TSTP Solution File: ALG201+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 14 15:37:30 EDT 2022
% Result : Theorem 1.79s 0.98s
% Output : Proof 2.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% 0.05/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 8 11:08:36 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.13/0.46 ____ _
% 0.13/0.46 ___ / __ \_____(_)___ ________ __________
% 0.13/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.46
% 0.13/0.46 A Theorem Prover for First-Order Logic
% 0.13/0.46 (ePrincess v.1.0)
% 0.13/0.46
% 0.13/0.46 (c) Philipp Rümmer, 2009-2015
% 0.13/0.46 (c) Peter Backeman, 2014-2015
% 0.13/0.46 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.46 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.46 Bug reports to peter@backeman.se
% 0.13/0.46
% 0.13/0.46 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.46
% 0.13/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 0.99/0.73 Prover 0: Preprocessing ...
% 1.43/0.88 Prover 0: Constructing countermodel ...
% 1.79/0.97 Prover 0: proved (465ms)
% 1.79/0.98
% 1.79/0.98 No countermodel exists, formula is valid
% 1.79/0.98 % SZS status Theorem for theBenchmark
% 1.79/0.98
% 1.79/0.98 Generating proof ... found it (size 30)
% 2.33/1.15
% 2.33/1.15 % SZS output start Proof for theBenchmark
% 2.33/1.15 Assumed formulas after preprocessing and simplification:
% 2.33/1.15 | (0) ? [v0] : (op2(v0, v0) = v0 & sorti2(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op2(v4, v3) = v2) | ~ (op2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (op1(v4, v3) = v2) | ~ (op1(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (j(v3) = v2) | ~ (j(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (h(v3) = v2) | ~ (h(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op2(v1, v2) = v3) | ~ sorti2(v2) | ~ sorti2(v1) | sorti2(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (op1(v1, v2) = v3) | ~ sorti1(v2) | ~ sorti1(v1) | sorti1(v3)) & ! [v1] : ( ~ (op1(v1, v1) = v1) | ~ sorti1(v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & h(v2) = v1)) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & sorti1(v2))) & ! [v1] : ( ~ sorti2(v1) | ? [v2] : (j(v1) = v2 & ! [v3] : ( ~ sorti2(v3) | ? [v4] : ? [v5] : ? [v6] : (j(v4) = v5 & j(v3) = v6 & op2(v1, v3) = v4 & op1(v2, v6) = v5)))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (j(v2) = v1 & h(v1) = v2)) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & sorti2(v2))) & ! [v1] : ( ~ sorti1(v1) | ? [v2] : (h(v1) = v2 & ! [v3] : ( ~ sorti1(v3) | ? [v4] : ? [v5] : ? [v6] : (h(v4) = v5 & h(v3) = v6 & op2(v2, v6) = v5 & op1(v1, v3) = v4)))))
% 2.38/1.19 | Instantiating (0) with all_0_0_0 yields:
% 2.38/1.19 | (1) op2(all_0_0_0, all_0_0_0) = all_0_0_0 & sorti2(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2)) & ! [v0] : ( ~ (op1(v0, v0) = v0) | ~ sorti1(v0)) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0)) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1))) & ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & ! [v2] : ( ~ sorti2(v2) | ? [v3] : ? [v4] : ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4)))) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1)) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1))) & ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & ! [v2] : ( ~ sorti1(v2) | ? [v3] : ? [v4] : ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3))))
% 2.38/1.19 |
% 2.38/1.19 | Applying alpha-rule on (1) yields:
% 2.38/1.19 | (2) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1)))
% 2.38/1.19 | (3) sorti2(all_0_0_0)
% 2.38/1.19 | (4) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & ! [v2] : ( ~ sorti2(v2) | ? [v3] : ? [v4] : ? [v5] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4))))
% 2.38/1.19 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 2.38/1.19 | (6) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1))
% 2.38/1.20 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0))
% 2.38/1.20 | (8) ! [v0] : ( ~ (op1(v0, v0) = v0) | ~ sorti1(v0))
% 2.38/1.20 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 2.38/1.20 | (10) op2(all_0_0_0, all_0_0_0) = all_0_0_0
% 2.38/1.20 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 2.38/1.20 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2))
% 2.38/1.20 | (13) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1)))
% 2.38/1.20 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2))
% 2.38/1.20 | (15) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & ! [v2] : ( ~ sorti1(v2) | ? [v3] : ? [v4] : ? [v5] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3))))
% 2.38/1.20 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 2.38/1.20 |
% 2.38/1.20 | Instantiating formula (7) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 2.38/1.20 | (17) ? [v0] : (j(all_0_0_0) = v0 & h(v0) = all_0_0_0)
% 2.38/1.20 |
% 2.38/1.20 | Instantiating formula (13) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 2.38/1.20 | (18) ? [v0] : (j(all_0_0_0) = v0 & sorti1(v0))
% 2.38/1.20 |
% 2.38/1.20 | Instantiating formula (4) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 2.38/1.20 | (19) ? [v0] : (j(all_0_0_0) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_0_0, v1) = v2 & op1(v0, v4) = v3)))
% 2.38/1.20 |
% 2.38/1.20 | Instantiating (19) with all_8_0_1 yields:
% 2.38/1.20 | (20) j(all_0_0_0) = all_8_0_1 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_8_0_1, v3) = v2))
% 2.38/1.20 |
% 2.38/1.20 | Applying alpha-rule on (20) yields:
% 2.38/1.20 | (21) j(all_0_0_0) = all_8_0_1
% 2.38/1.20 | (22) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_0_0, v0) = v1 & op1(all_8_0_1, v3) = v2))
% 2.38/1.20 |
% 2.38/1.20 | Instantiating formula (22) with all_0_0_0 and discharging atoms sorti2(all_0_0_0), yields:
% 2.38/1.20 | (23) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_0_0_0) = v2 & op2(all_0_0_0, all_0_0_0) = v0 & op1(all_8_0_1, v2) = v1)
% 2.38/1.20 |
% 2.38/1.20 | Instantiating (18) with all_11_0_2 yields:
% 2.38/1.20 | (24) j(all_0_0_0) = all_11_0_2 & sorti1(all_11_0_2)
% 2.38/1.20 |
% 2.38/1.20 | Applying alpha-rule on (24) yields:
% 2.38/1.20 | (25) j(all_0_0_0) = all_11_0_2
% 2.38/1.20 | (26) sorti1(all_11_0_2)
% 2.38/1.20 |
% 2.38/1.20 | Instantiating (17) with all_13_0_3 yields:
% 2.38/1.20 | (27) j(all_0_0_0) = all_13_0_3 & h(all_13_0_3) = all_0_0_0
% 2.38/1.20 |
% 2.38/1.20 | Applying alpha-rule on (27) yields:
% 2.38/1.20 | (28) j(all_0_0_0) = all_13_0_3
% 2.38/1.20 | (29) h(all_13_0_3) = all_0_0_0
% 2.38/1.20 |
% 2.38/1.20 | Instantiating (23) with all_15_0_4, all_15_1_5, all_15_2_6 yields:
% 2.38/1.20 | (30) j(all_15_2_6) = all_15_1_5 & j(all_0_0_0) = all_15_0_4 & op2(all_0_0_0, all_0_0_0) = all_15_2_6 & op1(all_8_0_1, all_15_0_4) = all_15_1_5
% 2.38/1.20 |
% 2.38/1.20 | Applying alpha-rule on (30) yields:
% 2.38/1.20 | (31) j(all_15_2_6) = all_15_1_5
% 2.38/1.20 | (32) j(all_0_0_0) = all_15_0_4
% 2.38/1.20 | (33) op2(all_0_0_0, all_0_0_0) = all_15_2_6
% 2.38/1.20 | (34) op1(all_8_0_1, all_15_0_4) = all_15_1_5
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (9) with all_0_0_0, all_13_0_3, all_15_0_4 and discharging atoms j(all_0_0_0) = all_15_0_4, j(all_0_0_0) = all_13_0_3, yields:
% 2.38/1.21 | (35) all_15_0_4 = all_13_0_3
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (9) with all_0_0_0, all_11_0_2, all_15_0_4 and discharging atoms j(all_0_0_0) = all_15_0_4, j(all_0_0_0) = all_11_0_2, yields:
% 2.38/1.21 | (36) all_15_0_4 = all_11_0_2
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (9) with all_0_0_0, all_8_0_1, all_13_0_3 and discharging atoms j(all_0_0_0) = all_13_0_3, j(all_0_0_0) = all_8_0_1, yields:
% 2.38/1.21 | (37) all_13_0_3 = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (16) with all_0_0_0, all_0_0_0, all_15_2_6, all_0_0_0 and discharging atoms op2(all_0_0_0, all_0_0_0) = all_15_2_6, op2(all_0_0_0, all_0_0_0) = all_0_0_0, yields:
% 2.38/1.21 | (38) all_15_2_6 = all_0_0_0
% 2.38/1.21 |
% 2.38/1.21 | Combining equations (35,36) yields a new equation:
% 2.38/1.21 | (39) all_13_0_3 = all_11_0_2
% 2.38/1.21 |
% 2.38/1.21 | Simplifying 39 yields:
% 2.38/1.21 | (40) all_13_0_3 = all_11_0_2
% 2.38/1.21 |
% 2.38/1.21 | Combining equations (37,40) yields a new equation:
% 2.38/1.21 | (41) all_11_0_2 = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | Combining equations (41,36) yields a new equation:
% 2.38/1.21 | (42) all_15_0_4 = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | From (38) and (31) follows:
% 2.38/1.21 | (43) j(all_0_0_0) = all_15_1_5
% 2.38/1.21 |
% 2.38/1.21 | From (41) and (25) follows:
% 2.38/1.21 | (21) j(all_0_0_0) = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | From (42) and (34) follows:
% 2.38/1.21 | (45) op1(all_8_0_1, all_8_0_1) = all_15_1_5
% 2.38/1.21 |
% 2.38/1.21 | From (41) and (26) follows:
% 2.38/1.21 | (46) sorti1(all_8_0_1)
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (9) with all_0_0_0, all_15_1_5, all_8_0_1 and discharging atoms j(all_0_0_0) = all_15_1_5, j(all_0_0_0) = all_8_0_1, yields:
% 2.38/1.21 | (47) all_15_1_5 = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | From (47) and (45) follows:
% 2.38/1.21 | (48) op1(all_8_0_1, all_8_0_1) = all_8_0_1
% 2.38/1.21 |
% 2.38/1.21 | Instantiating formula (8) with all_8_0_1 and discharging atoms op1(all_8_0_1, all_8_0_1) = all_8_0_1, sorti1(all_8_0_1), yields:
% 2.38/1.21 | (49) $false
% 2.38/1.21 |
% 2.38/1.21 |-The branch is then unsatisfiable
% 2.38/1.21 % SZS output end Proof for theBenchmark
% 2.38/1.21
% 2.38/1.21 738ms
%------------------------------------------------------------------------------