TSTP Solution File: ALG202+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% 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 14 15:37:30 EDT 2022
% Result : Theorem 2.46s 1.26s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % 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 : Wed Jun 8 10:59:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.59/0.57 ____ _
% 0.59/0.57 ___ / __ \_____(_)___ ________ __________
% 0.59/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.57
% 0.59/0.57 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.93 Prover 0: Preprocessing ...
% 1.89/1.10 Prover 0: Constructing countermodel ...
% 2.46/1.26 Prover 0: proved (634ms)
% 2.46/1.26
% 2.46/1.26 No countermodel exists, formula is valid
% 2.46/1.26 % SZS status Theorem for theBenchmark
% 2.46/1.26
% 2.46/1.26 Generating proof ... found it (size 45)
% 3.44/1.57
% 3.44/1.57 % SZS output start Proof for theBenchmark
% 3.44/1.57 Assumed formulas after preprocessing and simplification:
% 3.44/1.57 | (0) ? [v0] : ? [v1] : ( ~ (v1 = v0) & op2(v0, v0) = v1 & sorti2(v0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (op2(v5, v4) = v3) | ~ (op2(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (op1(v5, v4) = v3) | ~ (op1(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (j(v4) = v3) | ~ (j(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (h(v4) = v3) | ~ (h(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (op2(v2, v3) = v4) | ~ sorti2(v3) | ~ sorti2(v2) | sorti2(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (op1(v2, v3) = v4) | ~ sorti1(v3) | ~ sorti1(v2) | sorti1(v4)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (op1(v2, v2) = v3) | ~ sorti1(v2)) & ! [v2] : ( ~ sorti2(v2) | ? [v3] : (j(v2) = v3 & h(v3) = v2)) & ! [v2] : ( ~ sorti2(v2) | ? [v3] : (j(v2) = v3 & sorti1(v3))) & ! [v2] : ( ~ sorti2(v2) | ? [v3] : (j(v2) = v3 & ! [v4] : ( ~ sorti2(v4) | ? [v5] : ? [v6] : ? [v7] : (j(v5) = v6 & j(v4) = v7 & op2(v2, v4) = v5 & op1(v3, v7) = v6)))) & ! [v2] : ( ~ sorti1(v2) | ? [v3] : (j(v3) = v2 & h(v2) = v3)) & ! [v2] : ( ~ sorti1(v2) | ? [v3] : (h(v2) = v3 & sorti2(v3))) & ! [v2] : ( ~ sorti1(v2) | ? [v3] : (h(v2) = v3 & ! [v4] : ( ~ sorti1(v4) | ? [v5] : ? [v6] : ? [v7] : (h(v5) = v6 & h(v4) = v7 & op2(v3, v7) = v6 & op1(v2, v4) = v5)))))
% 3.44/1.60 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.44/1.60 | (1) ~ (all_0_0_0 = all_0_1_1) & op2(all_0_1_1, all_0_1_1) = all_0_0_0 & sorti2(all_0_1_1) & ! [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] : ! [v1] : (v1 = v0 | ~ (op1(v0, v0) = v1) | ~ 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))))
% 3.44/1.61 |
% 3.44/1.61 | Applying alpha-rule on (1) yields:
% 3.44/1.61 | (2) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (h(v0) = v1 & sorti2(v1)))
% 3.44/1.61 | (3) sorti2(all_0_1_1)
% 3.44/1.61 | (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))))
% 3.44/1.61 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 3.44/1.61 | (6) ! [v0] : ( ~ sorti1(v0) | ? [v1] : (j(v1) = v0 & h(v0) = v1))
% 3.44/1.61 | (7) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & h(v1) = v0))
% 3.44/1.61 | (8) op2(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.44/1.61 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 3.44/1.61 | (10) ~ (all_0_0_0 = all_0_1_1)
% 3.44/1.61 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 3.44/1.61 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (op2(v0, v1) = v2) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2))
% 3.44/1.61 | (13) ! [v0] : ( ~ sorti2(v0) | ? [v1] : (j(v0) = v1 & sorti1(v1)))
% 3.44/1.61 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (op1(v0, v1) = v2) | ~ sorti1(v1) | ~ sorti1(v0) | sorti1(v2))
% 3.44/1.61 | (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))))
% 3.44/1.61 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (op1(v0, v0) = v1) | ~ sorti1(v0))
% 3.44/1.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 3.44/1.61 |
% 3.44/1.61 | Instantiating formula (7) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 3.44/1.61 | (18) ? [v0] : (j(all_0_1_1) = v0 & h(v0) = all_0_1_1)
% 3.44/1.61 |
% 3.44/1.61 | Instantiating formula (13) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 3.44/1.61 | (19) ? [v0] : (j(all_0_1_1) = v0 & sorti1(v0))
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (4) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 3.44/1.62 | (20) ? [v0] : (j(all_0_1_1) = v0 & ! [v1] : ( ~ sorti2(v1) | ? [v2] : ? [v3] : ? [v4] : (j(v2) = v3 & j(v1) = v4 & op2(all_0_1_1, v1) = v2 & op1(v0, v4) = v3)))
% 3.44/1.62 |
% 3.44/1.62 | Instantiating (20) with all_9_0_2 yields:
% 3.44/1.62 | (21) j(all_0_1_1) = all_9_0_2 & ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_1_1, v0) = v1 & op1(all_9_0_2, v3) = v2))
% 3.44/1.62 |
% 3.44/1.62 | Applying alpha-rule on (21) yields:
% 3.44/1.62 | (22) j(all_0_1_1) = all_9_0_2
% 3.44/1.62 | (23) ! [v0] : ( ~ sorti2(v0) | ? [v1] : ? [v2] : ? [v3] : (j(v1) = v2 & j(v0) = v3 & op2(all_0_1_1, v0) = v1 & op1(all_9_0_2, v3) = v2))
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (23) with all_0_1_1 and discharging atoms sorti2(all_0_1_1), yields:
% 3.44/1.62 | (24) ? [v0] : ? [v1] : ? [v2] : (j(v0) = v1 & j(all_0_1_1) = v2 & op2(all_0_1_1, all_0_1_1) = v0 & op1(all_9_0_2, v2) = v1)
% 3.44/1.62 |
% 3.44/1.62 | Instantiating (19) with all_12_0_3 yields:
% 3.44/1.62 | (25) j(all_0_1_1) = all_12_0_3 & sorti1(all_12_0_3)
% 3.44/1.62 |
% 3.44/1.62 | Applying alpha-rule on (25) yields:
% 3.44/1.62 | (26) j(all_0_1_1) = all_12_0_3
% 3.44/1.62 | (27) sorti1(all_12_0_3)
% 3.44/1.62 |
% 3.44/1.62 | Instantiating (18) with all_14_0_4 yields:
% 3.44/1.62 | (28) j(all_0_1_1) = all_14_0_4 & h(all_14_0_4) = all_0_1_1
% 3.44/1.62 |
% 3.44/1.62 | Applying alpha-rule on (28) yields:
% 3.44/1.62 | (29) j(all_0_1_1) = all_14_0_4
% 3.44/1.62 | (30) h(all_14_0_4) = all_0_1_1
% 3.44/1.62 |
% 3.44/1.62 | Instantiating (24) with all_16_0_5, all_16_1_6, all_16_2_7 yields:
% 3.44/1.62 | (31) j(all_16_2_7) = all_16_1_6 & j(all_0_1_1) = all_16_0_5 & op2(all_0_1_1, all_0_1_1) = all_16_2_7 & op1(all_9_0_2, all_16_0_5) = all_16_1_6
% 3.44/1.62 |
% 3.44/1.62 | Applying alpha-rule on (31) yields:
% 3.44/1.62 | (32) j(all_16_2_7) = all_16_1_6
% 3.44/1.62 | (33) j(all_0_1_1) = all_16_0_5
% 3.44/1.62 | (34) op2(all_0_1_1, all_0_1_1) = all_16_2_7
% 3.44/1.62 | (35) op1(all_9_0_2, all_16_0_5) = all_16_1_6
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (9) with all_0_1_1, all_14_0_4, all_16_0_5 and discharging atoms j(all_0_1_1) = all_16_0_5, j(all_0_1_1) = all_14_0_4, yields:
% 3.44/1.62 | (36) all_16_0_5 = all_14_0_4
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (9) with all_0_1_1, all_12_0_3, all_16_0_5 and discharging atoms j(all_0_1_1) = all_16_0_5, j(all_0_1_1) = all_12_0_3, yields:
% 3.44/1.62 | (37) all_16_0_5 = all_12_0_3
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (9) with all_0_1_1, all_9_0_2, all_14_0_4 and discharging atoms j(all_0_1_1) = all_14_0_4, j(all_0_1_1) = all_9_0_2, yields:
% 3.44/1.62 | (38) all_14_0_4 = all_9_0_2
% 3.44/1.62 |
% 3.44/1.62 | Instantiating formula (17) with all_0_1_1, all_0_1_1, all_16_2_7, all_0_0_0 and discharging atoms op2(all_0_1_1, all_0_1_1) = all_16_2_7, op2(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.44/1.62 | (39) all_16_2_7 = all_0_0_0
% 3.44/1.62 |
% 3.44/1.62 | Combining equations (36,37) yields a new equation:
% 3.44/1.62 | (40) all_14_0_4 = all_12_0_3
% 3.44/1.62 |
% 3.44/1.62 | Simplifying 40 yields:
% 3.44/1.62 | (41) all_14_0_4 = all_12_0_3
% 3.44/1.62 |
% 3.44/1.62 | Combining equations (38,41) yields a new equation:
% 3.44/1.62 | (42) all_12_0_3 = all_9_0_2
% 3.44/1.62 |
% 3.44/1.62 | Combining equations (42,41) yields a new equation:
% 3.44/1.62 | (38) all_14_0_4 = all_9_0_2
% 3.44/1.62 |
% 3.44/1.62 | From (38) and (30) follows:
% 3.44/1.62 | (44) h(all_9_0_2) = all_0_1_1
% 3.44/1.62 |
% 3.44/1.62 | From (39) and (34) follows:
% 3.44/1.62 | (8) op2(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.44/1.62 |
% 3.44/1.62 | From (42) and (27) follows:
% 3.44/1.62 | (46) sorti1(all_9_0_2)
% 3.44/1.63 |
% 3.44/1.63 | Instantiating formula (15) with all_9_0_2 and discharging atoms sorti1(all_9_0_2), yields:
% 3.44/1.63 | (47) ? [v0] : (h(all_9_0_2) = v0 & ! [v1] : ( ~ sorti1(v1) | ? [v2] : ? [v3] : ? [v4] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_9_0_2, v1) = v2)))
% 3.44/1.63 |
% 3.44/1.63 | Instantiating (47) with all_31_0_8 yields:
% 3.44/1.63 | (48) h(all_9_0_2) = all_31_0_8 & ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_31_0_8, v3) = v2 & op1(all_9_0_2, v0) = v1))
% 3.44/1.63 |
% 3.44/1.63 | Applying alpha-rule on (48) yields:
% 3.44/1.63 | (49) h(all_9_0_2) = all_31_0_8
% 3.44/1.63 | (50) ! [v0] : ( ~ sorti1(v0) | ? [v1] : ? [v2] : ? [v3] : (h(v1) = v2 & h(v0) = v3 & op2(all_31_0_8, v3) = v2 & op1(all_9_0_2, v0) = v1))
% 3.44/1.63 |
% 3.44/1.63 | Instantiating formula (50) with all_9_0_2 and discharging atoms sorti1(all_9_0_2), yields:
% 3.44/1.63 | (51) ? [v0] : ? [v1] : ? [v2] : (h(v0) = v1 & h(all_9_0_2) = v2 & op2(all_31_0_8, v2) = v1 & op1(all_9_0_2, all_9_0_2) = v0)
% 3.44/1.63 |
% 3.44/1.63 | Instantiating (51) with all_41_0_14, all_41_1_15, all_41_2_16 yields:
% 3.44/1.63 | (52) h(all_41_2_16) = all_41_1_15 & h(all_9_0_2) = all_41_0_14 & op2(all_31_0_8, all_41_0_14) = all_41_1_15 & op1(all_9_0_2, all_9_0_2) = all_41_2_16
% 3.44/1.63 |
% 3.44/1.63 | Applying alpha-rule on (52) yields:
% 3.44/1.63 | (53) h(all_41_2_16) = all_41_1_15
% 3.44/1.63 | (54) h(all_9_0_2) = all_41_0_14
% 3.44/1.63 | (55) op2(all_31_0_8, all_41_0_14) = all_41_1_15
% 3.44/1.63 | (56) op1(all_9_0_2, all_9_0_2) = all_41_2_16
% 3.44/1.63 |
% 3.44/1.63 | Instantiating formula (11) with all_9_0_2, all_41_0_14, all_0_1_1 and discharging atoms h(all_9_0_2) = all_41_0_14, h(all_9_0_2) = all_0_1_1, yields:
% 3.44/1.63 | (57) all_41_0_14 = all_0_1_1
% 3.44/1.63 |
% 3.44/1.63 | Instantiating formula (11) with all_9_0_2, all_31_0_8, all_41_0_14 and discharging atoms h(all_9_0_2) = all_41_0_14, h(all_9_0_2) = all_31_0_8, yields:
% 3.74/1.63 | (58) all_41_0_14 = all_31_0_8
% 3.74/1.63 |
% 3.74/1.63 | Instantiating formula (16) with all_41_2_16, all_9_0_2 and discharging atoms op1(all_9_0_2, all_9_0_2) = all_41_2_16, sorti1(all_9_0_2), yields:
% 3.74/1.63 | (59) all_41_2_16 = all_9_0_2
% 3.74/1.63 |
% 3.74/1.63 | Combining equations (57,58) yields a new equation:
% 3.74/1.63 | (60) all_31_0_8 = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | Combining equations (60,58) yields a new equation:
% 3.74/1.63 | (57) all_41_0_14 = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | From (59) and (53) follows:
% 3.74/1.63 | (62) h(all_9_0_2) = all_41_1_15
% 3.74/1.63 |
% 3.74/1.63 | From (60) and (49) follows:
% 3.74/1.63 | (44) h(all_9_0_2) = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | From (60)(57) and (55) follows:
% 3.74/1.63 | (64) op2(all_0_1_1, all_0_1_1) = all_41_1_15
% 3.74/1.63 |
% 3.74/1.63 | Instantiating formula (11) with all_9_0_2, all_41_1_15, all_0_1_1 and discharging atoms h(all_9_0_2) = all_41_1_15, h(all_9_0_2) = all_0_1_1, yields:
% 3.74/1.63 | (65) all_41_1_15 = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | Instantiating formula (17) with all_0_1_1, all_0_1_1, all_41_1_15, all_0_0_0 and discharging atoms op2(all_0_1_1, all_0_1_1) = all_41_1_15, op2(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.74/1.63 | (66) all_41_1_15 = all_0_0_0
% 3.74/1.63 |
% 3.74/1.63 | Combining equations (66,65) yields a new equation:
% 3.74/1.63 | (67) all_0_0_0 = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | Simplifying 67 yields:
% 3.74/1.63 | (68) all_0_0_0 = all_0_1_1
% 3.74/1.63 |
% 3.74/1.63 | Equations (68) can reduce 10 to:
% 3.74/1.63 | (69) $false
% 3.74/1.63 |
% 3.74/1.64 |-The branch is then unsatisfiable
% 3.74/1.64 % SZS output end Proof for theBenchmark
% 3.74/1.64
% 3.74/1.64 1049ms
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