TSTP Solution File: SYN365+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN365+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Jul 21 05:01:50 EDT 2022
% Result : Theorem 27.85s 8.62s
% Output : Proof 28.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN365+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % 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 : Mon Jul 11 17:20:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.89 Prover 0: Preprocessing ...
% 1.47/0.97 Prover 0: Warning: ignoring some quantifiers
% 1.47/0.98 Prover 0: Constructing countermodel ...
% 16.73/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.73/5.94 Prover 1: Preprocessing ...
% 16.73/6.00 Prover 1: Constructing countermodel ...
% 27.33/8.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 27.33/8.53 Prover 2: Preprocessing ...
% 27.57/8.58 Prover 2: Warning: ignoring some quantifiers
% 27.57/8.58 Prover 2: Constructing countermodel ...
% 27.85/8.62 Prover 2: proved (99ms)
% 27.85/8.62 Prover 0: stopped
% 27.85/8.62 Prover 1: stopped
% 27.85/8.62
% 27.85/8.62 No countermodel exists, formula is valid
% 27.85/8.62 % SZS status Theorem for theBenchmark
% 27.85/8.62
% 27.85/8.62 Generating proof ... Warning: ignoring some quantifiers
% 28.18/8.74 found it (size 27)
% 28.18/8.74
% 28.18/8.74 % SZS output start Proof for theBenchmark
% 28.18/8.74 Assumed formulas after preprocessing and simplification:
% 28.18/8.74 | (0) ? [v0] : (big_p(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (big_r(v4, v3) = v2) | ~ (big_r(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (h(v3) = v2) | ~ (h(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (g(v3) = v2) | ~ (g(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_p(v3) = v2) | ~ (big_p(v3) = v1)) & ! [v1] : ! [v2] : ( ~ (h(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & g(v1) = v3 & big_p(v3) = 0 & big_p(v2) = 0) | ( ~ (v3 = 0) & big_p(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (g(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & h(v1) = v4 & big_p(v4) = 0 & big_p(v2) = 0) | ( ~ (v3 = 0) & big_p(v1) = v3))) & ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_p(v1) = v2)) & ! [v1] : ( ~ (big_p(v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & g(v3) = v4 & big_r(v1, v4) = 0 & big_p(v2) = 0)) & ! [v1] : ( ~ (big_p(v1) = 0) | ? [v2] : ? [v3] : (h(v1) = v3 & g(v1) = v2 & big_p(v3) = 0 & big_p(v2) = 0)) & ! [v1] : ( ~ (big_p(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v0, v1) = v2)) & ? [v1] : ? [v2] : ? [v3] : big_r(v2, v1) = v3 & ? [v1] : ? [v2] : h(v1) = v2 & ? [v1] : ? [v2] : g(v1) = v2 & ? [v1] : ? [v2] : big_p(v1) = v2)
% 28.57/8.78 | Instantiating (0) with all_0_0_0 yields:
% 28.57/8.78 | (1) big_p(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (h(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & g(v0) = v2 & big_p(v2) = 0 & big_p(v1) = 0) | ( ~ (v2 = 0) & big_p(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & h(v0) = v3 & big_p(v3) = 0 & big_p(v1) = 0) | ( ~ (v2 = 0) & big_p(v0) = v2))) & ! [v0] : ( ~ (big_r(all_0_0_0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_p(v0) = v1)) & ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & g(v2) = v3 & big_r(v0, v3) = 0 & big_p(v1) = 0)) & ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ? [v2] : (h(v0) = v2 & g(v0) = v1 & big_p(v2) = 0 & big_p(v1) = 0)) & ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_r(all_0_0_0, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : big_r(v1, v0) = v2 & ? [v0] : ? [v1] : h(v0) = v1 & ? [v0] : ? [v1] : g(v0) = v1 & ? [v0] : ? [v1] : big_p(v0) = v1
% 28.57/8.78 |
% 28.57/8.78 | Applying alpha-rule on (1) yields:
% 28.57/8.78 | (2) ! [v0] : ! [v1] : ( ~ (h(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & g(v0) = v2 & big_p(v2) = 0 & big_p(v1) = 0) | ( ~ (v2 = 0) & big_p(v0) = v2)))
% 28.57/8.78 | (3) ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_r(all_0_0_0, v0) = v1))
% 28.57/8.78 | (4) ! [v0] : ( ~ (big_r(all_0_0_0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_p(v0) = v1))
% 28.57/8.79 | (5) ? [v0] : ? [v1] : g(v0) = v1
% 28.57/8.79 | (6) ? [v0] : ? [v1] : ? [v2] : big_r(v1, v0) = v2
% 28.57/8.79 | (7) ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & h(v0) = v3 & big_p(v3) = 0 & big_p(v1) = 0) | ( ~ (v2 = 0) & big_p(v0) = v2)))
% 28.57/8.79 | (8) ? [v0] : ? [v1] : h(v0) = v1
% 28.57/8.79 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 28.57/8.79 | (10) ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & g(v2) = v3 & big_r(v0, v3) = 0 & big_p(v1) = 0))
% 28.57/8.79 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0))
% 28.57/8.79 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0))
% 28.57/8.79 | (13) ! [v0] : ( ~ (big_p(v0) = 0) | ? [v1] : ? [v2] : (h(v0) = v2 & g(v0) = v1 & big_p(v2) = 0 & big_p(v1) = 0))
% 28.57/8.79 | (14) ? [v0] : ? [v1] : big_p(v0) = v1
% 28.57/8.79 | (15) big_p(all_0_0_0) = 0
% 28.57/8.79 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 28.57/8.79 |
% 28.57/8.79 | Instantiating formula (10) with all_0_0_0 and discharging atoms big_p(all_0_0_0) = 0, yields:
% 28.57/8.79 | (17) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & g(v1) = v2 & big_r(all_0_0_0, v2) = 0 & big_p(v0) = 0)
% 28.57/8.79 |
% 28.57/8.79 | Instantiating (17) with all_20_0_13, all_20_1_14, all_20_2_15 yields:
% 28.57/8.79 | (18) h(all_20_2_15) = all_20_1_14 & g(all_20_1_14) = all_20_0_13 & big_r(all_0_0_0, all_20_0_13) = 0 & big_p(all_20_2_15) = 0
% 28.57/8.79 |
% 28.57/8.79 | Applying alpha-rule on (18) yields:
% 28.57/8.79 | (19) h(all_20_2_15) = all_20_1_14
% 28.57/8.79 | (20) g(all_20_1_14) = all_20_0_13
% 28.57/8.79 | (21) big_r(all_0_0_0, all_20_0_13) = 0
% 28.57/8.79 | (22) big_p(all_20_2_15) = 0
% 28.57/8.79 |
% 28.57/8.79 | Instantiating formula (2) with all_20_1_14, all_20_2_15 and discharging atoms h(all_20_2_15) = all_20_1_14, yields:
% 28.57/8.79 | (23) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & g(all_20_2_15) = v0 & big_p(v0) = 0 & big_p(all_20_1_14) = 0) | ( ~ (v0 = 0) & big_p(all_20_2_15) = v0))
% 28.57/8.79 |
% 28.57/8.79 | Instantiating formula (7) with all_20_0_13, all_20_1_14 and discharging atoms g(all_20_1_14) = all_20_0_13, yields:
% 28.57/8.79 | (24) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & h(all_20_1_14) = v1 & big_p(v1) = 0 & big_p(all_20_0_13) = 0) | ( ~ (v0 = 0) & big_p(all_20_1_14) = v0))
% 28.57/8.79 |
% 28.57/8.79 | Instantiating formula (4) with all_20_0_13 and discharging atoms big_r(all_0_0_0, all_20_0_13) = 0, yields:
% 28.57/8.79 | (25) ? [v0] : ( ~ (v0 = 0) & big_p(all_20_0_13) = v0)
% 28.57/8.79 |
% 28.57/8.79 | Instantiating (25) with all_45_0_34 yields:
% 28.57/8.79 | (26) ~ (all_45_0_34 = 0) & big_p(all_20_0_13) = all_45_0_34
% 28.57/8.79 |
% 28.57/8.79 | Applying alpha-rule on (26) yields:
% 28.57/8.79 | (27) ~ (all_45_0_34 = 0)
% 28.57/8.79 | (28) big_p(all_20_0_13) = all_45_0_34
% 28.57/8.79 |
% 28.57/8.79 | Instantiating (24) with all_47_0_35, all_47_1_36, all_47_2_37 yields:
% 28.57/8.79 | (29) (all_47_0_35 = 0 & all_47_2_37 = 0 & h(all_20_1_14) = all_47_1_36 & big_p(all_47_1_36) = 0 & big_p(all_20_0_13) = 0) | ( ~ (all_47_2_37 = 0) & big_p(all_20_1_14) = all_47_2_37)
% 28.57/8.79 |
% 28.57/8.79 | Instantiating (23) with all_48_0_38, all_48_1_39, all_48_2_40 yields:
% 28.57/8.79 | (30) (all_48_0_38 = 0 & all_48_1_39 = 0 & g(all_20_2_15) = all_48_2_40 & big_p(all_48_2_40) = 0 & big_p(all_20_1_14) = 0) | ( ~ (all_48_2_40 = 0) & big_p(all_20_2_15) = all_48_2_40)
% 28.57/8.79 |
% 28.57/8.79 +-Applying beta-rule and splitting (29), into two cases.
% 28.57/8.79 |-Branch one:
% 28.57/8.79 | (31) all_47_0_35 = 0 & all_47_2_37 = 0 & h(all_20_1_14) = all_47_1_36 & big_p(all_47_1_36) = 0 & big_p(all_20_0_13) = 0
% 28.57/8.79 |
% 28.57/8.79 | Applying alpha-rule on (31) yields:
% 28.57/8.79 | (32) all_47_0_35 = 0
% 28.57/8.79 | (33) all_47_2_37 = 0
% 28.57/8.79 | (34) h(all_20_1_14) = all_47_1_36
% 28.57/8.79 | (35) big_p(all_20_0_13) = 0
% 28.57/8.79 | (36) big_p(all_47_1_36) = 0
% 28.57/8.79 |
% 28.57/8.79 | Instantiating formula (16) with all_20_0_13, 0, all_45_0_34 and discharging atoms big_p(all_20_0_13) = all_45_0_34, big_p(all_20_0_13) = 0, yields:
% 28.57/8.80 | (37) all_45_0_34 = 0
% 28.57/8.80 |
% 28.57/8.80 | Equations (37) can reduce 27 to:
% 28.57/8.80 | (38) $false
% 28.57/8.80 |
% 28.57/8.80 |-The branch is then unsatisfiable
% 28.57/8.80 |-Branch two:
% 28.57/8.80 | (39) ~ (all_47_2_37 = 0) & big_p(all_20_1_14) = all_47_2_37
% 28.57/8.80 |
% 28.57/8.80 | Applying alpha-rule on (39) yields:
% 28.57/8.80 | (40) ~ (all_47_2_37 = 0)
% 28.57/8.80 | (41) big_p(all_20_1_14) = all_47_2_37
% 28.57/8.80 |
% 28.57/8.80 +-Applying beta-rule and splitting (30), into two cases.
% 28.57/8.80 |-Branch one:
% 28.57/8.80 | (42) all_48_0_38 = 0 & all_48_1_39 = 0 & g(all_20_2_15) = all_48_2_40 & big_p(all_48_2_40) = 0 & big_p(all_20_1_14) = 0
% 28.57/8.80 |
% 28.57/8.80 | Applying alpha-rule on (42) yields:
% 28.57/8.80 | (43) all_48_1_39 = 0
% 28.57/8.80 | (44) all_48_0_38 = 0
% 28.57/8.80 | (45) big_p(all_20_1_14) = 0
% 28.57/8.80 | (46) g(all_20_2_15) = all_48_2_40
% 28.57/8.80 | (47) big_p(all_48_2_40) = 0
% 28.57/8.80 |
% 28.57/8.80 | Instantiating formula (16) with all_20_1_14, 0, all_47_2_37 and discharging atoms big_p(all_20_1_14) = all_47_2_37, big_p(all_20_1_14) = 0, yields:
% 28.57/8.80 | (33) all_47_2_37 = 0
% 28.57/8.80 |
% 28.57/8.80 | Equations (33) can reduce 40 to:
% 28.57/8.80 | (38) $false
% 28.57/8.80 |
% 28.57/8.80 |-The branch is then unsatisfiable
% 28.57/8.80 |-Branch two:
% 28.57/8.80 | (50) ~ (all_48_2_40 = 0) & big_p(all_20_2_15) = all_48_2_40
% 28.57/8.80 |
% 28.57/8.80 | Applying alpha-rule on (50) yields:
% 28.57/8.80 | (51) ~ (all_48_2_40 = 0)
% 28.57/8.80 | (52) big_p(all_20_2_15) = all_48_2_40
% 28.57/8.80 |
% 28.57/8.80 | Instantiating formula (16) with all_20_2_15, all_48_2_40, 0 and discharging atoms big_p(all_20_2_15) = all_48_2_40, big_p(all_20_2_15) = 0, yields:
% 28.57/8.80 | (53) all_48_2_40 = 0
% 28.57/8.80 |
% 28.57/8.80 | Equations (53) can reduce 51 to:
% 28.57/8.80 | (38) $false
% 28.57/8.80 |
% 28.57/8.80 |-The branch is then unsatisfiable
% 28.57/8.80 % SZS output end Proof for theBenchmark
% 28.57/8.80
% 28.57/8.80 8212ms
%------------------------------------------------------------------------------