TSTP Solution File: NUN087+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 : 600s
% DateTime : Mon Jul 18 16:25:11 EDT 2022
% Result : Theorem 29.65s 13.11s
% Output : Proof 30.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 06:33:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.58 Bug reports to peter@backeman.se
% 0.20/0.58
% 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.95 Prover 0: Preprocessing ...
% 2.12/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.12/1.11 Prover 0: Constructing countermodel ...
% 2.90/1.34 Prover 0: gave up
% 2.90/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.14/1.37 Prover 1: Preprocessing ...
% 3.14/1.45 Prover 1: Warning: ignoring some quantifiers
% 3.14/1.45 Prover 1: Constructing countermodel ...
% 4.14/1.61 Prover 1: gave up
% 4.14/1.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.14/1.63 Prover 2: Preprocessing ...
% 4.14/1.68 Prover 2: Warning: ignoring some quantifiers
% 4.14/1.68 Prover 2: Constructing countermodel ...
% 4.88/1.80 Prover 2: gave up
% 4.88/1.80 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.99/1.82 Prover 3: Preprocessing ...
% 5.07/1.83 Prover 3: Warning: ignoring some quantifiers
% 5.07/1.84 Prover 3: Constructing countermodel ...
% 5.07/1.90 Prover 3: gave up
% 5.07/1.90 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.51/1.92 Prover 4: Preprocessing ...
% 5.51/1.96 Prover 4: Warning: ignoring some quantifiers
% 5.51/1.96 Prover 4: Constructing countermodel ...
% 6.47/2.14 Prover 4: gave up
% 6.47/2.14 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.47/2.16 Prover 5: Preprocessing ...
% 6.47/2.19 Prover 5: Warning: ignoring some quantifiers
% 6.47/2.19 Prover 5: Constructing countermodel ...
% 6.90/2.26 Prover 5: gave up
% 6.90/2.26 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.90/2.27 Prover 6: Preprocessing ...
% 6.90/2.30 Prover 6: Warning: ignoring some quantifiers
% 6.90/2.30 Prover 6: Constructing countermodel ...
% 7.32/2.38 Prover 6: gave up
% 7.32/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 7.68/2.39 Prover 7: Preprocessing ...
% 7.73/2.40 Prover 7: Proving ...
% 29.10/12.98 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 29.29/13.02 Prover 8: Preprocessing ...
% 29.29/13.05 Prover 8: Proving ...
% 29.65/13.10 Prover 8: proved (123ms)
% 29.65/13.11 Prover 7: stopped
% 29.65/13.11
% 29.65/13.11 % SZS status Theorem for theBenchmark
% 29.65/13.11
% 29.65/13.11 Generating proof ... found it (size 23)
% 30.24/13.28
% 30.24/13.28 % SZS output start Proof for theBenchmark
% 30.24/13.28 Assumed formulas after preprocessing and simplification:
% 30.24/13.28 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) | ~ (r3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2(v3, v2) = v1) | ~ (r2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2) = v0)) & ! [v0] : ! [v1] : ? [v2] : ! [v3] : ! [v4] : ( ~ (r4(v0, v1, v3) = v4) | (v4 = 0 & v3 = v2) | ( ~ (v4 = 0) & ~ (v3 = v2))) & ! [v0] : ! [v1] : ? [v2] : ! [v3] : ! [v4] : ( ~ (r3(v0, v1, v3) = v4) | (v4 = 0 & v3 = v2) | ( ~ (v4 = 0) & ~ (v3 = v2))) & ! [v0] : ? [v1] : ! [v2] : ! [v3] : ( ~ (r2(v0, v2) = v3) | (v3 = 0 & v2 = v1) | ( ~ (v3 = 0) & ~ (v2 = v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (r1(v1) = v2) | (v2 = 0 & v1 = v0) | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0] : ! [v1] : (v1 = v0 | ! [v2] : ( ~ (r2(v1, v2) = 0) | ~ (r2(v0, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0)) & ! [v0] : ( ~ (r1(v0) = 0) | ! [v1] : ( ~ (r4(v1, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & r1(v1) = v2))) & ! [v0] : (r1(v0) = 0 | ? [v1] : r2(v1, v0) = 0) & ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r4(v0, v3, v2) = 0 & r2(v1, v3) = 0) & ? [v3] : (r4(v0, v1, v3) = 0 & r3(v3, v0, v2) = 0)) & ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r3(v0, v3, v2) = 0 & r2(v1, v3) = 0) & ? [v3] : (r3(v0, v1, v3) = 0 & r2(v3, v2) = 0)) & ! [v0] : ? [v1] : (r3(v0, v1, v0) = 0 & r1(v1) = 0) & ! [v0] : ? [v1] : (r1(v1) = 0 & ? [v2] : (r4(v0, v2, v1) = 0 & r1(v2) = 0))
% 30.24/13.30 | Applying alpha-rule on (0) yields:
% 30.24/13.30 | (1) ! [v0] : ! [v1] : ? [v2] : ! [v3] : ! [v4] : ( ~ (r4(v0, v1, v3) = v4) | (v4 = 0 & v3 = v2) | ( ~ (v4 = 0) & ~ (v3 = v2)))
% 30.24/13.31 | (2) ? [v0] : ! [v1] : ! [v2] : ( ~ (r1(v1) = v2) | (v2 = 0 & v1 = v0) | ( ~ (v2 = 0) & ~ (v1 = v0)))
% 30.24/13.31 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) | ~ (r3(v4, v3, v2) = v0))
% 30.24/13.31 | (4) ! [v0] : ? [v1] : (r1(v1) = 0 & ? [v2] : (r4(v0, v2, v1) = 0 & r1(v2) = 0))
% 30.24/13.31 | (5) ! [v0] : ? [v1] : (r3(v0, v1, v0) = 0 & r1(v1) = 0)
% 30.24/13.31 | (6) ! [v0] : ! [v1] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0))
% 30.24/13.31 | (7) ! [v0] : (r1(v0) = 0 | ? [v1] : r2(v1, v0) = 0)
% 30.24/13.31 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2(v3, v2) = v1) | ~ (r2(v3, v2) = v0))
% 30.24/13.31 | (9) ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r3(v0, v3, v2) = 0 & r2(v1, v3) = 0) & ? [v3] : (r3(v0, v1, v3) = 0 & r2(v3, v2) = 0))
% 30.24/13.31 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3, v2) = v0))
% 30.24/13.31 | (11) ! [v0] : ! [v1] : ? [v2] : ! [v3] : ! [v4] : ( ~ (r3(v0, v1, v3) = v4) | (v4 = 0 & v3 = v2) | ( ~ (v4 = 0) & ~ (v3 = v2)))
% 30.24/13.31 | (12) ! [v0] : ? [v1] : ! [v2] : ! [v3] : ( ~ (r2(v0, v2) = v3) | (v3 = 0 & v2 = v1) | ( ~ (v3 = 0) & ~ (v2 = v1)))
% 30.24/13.31 | (13) ! [v0] : ! [v1] : (v1 = v0 | ! [v2] : ( ~ (r2(v1, v2) = 0) | ~ (r2(v0, v2) = 0)))
% 30.24/13.31 | (14) ! [v0] : ( ~ (r1(v0) = 0) | ! [v1] : ( ~ (r4(v1, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & r1(v1) = v2)))
% 30.64/13.31 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2) = v0))
% 30.64/13.31 | (16) ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r4(v0, v3, v2) = 0 & r2(v1, v3) = 0) & ? [v3] : (r4(v0, v1, v3) = 0 & r3(v3, v0, v2) = 0))
% 30.64/13.31 |
% 30.64/13.31 | Instantiating (2) with all_1_0_0 yields:
% 30.64/13.31 | (17) ! [v0] : ! [v1] : ( ~ (r1(v0) = v1) | (v1 = 0 & v0 = all_1_0_0) | ( ~ (v1 = 0) & ~ (v0 = all_1_0_0)))
% 30.64/13.32 |
% 30.64/13.32 | Introducing new symbol ex_15_0_7 defined by:
% 30.64/13.32 | (18) ex_15_0_7 = all_1_0_0
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (4) with ex_15_0_7 yields:
% 30.64/13.32 | (19) ? [v0] : (r1(v0) = 0 & ? [v1] : (r4(ex_15_0_7, v1, v0) = 0 & r1(v1) = 0))
% 30.64/13.32 |
% 30.64/13.32 | Instantiating (19) with all_16_0_8 yields:
% 30.64/13.32 | (20) r1(all_16_0_8) = 0 & ? [v0] : (r4(ex_15_0_7, v0, all_16_0_8) = 0 & r1(v0) = 0)
% 30.64/13.32 |
% 30.64/13.32 | Applying alpha-rule on (20) yields:
% 30.64/13.32 | (21) r1(all_16_0_8) = 0
% 30.64/13.32 | (22) ? [v0] : (r4(ex_15_0_7, v0, all_16_0_8) = 0 & r1(v0) = 0)
% 30.64/13.32 |
% 30.64/13.32 | Instantiating (22) with all_18_0_9 yields:
% 30.64/13.32 | (23) r4(ex_15_0_7, all_18_0_9, all_16_0_8) = 0 & r1(all_18_0_9) = 0
% 30.64/13.32 |
% 30.64/13.32 | Applying alpha-rule on (23) yields:
% 30.64/13.32 | (24) r4(ex_15_0_7, all_18_0_9, all_16_0_8) = 0
% 30.64/13.32 | (25) r1(all_18_0_9) = 0
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (17) with 0, all_18_0_9 and discharging atoms r1(all_18_0_9) = 0, yields:
% 30.64/13.32 | (26) all_18_0_9 = all_1_0_0
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (17) with 0, all_16_0_8 and discharging atoms r1(all_16_0_8) = 0, yields:
% 30.64/13.32 | (27) all_16_0_8 = all_1_0_0
% 30.64/13.32 |
% 30.64/13.32 | From (26)(27) and (24) follows:
% 30.64/13.32 | (28) r4(ex_15_0_7, all_1_0_0, all_1_0_0) = 0
% 30.64/13.32 |
% 30.64/13.32 | From (27) and (21) follows:
% 30.64/13.32 | (29) r1(all_1_0_0) = 0
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (14) with all_1_0_0 and discharging atoms r1(all_1_0_0) = 0, yields:
% 30.64/13.32 | (30) ! [v0] : ( ~ (r4(v0, v0, all_1_0_0) = 0) | ? [v1] : ( ~ (v1 = 0) & r1(v0) = v1))
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (30) with all_1_0_0 yields:
% 30.64/13.32 | (31) ~ (r4(all_1_0_0, all_1_0_0, all_1_0_0) = 0) | ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0) = v0)
% 30.64/13.32 |
% 30.64/13.32 +-Applying beta-rule and splitting (31), into two cases.
% 30.64/13.32 |-Branch one:
% 30.64/13.32 | (32) ~ (r4(all_1_0_0, all_1_0_0, all_1_0_0) = 0)
% 30.64/13.32 |
% 30.64/13.32 | From (18) and (28) follows:
% 30.64/13.32 | (33) r4(all_1_0_0, all_1_0_0, all_1_0_0) = 0
% 30.64/13.32 |
% 30.64/13.32 | Using (33) and (32) yields:
% 30.64/13.32 | (34) $false
% 30.64/13.32 |
% 30.64/13.32 |-The branch is then unsatisfiable
% 30.64/13.32 |-Branch two:
% 30.64/13.32 | (35) ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0) = v0)
% 30.64/13.32 |
% 30.64/13.32 | Instantiating (35) with all_33_0_10 yields:
% 30.64/13.32 | (36) ~ (all_33_0_10 = 0) & r1(all_1_0_0) = all_33_0_10
% 30.64/13.32 |
% 30.64/13.32 | Applying alpha-rule on (36) yields:
% 30.64/13.32 | (37) ~ (all_33_0_10 = 0)
% 30.64/13.32 | (38) r1(all_1_0_0) = all_33_0_10
% 30.64/13.32 |
% 30.64/13.32 | Instantiating formula (17) with all_33_0_10, all_1_0_0 and discharging atoms r1(all_1_0_0) = all_33_0_10, yields:
% 30.64/13.32 | (39) all_33_0_10 = 0
% 30.64/13.32 |
% 30.64/13.32 | Equations (39) can reduce 37 to:
% 30.64/13.32 | (40) $false
% 30.64/13.32 |
% 30.64/13.32 |-The branch is then unsatisfiable
% 30.64/13.32 % SZS output end Proof for theBenchmark
% 30.64/13.33
% 30.64/13.33 12729ms
%------------------------------------------------------------------------------