TSTP Solution File: SYN331+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 : Thu Jul 21 05:01:27 EDT 2022
% Result : Theorem 3.53s 1.57s
% Output : Proof 10.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 20:04:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.59 ____ _
% 0.48/0.59 ___ / __ \_____(_)___ ________ __________
% 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.59
% 0.48/0.59 A Theorem Prover for First-Order Logic
% 0.48/0.59 (ePrincess v.1.0)
% 0.48/0.59
% 0.48/0.59 (c) Philipp Rümmer, 2009-2015
% 0.48/0.59 (c) Peter Backeman, 2014-2015
% 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.59 Bug reports to peter@backeman.se
% 0.48/0.59
% 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.59
% 0.48/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.20/0.90 Prover 0: Preprocessing ...
% 1.39/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.39/0.95 Prover 0: Constructing countermodel ...
% 1.50/1.04 Prover 0: gave up
% 1.50/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.71/1.06 Prover 1: Preprocessing ...
% 1.96/1.12 Prover 1: Constructing countermodel ...
% 1.96/1.12 Prover 1: gave up
% 1.96/1.13 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.96/1.14 Prover 2: Preprocessing ...
% 2.12/1.18 Prover 2: Warning: ignoring some quantifiers
% 2.12/1.18 Prover 2: Constructing countermodel ...
% 2.12/1.20 Prover 2: gave up
% 2.12/1.20 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.12/1.21 Prover 3: Preprocessing ...
% 2.12/1.22 Prover 3: Warning: ignoring some quantifiers
% 2.12/1.22 Prover 3: Constructing countermodel ...
% 2.43/1.24 Prover 3: gave up
% 2.43/1.24 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.43/1.24 Prover 4: Preprocessing ...
% 2.58/1.28 Prover 4: Warning: ignoring some quantifiers
% 2.58/1.29 Prover 4: Constructing countermodel ...
% 3.53/1.57 Prover 4: proved (330ms)
% 3.53/1.57
% 3.53/1.57 No countermodel exists, formula is valid
% 3.53/1.57 % SZS status Theorem for theBenchmark
% 3.53/1.57
% 3.53/1.57 Generating proof ... Warning: ignoring some quantifiers
% 10.40/3.19 found it (size 25)
% 10.40/3.19
% 10.40/3.19 % SZS output start Proof for theBenchmark
% 10.40/3.19 Assumed formulas after preprocessing and simplification:
% 10.40/3.19 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v0, v4) = 0 & big_f(v0, v1) = v3 & ( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0) & (v5 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & big_f(v0, v1) = v2 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0))
% 10.54/3.22 | Applying alpha-rule on (0) yields:
% 10.54/3.22 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0))
% 10.54/3.22 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v0, v4) = 0 & big_f(v0, v1) = v3 & ( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0) & (v5 = 0 | v2 = 0)))
% 10.54/3.22 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_f(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0)))
% 10.54/3.22 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & big_f(v4, v4) = v5 & big_f(v4, v1) = v7 & big_f(v4, v0) = v6 & big_f(v1, v4) = 0 & big_f(v1, v0) = v3 & big_f(v0, v4) = 0 & big_f(v0, v1) = v2 & ( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0) & (v5 = 0 | v3 = 0))
% 10.54/3.22 |
% 10.54/3.22 | Instantiating (4) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5, all_1_6_6, all_1_7_7 yields:
% 10.54/3.22 | (5) ~ (all_1_0_0 = 0) & ~ (all_1_1_1 = 0) & big_f(all_1_3_3, all_1_3_3) = all_1_2_2 & big_f(all_1_3_3, all_1_6_6) = all_1_0_0 & big_f(all_1_3_3, all_1_7_7) = all_1_1_1 & big_f(all_1_6_6, all_1_3_3) = 0 & big_f(all_1_6_6, all_1_7_7) = all_1_4_4 & big_f(all_1_7_7, all_1_3_3) = 0 & big_f(all_1_7_7, all_1_6_6) = all_1_5_5 & ( ~ (all_1_2_2 = 0) | all_1_5_5 = 0) & ( ~ (all_1_5_5 = 0) | all_1_2_2 = 0) & (all_1_2_2 = 0 | all_1_4_4 = 0)
% 10.54/3.23 |
% 10.54/3.23 | Applying alpha-rule on (5) yields:
% 10.54/3.23 | (6) big_f(all_1_3_3, all_1_3_3) = all_1_2_2
% 10.54/3.23 | (7) big_f(all_1_3_3, all_1_6_6) = all_1_0_0
% 10.54/3.23 | (8) ~ (all_1_5_5 = 0) | all_1_2_2 = 0
% 10.54/3.23 | (9) ~ (all_1_1_1 = 0)
% 10.54/3.23 | (10) big_f(all_1_6_6, all_1_3_3) = 0
% 10.54/3.23 | (11) ~ (all_1_0_0 = 0)
% 10.54/3.23 | (12) big_f(all_1_7_7, all_1_3_3) = 0
% 10.54/3.23 | (13) big_f(all_1_6_6, all_1_7_7) = all_1_4_4
% 10.54/3.23 | (14) all_1_2_2 = 0 | all_1_4_4 = 0
% 10.54/3.23 | (15) ~ (all_1_2_2 = 0) | all_1_5_5 = 0
% 10.54/3.23 | (16) big_f(all_1_3_3, all_1_7_7) = all_1_1_1
% 10.54/3.23 | (17) big_f(all_1_7_7, all_1_6_6) = all_1_5_5
% 10.54/3.23 |
% 10.54/3.23 | Instantiating formula (3) with all_1_0_0, all_1_6_6, all_1_3_3 and discharging atoms big_f(all_1_3_3, all_1_6_6) = all_1_0_0, yields:
% 10.54/3.23 | (18) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & big_f(v1, v1) = v2 & big_f(v1, all_1_3_3) = v3 & big_f(v1, all_1_6_6) = v4 & big_f(all_1_3_3, v1) = 0 & big_f(all_1_6_6, v1) = 0 & big_f(all_1_6_6, all_1_3_3) = v0 & ( ~ (v2 = 0) | all_1_0_0 = 0) & ( ~ (all_1_0_0 = 0) | v2 = 0) & (v2 = 0 | v0 = 0))
% 10.54/3.23 |
% 10.54/3.23 | Instantiating (18) with all_14_0_22, all_14_1_23, all_14_2_24, all_14_3_25, all_14_4_26 yields:
% 10.54/3.23 | (19) ~ (all_14_0_22 = 0) & ~ (all_14_1_23 = 0) & big_f(all_14_3_25, all_14_3_25) = all_14_2_24 & big_f(all_14_3_25, all_1_3_3) = all_14_1_23 & big_f(all_14_3_25, all_1_6_6) = all_14_0_22 & big_f(all_1_3_3, all_14_3_25) = 0 & big_f(all_1_6_6, all_14_3_25) = 0 & big_f(all_1_6_6, all_1_3_3) = all_14_4_26 & ( ~ (all_14_2_24 = 0) | all_1_0_0 = 0) & ( ~ (all_1_0_0 = 0) | all_14_2_24 = 0) & (all_14_2_24 = 0 | all_14_4_26 = 0)
% 10.54/3.23 |
% 10.54/3.23 | Applying alpha-rule on (19) yields:
% 10.54/3.23 | (20) big_f(all_14_3_25, all_14_3_25) = all_14_2_24
% 10.54/3.23 | (21) ~ (all_14_2_24 = 0) | all_1_0_0 = 0
% 10.54/3.23 | (22) ~ (all_14_1_23 = 0)
% 10.54/3.23 | (23) big_f(all_1_6_6, all_1_3_3) = all_14_4_26
% 10.54/3.23 | (24) big_f(all_14_3_25, all_1_6_6) = all_14_0_22
% 10.54/3.23 | (25) big_f(all_14_3_25, all_1_3_3) = all_14_1_23
% 10.54/3.23 | (26) big_f(all_1_6_6, all_14_3_25) = 0
% 10.54/3.23 | (27) all_14_2_24 = 0 | all_14_4_26 = 0
% 10.54/3.23 | (28) ~ (all_14_0_22 = 0)
% 10.54/3.23 | (29) ~ (all_1_0_0 = 0) | all_14_2_24 = 0
% 10.54/3.23 | (30) big_f(all_1_3_3, all_14_3_25) = 0
% 10.54/3.23 |
% 10.54/3.23 +-Applying beta-rule and splitting (21), into two cases.
% 10.54/3.23 |-Branch one:
% 10.54/3.23 | (31) ~ (all_14_2_24 = 0)
% 10.54/3.23 |
% 10.54/3.23 +-Applying beta-rule and splitting (27), into two cases.
% 10.54/3.23 |-Branch one:
% 10.54/3.23 | (32) all_14_2_24 = 0
% 10.54/3.23 |
% 10.54/3.23 | Equations (32) can reduce 31 to:
% 10.54/3.23 | (33) $false
% 10.54/3.23 |
% 10.54/3.23 |-The branch is then unsatisfiable
% 10.54/3.23 |-Branch two:
% 10.54/3.23 | (31) ~ (all_14_2_24 = 0)
% 10.54/3.23 | (35) all_14_4_26 = 0
% 10.54/3.23 |
% 10.54/3.23 | Instantiating formula (2) with all_14_2_24, all_14_3_25, all_14_3_25 and discharging atoms big_f(all_14_3_25, all_14_3_25) = all_14_2_24, yields:
% 10.54/3.23 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & big_f(v1, v1) = v2 & big_f(v1, all_14_3_25) = v4 & big_f(v1, all_14_3_25) = v3 & big_f(all_14_3_25, v1) = 0 & big_f(all_14_3_25, all_14_3_25) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0) & (v2 = 0 | all_14_2_24 = 0))
% 10.54/3.23 |
% 10.54/3.23 | Instantiating (36) with all_315_0_625, all_315_1_626, all_315_2_627, all_315_3_628, all_315_4_629 yields:
% 10.54/3.23 | (37) ~ (all_315_0_625 = 0) & ~ (all_315_1_626 = 0) & big_f(all_315_3_628, all_315_3_628) = all_315_2_627 & big_f(all_315_3_628, all_14_3_25) = all_315_0_625 & big_f(all_315_3_628, all_14_3_25) = all_315_1_626 & big_f(all_14_3_25, all_315_3_628) = 0 & big_f(all_14_3_25, all_14_3_25) = all_315_4_629 & ( ~ (all_315_2_627 = 0) | all_315_4_629 = 0) & ( ~ (all_315_4_629 = 0) | all_315_2_627 = 0) & (all_315_2_627 = 0 | all_14_2_24 = 0)
% 10.54/3.23 |
% 10.54/3.23 | Applying alpha-rule on (37) yields:
% 10.54/3.23 | (38) big_f(all_315_3_628, all_14_3_25) = all_315_1_626
% 10.54/3.23 | (39) ~ (all_315_1_626 = 0)
% 10.54/3.23 | (40) ~ (all_315_0_625 = 0)
% 10.54/3.23 | (41) big_f(all_14_3_25, all_14_3_25) = all_315_4_629
% 10.54/3.23 | (42) big_f(all_315_3_628, all_315_3_628) = all_315_2_627
% 10.54/3.23 | (43) ~ (all_315_4_629 = 0) | all_315_2_627 = 0
% 10.54/3.23 | (44) ~ (all_315_2_627 = 0) | all_315_4_629 = 0
% 10.54/3.23 | (45) big_f(all_315_3_628, all_14_3_25) = all_315_0_625
% 10.54/3.23 | (46) big_f(all_14_3_25, all_315_3_628) = 0
% 10.54/3.23 | (47) all_315_2_627 = 0 | all_14_2_24 = 0
% 10.54/3.23 |
% 10.54/3.23 +-Applying beta-rule and splitting (47), into two cases.
% 10.54/3.23 |-Branch one:
% 10.54/3.23 | (48) all_315_2_627 = 0
% 10.54/3.23 |
% 10.54/3.24 +-Applying beta-rule and splitting (44), into two cases.
% 10.54/3.24 |-Branch one:
% 10.54/3.24 | (49) ~ (all_315_2_627 = 0)
% 10.54/3.24 |
% 10.54/3.24 | Equations (48) can reduce 49 to:
% 10.54/3.24 | (33) $false
% 10.54/3.24 |
% 10.54/3.24 |-The branch is then unsatisfiable
% 10.54/3.24 |-Branch two:
% 10.54/3.24 | (48) all_315_2_627 = 0
% 10.54/3.24 | (52) all_315_4_629 = 0
% 10.54/3.24 |
% 10.54/3.24 | From (52) and (41) follows:
% 10.54/3.24 | (53) big_f(all_14_3_25, all_14_3_25) = 0
% 10.54/3.24 |
% 10.54/3.24 | Instantiating formula (1) with all_14_3_25, all_14_3_25, 0, all_14_2_24 and discharging atoms big_f(all_14_3_25, all_14_3_25) = all_14_2_24, big_f(all_14_3_25, all_14_3_25) = 0, yields:
% 10.54/3.24 | (32) all_14_2_24 = 0
% 10.54/3.24 |
% 10.54/3.24 | Equations (32) can reduce 31 to:
% 10.54/3.24 | (33) $false
% 10.54/3.24 |
% 10.54/3.24 |-The branch is then unsatisfiable
% 10.54/3.24 |-Branch two:
% 10.54/3.24 | (49) ~ (all_315_2_627 = 0)
% 10.54/3.24 | (32) all_14_2_24 = 0
% 10.54/3.24 |
% 10.54/3.24 | Equations (32) can reduce 31 to:
% 10.54/3.24 | (33) $false
% 10.54/3.24 |
% 10.54/3.24 |-The branch is then unsatisfiable
% 10.54/3.24 |-Branch two:
% 10.54/3.24 | (32) all_14_2_24 = 0
% 10.54/3.24 | (60) all_1_0_0 = 0
% 10.54/3.24 |
% 10.54/3.24 | Equations (60) can reduce 11 to:
% 10.54/3.24 | (33) $false
% 10.54/3.24 |
% 10.54/3.24 |-The branch is then unsatisfiable
% 10.54/3.24 % SZS output end Proof for theBenchmark
% 10.54/3.24
% 10.54/3.24 2636ms
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