TSTP Solution File: GRP194+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 : Sat Jul 16 08:41:51 EDT 2022
% Result : Theorem 2.53s 1.20s
% Output : Proof 3.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n016.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 Jun 13 12:29:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.60/0.87 Prover 0: Preprocessing ...
% 2.01/1.04 Prover 0: Constructing countermodel ...
% 2.53/1.20 Prover 0: proved (577ms)
% 2.53/1.20
% 2.53/1.20 No countermodel exists, formula is valid
% 2.53/1.20 % SZS status Theorem for theBenchmark
% 2.53/1.20
% 2.53/1.20 Generating proof ... found it (size 18)
% 3.39/1.45
% 3.39/1.45 % SZS output start Proof for theBenchmark
% 3.39/1.45 Assumed formulas after preprocessing and simplification:
% 3.39/1.45 | (0) ? [v0] : (phi(f_left_zero) = v0 & left_zero(f, f_left_zero) & ~ left_zero(h, v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiply(v1, v5, v4) = v6) | ~ (multiply(v1, v2, v3) = v5) | ~ group_member(v4, v1) | ~ group_member(v3, v1) | ~ group_member(v2, v1) | ? [v7] : (multiply(v1, v3, v4) = v7 & multiply(v1, v2, v7) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiply(v1, v3, v4) = v5) | ~ (multiply(v1, v2, v5) = v6) | ~ group_member(v4, v1) | ~ group_member(v3, v1) | ~ group_member(v2, v1) | ? [v7] : (multiply(v1, v7, v4) = v6 & multiply(v1, v2, v3) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (multiply(v5, v4, v3) = v2) | ~ (multiply(v5, v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (phi(v2) = v4) | ~ (phi(v1) = v3) | ~ (multiply(h, v3, v4) = v5) | ~ group_member(v2, f) | ~ group_member(v1, f) | ? [v6] : (phi(v6) = v5 & multiply(f, v1, v2) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (multiply(v1, v2, v3) = v4) | ~ left_zero(v1, v2) | ~ group_member(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiply(v1, v2, v3) = v4) | ~ group_member(v3, v1) | ~ group_member(v2, v1) | group_member(v4, v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (phi(v3) = v2) | ~ (phi(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (multiply(f, v1, v2) = v3) | ~ group_member(v2, f) | ~ group_member(v1, f) | ? [v4] : ? [v5] : ? [v6] : (phi(v3) = v6 & phi(v2) = v5 & phi(v1) = v4 & multiply(h, v4, v5) = v6)) & ! [v1] : ! [v2] : ( ~ (phi(v1) = v2) | ~ group_member(v1, f) | group_member(v2, h)) & ! [v1] : ! [v2] : ( ~ left_zero(v1, v2) | group_member(v2, v1)) & ! [v1] : ! [v2] : ( ~ group_member(v2, v1) | left_zero(v1, v2) | ? [v3] : ? [v4] : ( ~ (v4 = v2) & multiply(v1, v2, v3) = v4 & group_member(v3, v1))) & ! [v1] : ( ~ group_member(v1, h) | ? [v2] : (phi(v2) = v1 & group_member(v2, f))))
% 3.46/1.48 | Instantiating (0) with all_0_0_0 yields:
% 3.46/1.48 | (1) phi(f_left_zero) = all_0_0_0 & left_zero(f, f_left_zero) & ~ left_zero(h, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiply(v0, v4, v3) = v5) | ~ (multiply(v0, v1, v2) = v4) | ~ group_member(v3, v0) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | ? [v6] : (multiply(v0, v2, v3) = v6 & multiply(v0, v1, v6) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiply(v0, v2, v3) = v4) | ~ (multiply(v0, v1, v4) = v5) | ~ group_member(v3, v0) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | ? [v6] : (multiply(v0, v6, v3) = v5 & multiply(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (multiply(v4, v3, v2) = v1) | ~ (multiply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (phi(v1) = v3) | ~ (phi(v0) = v2) | ~ (multiply(h, v2, v3) = v4) | ~ group_member(v1, f) | ~ group_member(v0, f) | ? [v5] : (phi(v5) = v4 & multiply(f, v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (multiply(v0, v1, v2) = v3) | ~ left_zero(v0, v1) | ~ group_member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (multiply(v0, v1, v2) = v3) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | group_member(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiply(f, v0, v1) = v2) | ~ group_member(v1, f) | ~ group_member(v0, f) | ? [v3] : ? [v4] : ? [v5] : (phi(v2) = v5 & phi(v1) = v4 & phi(v0) = v3 & multiply(h, v3, v4) = v5)) & ! [v0] : ! [v1] : ( ~ (phi(v0) = v1) | ~ group_member(v0, f) | group_member(v1, h)) & ! [v0] : ! [v1] : ( ~ left_zero(v0, v1) | group_member(v1, v0)) & ! [v0] : ! [v1] : ( ~ group_member(v1, v0) | left_zero(v0, v1) | ? [v2] : ? [v3] : ( ~ (v3 = v1) & multiply(v0, v1, v2) = v3 & group_member(v2, v0))) & ! [v0] : ( ~ group_member(v0, h) | ? [v1] : (phi(v1) = v0 & group_member(v1, f)))
% 3.46/1.49 |
% 3.46/1.49 | Applying alpha-rule on (1) yields:
% 3.46/1.49 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (multiply(v4, v3, v2) = v1) | ~ (multiply(v4, v3, v2) = v0))
% 3.46/1.49 | (3) ! [v0] : ! [v1] : ( ~ (phi(v0) = v1) | ~ group_member(v0, f) | group_member(v1, h))
% 3.46/1.49 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiply(f, v0, v1) = v2) | ~ group_member(v1, f) | ~ group_member(v0, f) | ? [v3] : ? [v4] : ? [v5] : (phi(v2) = v5 & phi(v1) = v4 & phi(v0) = v3 & multiply(h, v3, v4) = v5))
% 3.46/1.49 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiply(v0, v4, v3) = v5) | ~ (multiply(v0, v1, v2) = v4) | ~ group_member(v3, v0) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | ? [v6] : (multiply(v0, v2, v3) = v6 & multiply(v0, v1, v6) = v5))
% 3.46/1.49 | (6) ! [v0] : ! [v1] : ( ~ left_zero(v0, v1) | group_member(v1, v0))
% 3.46/1.49 | (7) left_zero(f, f_left_zero)
% 3.46/1.49 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (multiply(v0, v1, v2) = v3) | ~ left_zero(v0, v1) | ~ group_member(v2, v0))
% 3.46/1.49 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiply(v0, v2, v3) = v4) | ~ (multiply(v0, v1, v4) = v5) | ~ group_member(v3, v0) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | ? [v6] : (multiply(v0, v6, v3) = v5 & multiply(v0, v1, v2) = v6))
% 3.46/1.49 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0))
% 3.46/1.50 | (11) phi(f_left_zero) = all_0_0_0
% 3.46/1.50 | (12) ! [v0] : ( ~ group_member(v0, h) | ? [v1] : (phi(v1) = v0 & group_member(v1, f)))
% 3.46/1.50 | (13) ~ left_zero(h, all_0_0_0)
% 3.46/1.50 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (phi(v1) = v3) | ~ (phi(v0) = v2) | ~ (multiply(h, v2, v3) = v4) | ~ group_member(v1, f) | ~ group_member(v0, f) | ? [v5] : (phi(v5) = v4 & multiply(f, v0, v1) = v5))
% 3.46/1.50 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (multiply(v0, v1, v2) = v3) | ~ group_member(v2, v0) | ~ group_member(v1, v0) | group_member(v3, v0))
% 3.46/1.50 | (16) ! [v0] : ! [v1] : ( ~ group_member(v1, v0) | left_zero(v0, v1) | ? [v2] : ? [v3] : ( ~ (v3 = v1) & multiply(v0, v1, v2) = v3 & group_member(v2, v0)))
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (6) with f_left_zero, f and discharging atoms left_zero(f, f_left_zero), yields:
% 3.46/1.50 | (17) group_member(f_left_zero, f)
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (3) with all_0_0_0, f_left_zero and discharging atoms phi(f_left_zero) = all_0_0_0, group_member(f_left_zero, f), yields:
% 3.46/1.50 | (18) group_member(all_0_0_0, h)
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (16) with all_0_0_0, h and discharging atoms group_member(all_0_0_0, h), ~ left_zero(h, all_0_0_0), yields:
% 3.46/1.50 | (19) ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & multiply(h, all_0_0_0, v0) = v1 & group_member(v0, h))
% 3.46/1.50 |
% 3.46/1.50 | Instantiating (19) with all_20_0_1, all_20_1_2 yields:
% 3.46/1.50 | (20) ~ (all_20_0_1 = all_0_0_0) & multiply(h, all_0_0_0, all_20_1_2) = all_20_0_1 & group_member(all_20_1_2, h)
% 3.46/1.50 |
% 3.46/1.50 | Applying alpha-rule on (20) yields:
% 3.46/1.50 | (21) ~ (all_20_0_1 = all_0_0_0)
% 3.46/1.50 | (22) multiply(h, all_0_0_0, all_20_1_2) = all_20_0_1
% 3.46/1.50 | (23) group_member(all_20_1_2, h)
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (12) with all_20_1_2 and discharging atoms group_member(all_20_1_2, h), yields:
% 3.46/1.50 | (24) ? [v0] : (phi(v0) = all_20_1_2 & group_member(v0, f))
% 3.46/1.50 |
% 3.46/1.50 | Instantiating (24) with all_30_0_4 yields:
% 3.46/1.50 | (25) phi(all_30_0_4) = all_20_1_2 & group_member(all_30_0_4, f)
% 3.46/1.50 |
% 3.46/1.50 | Applying alpha-rule on (25) yields:
% 3.46/1.50 | (26) phi(all_30_0_4) = all_20_1_2
% 3.46/1.50 | (27) group_member(all_30_0_4, f)
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (14) with all_20_0_1, all_20_1_2, all_0_0_0, all_30_0_4, f_left_zero and discharging atoms phi(all_30_0_4) = all_20_1_2, phi(f_left_zero) = all_0_0_0, multiply(h, all_0_0_0, all_20_1_2) = all_20_0_1, group_member(all_30_0_4, f), group_member(f_left_zero, f), yields:
% 3.46/1.50 | (28) ? [v0] : (phi(v0) = all_20_0_1 & multiply(f, f_left_zero, all_30_0_4) = v0)
% 3.46/1.50 |
% 3.46/1.50 | Instantiating (28) with all_39_0_6 yields:
% 3.46/1.50 | (29) phi(all_39_0_6) = all_20_0_1 & multiply(f, f_left_zero, all_30_0_4) = all_39_0_6
% 3.46/1.50 |
% 3.46/1.50 | Applying alpha-rule on (29) yields:
% 3.46/1.50 | (30) phi(all_39_0_6) = all_20_0_1
% 3.46/1.50 | (31) multiply(f, f_left_zero, all_30_0_4) = all_39_0_6
% 3.46/1.50 |
% 3.46/1.50 | Instantiating formula (8) with all_39_0_6, all_30_0_4, f_left_zero, f and discharging atoms multiply(f, f_left_zero, all_30_0_4) = all_39_0_6, left_zero(f, f_left_zero), group_member(all_30_0_4, f), yields:
% 3.46/1.50 | (32) all_39_0_6 = f_left_zero
% 3.46/1.50 |
% 3.46/1.50 | From (32) and (30) follows:
% 3.46/1.51 | (33) phi(f_left_zero) = all_20_0_1
% 3.46/1.51 |
% 3.46/1.51 | Instantiating formula (10) with f_left_zero, all_20_0_1, all_0_0_0 and discharging atoms phi(f_left_zero) = all_20_0_1, phi(f_left_zero) = all_0_0_0, yields:
% 3.46/1.51 | (34) all_20_0_1 = all_0_0_0
% 3.46/1.51 |
% 3.46/1.51 | Equations (34) can reduce 21 to:
% 3.46/1.51 | (35) $false
% 3.46/1.51 |
% 3.46/1.51 |-The branch is then unsatisfiable
% 3.46/1.51 % SZS output end Proof for theBenchmark
% 3.46/1.51
% 3.46/1.51 920ms
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