TSTP Solution File: SET971+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 : Tue Jul 19 00:23:31 EDT 2022
% Result : Theorem 2.22s 1.25s
% Output : Proof 3.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 08:25:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.67/0.62 ____ _
% 0.67/0.62 ___ / __ \_____(_)___ ________ __________
% 0.67/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.62
% 0.67/0.62 A Theorem Prover for First-Order Logic
% 0.67/0.63 (ePrincess v.1.0)
% 0.67/0.63
% 0.67/0.63 (c) Philipp Rümmer, 2009-2015
% 0.67/0.63 (c) Peter Backeman, 2014-2015
% 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.63 Bug reports to peter@backeman.se
% 0.67/0.63
% 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.63
% 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.95 Prover 0: Preprocessing ...
% 1.59/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.72/1.10 Prover 0: Constructing countermodel ...
% 2.22/1.24 Prover 0: proved (560ms)
% 2.22/1.25
% 2.22/1.25 No countermodel exists, formula is valid
% 2.22/1.25 % SZS status Theorem for theBenchmark
% 2.22/1.25
% 2.22/1.25 Generating proof ... Warning: ignoring some quantifiers
% 2.63/1.46 found it (size 20)
% 2.63/1.46
% 2.63/1.46 % SZS output start Proof for theBenchmark
% 2.63/1.46 Assumed formulas after preprocessing and simplification:
% 2.63/1.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v7 = v6) & cartesian_product2(v1, v2) = v5 & cartesian_product2(v0, v3) = v4 & cartesian_product2(v0, v2) = v7 & set_intersection2(v4, v5) = v6 & subset(v2, v3) & subset(v0, v1) & empty(v9) & ~ empty(v8) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v15) = v16) | ~ (set_intersection2(v12, v13) = v15) | ~ (set_intersection2(v10, v11) = v14) | ? [v17] : ? [v18] : (cartesian_product2(v11, v13) = v18 & cartesian_product2(v10, v12) = v17 & set_intersection2(v17, v18) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v11, v13) = v15) | ~ (cartesian_product2(v10, v12) = v14) | ~ (set_intersection2(v14, v15) = v16) | ? [v17] : ? [v18] : (cartesian_product2(v17, v18) = v16 & set_intersection2(v12, v13) = v18 & set_intersection2(v10, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_intersection2(v10, v11) = v12) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ? [v10] : subset(v10, v10))
% 3.06/1.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 3.06/1.49 | (1) ~ (all_0_2_2 = all_0_3_3) & cartesian_product2(all_0_8_8, all_0_7_7) = all_0_4_4 & cartesian_product2(all_0_9_9, all_0_6_6) = all_0_5_5 & cartesian_product2(all_0_9_9, all_0_7_7) = all_0_2_2 & set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_6_6) & subset(all_0_9_9, all_0_8_8) & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v4, v5) = v6) | ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) = v4) | ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_intersection2(v7, v8) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ? [v7] : ? [v8] : (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 & set_intersection2(v0, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ? [v0] : subset(v0, v0)
% 3.06/1.50 |
% 3.06/1.50 | Applying alpha-rule on (1) yields:
% 3.06/1.50 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 3.06/1.50 | (3) cartesian_product2(all_0_9_9, all_0_7_7) = all_0_2_2
% 3.06/1.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 3.06/1.50 | (5) subset(all_0_7_7, all_0_6_6)
% 3.06/1.50 | (6) cartesian_product2(all_0_9_9, all_0_6_6) = all_0_5_5
% 3.06/1.50 | (7) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_4_4
% 3.06/1.50 | (8) subset(all_0_9_9, all_0_8_8)
% 3.06/1.50 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 3.06/1.50 | (10) set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3
% 3.06/1.50 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ? [v7] : ? [v8] : (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 & set_intersection2(v0, v1) = v7))
% 3.06/1.50 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 3.06/1.50 | (13) empty(all_0_0_0)
% 3.06/1.50 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 3.06/1.50 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 3.06/1.51 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v4, v5) = v6) | ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) = v4) | ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_intersection2(v7, v8) = v6))
% 3.06/1.51 | (17) ~ empty(all_0_1_1)
% 3.06/1.51 | (18) ~ (all_0_2_2 = all_0_3_3)
% 3.06/1.51 | (19) ? [v0] : subset(v0, v0)
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (11) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_8_8, all_0_7_7) = all_0_4_4, cartesian_product2(all_0_9_9, all_0_6_6) = all_0_5_5, set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 3.06/1.51 | (20) ? [v0] : ? [v1] : (cartesian_product2(v0, v1) = all_0_3_3 & set_intersection2(all_0_6_6, all_0_7_7) = v1 & set_intersection2(all_0_9_9, all_0_8_8) = v0)
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (15) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 3.06/1.51 | (21) set_intersection2(all_0_4_4, all_0_5_5) = all_0_3_3
% 3.06/1.51 |
% 3.06/1.51 | Instantiating (20) with all_11_0_11, all_11_1_12 yields:
% 3.06/1.51 | (22) cartesian_product2(all_11_1_12, all_11_0_11) = all_0_3_3 & set_intersection2(all_0_6_6, all_0_7_7) = all_11_0_11 & set_intersection2(all_0_9_9, all_0_8_8) = all_11_1_12
% 3.06/1.51 |
% 3.06/1.51 | Applying alpha-rule on (22) yields:
% 3.06/1.51 | (23) cartesian_product2(all_11_1_12, all_11_0_11) = all_0_3_3
% 3.06/1.51 | (24) set_intersection2(all_0_6_6, all_0_7_7) = all_11_0_11
% 3.06/1.51 | (25) set_intersection2(all_0_9_9, all_0_8_8) = all_11_1_12
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (9) with all_11_1_12, all_0_8_8, all_0_9_9 and discharging atoms set_intersection2(all_0_9_9, all_0_8_8) = all_11_1_12, subset(all_0_9_9, all_0_8_8), yields:
% 3.06/1.51 | (26) all_11_1_12 = all_0_9_9
% 3.06/1.51 |
% 3.06/1.51 | From (26) and (23) follows:
% 3.06/1.51 | (27) cartesian_product2(all_0_9_9, all_11_0_11) = all_0_3_3
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (11) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms cartesian_product2(all_0_8_8, all_0_7_7) = all_0_4_4, cartesian_product2(all_0_9_9, all_0_6_6) = all_0_5_5, set_intersection2(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 3.06/1.51 | (28) ? [v0] : ? [v1] : (cartesian_product2(v0, v1) = all_0_3_3 & set_intersection2(all_0_7_7, all_0_6_6) = v1 & set_intersection2(all_0_8_8, all_0_9_9) = v0)
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (15) with all_11_0_11, all_0_6_6, all_0_7_7 and discharging atoms set_intersection2(all_0_6_6, all_0_7_7) = all_11_0_11, yields:
% 3.06/1.51 | (29) set_intersection2(all_0_7_7, all_0_6_6) = all_11_0_11
% 3.06/1.51 |
% 3.06/1.51 | Instantiating (28) with all_23_0_13, all_23_1_14 yields:
% 3.06/1.51 | (30) cartesian_product2(all_23_1_14, all_23_0_13) = all_0_3_3 & set_intersection2(all_0_7_7, all_0_6_6) = all_23_0_13 & set_intersection2(all_0_8_8, all_0_9_9) = all_23_1_14
% 3.06/1.51 |
% 3.06/1.51 | Applying alpha-rule on (30) yields:
% 3.06/1.51 | (31) cartesian_product2(all_23_1_14, all_23_0_13) = all_0_3_3
% 3.06/1.51 | (32) set_intersection2(all_0_7_7, all_0_6_6) = all_23_0_13
% 3.06/1.51 | (33) set_intersection2(all_0_8_8, all_0_9_9) = all_23_1_14
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (9) with all_23_0_13, all_0_6_6, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_6_6) = all_23_0_13, subset(all_0_7_7, all_0_6_6), yields:
% 3.06/1.51 | (34) all_23_0_13 = all_0_7_7
% 3.06/1.51 |
% 3.06/1.51 | Instantiating formula (4) with all_0_7_7, all_0_6_6, all_11_0_11, all_23_0_13 and discharging atoms set_intersection2(all_0_7_7, all_0_6_6) = all_23_0_13, set_intersection2(all_0_7_7, all_0_6_6) = all_11_0_11, yields:
% 3.06/1.51 | (35) all_23_0_13 = all_11_0_11
% 3.06/1.51 |
% 3.06/1.52 | Combining equations (35,34) yields a new equation:
% 3.06/1.52 | (36) all_11_0_11 = all_0_7_7
% 3.06/1.52 |
% 3.06/1.52 | Simplifying 36 yields:
% 3.06/1.52 | (37) all_11_0_11 = all_0_7_7
% 3.06/1.52 |
% 3.06/1.52 | From (37) and (27) follows:
% 3.06/1.52 | (38) cartesian_product2(all_0_9_9, all_0_7_7) = all_0_3_3
% 3.06/1.52 |
% 3.06/1.52 | Instantiating formula (12) with all_0_9_9, all_0_7_7, all_0_3_3, all_0_2_2 and discharging atoms cartesian_product2(all_0_9_9, all_0_7_7) = all_0_2_2, cartesian_product2(all_0_9_9, all_0_7_7) = all_0_3_3, yields:
% 3.06/1.52 | (39) all_0_2_2 = all_0_3_3
% 3.06/1.52 |
% 3.06/1.52 | Equations (39) can reduce 18 to:
% 3.06/1.52 | (40) $false
% 3.06/1.52 |
% 3.06/1.52 |-The branch is then unsatisfiable
% 3.06/1.52 % SZS output end Proof for theBenchmark
% 3.06/1.52
% 3.06/1.52 874ms
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