:
% 6.52/1.64 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.52/1.64 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 6.52/1.64 | (convergent_lines(v3, v2) = v0))
% 6.52/1.64 |
% 6.52/1.64 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1 gives:
% 6.52/1.64 | (2) ~ (all_20_0 = 0) & unorthogonal_lines(all_20_1, all_20_1) = all_20_0 &
% 6.52/1.64 | $i(all_20_1)
% 6.52/1.64 |
% 6.52/1.64 | ALPHA: (2) implies:
% 6.52/1.64 | (3) ~ (all_20_0 = 0)
% 6.52/1.64 | (4) $i(all_20_1)
% 6.52/1.64 | (5) unorthogonal_lines(all_20_1, all_20_1) = all_20_0
% 6.52/1.64 |
% 6.52/1.64 | GROUND_INST: instantiating (couo1) with all_20_1, all_20_1, all_20_1,
% 6.52/1.64 | all_20_0, all_20_0, simplifying with (4), (5) gives:
% 6.52/1.64 | (6) all_20_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_20_1,
% 6.52/1.64 | all_20_1) = v0)
% 6.52/1.64 |
% 6.52/1.64 | GROUND_INST: instantiating (coipo1) with all_20_1, all_20_1, all_20_0,
% 6.52/1.64 | simplifying with (4), (5) gives:
% 6.52/1.64 | (7) all_20_0 = 0 | convergent_lines(all_20_1, all_20_1) = 0
% 6.52/1.64 |
% 6.52/1.64 | BETA: splitting (7) gives:
% 6.52/1.64 |
% 6.52/1.65 | Case 1:
% 6.52/1.65 | |
% 6.52/1.65 | | (8) convergent_lines(all_20_1, all_20_1) = 0
% 6.52/1.65 | |
% 6.52/1.65 | | BETA: splitting (6) gives:
% 6.52/1.65 | |
% 6.52/1.65 | | Case 1:
% 6.52/1.65 | | |
% 6.52/1.65 | | | (9) all_20_0 = 0
% 6.52/1.65 | | |
% 6.52/1.65 | | | REDUCE: (3), (9) imply:
% 6.52/1.65 | | | (10) $false
% 6.52/1.65 | | |
% 6.52/1.65 | | | CLOSE: (10) is inconsistent.
% 6.52/1.65 | | |
% 6.52/1.65 | | Case 2:
% 6.52/1.65 | | |
% 6.52/1.65 | | | (11) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_20_1, all_20_1)
% 6.52/1.65 | | | = v0)
% 6.52/1.65 | | |
% 6.52/1.65 | | | DELTA: instantiating (11) with fresh symbol all_37_0 gives:
% 6.52/1.65 | | | (12) ~ (all_37_0 = 0) & convergent_lines(all_20_1, all_20_1) =
% 6.52/1.65 | | | all_37_0
% 6.52/1.65 | | |
% 6.52/1.65 | | | ALPHA: (12) implies:
% 6.52/1.65 | | | (13) ~ (all_37_0 = 0)
% 6.52/1.65 | | | (14) convergent_lines(all_20_1, all_20_1) = all_37_0
% 6.52/1.65 | | |
% 6.52/1.65 | | | GROUND_INST: instantiating (1) with 0, all_37_0, all_20_1, all_20_1,
% 6.52/1.65 | | | simplifying with (8), (14) gives:
% 6.52/1.65 | | | (15) all_37_0 = 0
% 6.52/1.65 | | |
% 6.52/1.65 | | | REDUCE: (13), (15) imply:
% 6.52/1.65 | | | (16) $false
% 6.52/1.65 | | |
% 6.52/1.65 | | | CLOSE: (16) is inconsistent.
% 6.52/1.65 | | |
% 6.52/1.65 | | End of split
% 6.52/1.65 | |
% 6.52/1.65 | Case 2:
% 6.52/1.65 | |
% 6.52/1.65 | | (17) all_20_0 = 0
% 6.52/1.65 | |
% 6.52/1.65 | | REDUCE: (3), (17) imply:
% 6.52/1.65 | | (18) $false
% 6.52/1.65 | |
% 6.52/1.65 | | CLOSE: (18) is inconsistent.
% 6.52/1.65 | |
% 6.52/1.65 | End of split
% 6.52/1.65 |
% 6.52/1.65 End of proof
% 6.52/1.65 % SZS output end Proof for theBenchmark
% 6.52/1.65
% 6.52/1.65 1019ms
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