TSTP Solution File: SEU172+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU172+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 : 300s
% DateTime : Thu Aug 31 17:43:02 EDT 2023
% Result : Theorem 18.09s 3.12s
% Output : Proof 23.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU172+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:11:01 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.69/1.23 Prover 1: Preprocessing ...
% 3.69/1.24 Prover 4: Preprocessing ...
% 4.34/1.28 Prover 5: Preprocessing ...
% 4.34/1.28 Prover 0: Preprocessing ...
% 4.34/1.28 Prover 3: Preprocessing ...
% 4.45/1.29 Prover 6: Preprocessing ...
% 4.45/1.29 Prover 2: Preprocessing ...
% 11.20/2.24 Prover 1: Warning: ignoring some quantifiers
% 11.59/2.25 Prover 5: Proving ...
% 11.59/2.34 Prover 1: Constructing countermodel ...
% 13.07/2.44 Prover 3: Warning: ignoring some quantifiers
% 13.08/2.48 Prover 3: Constructing countermodel ...
% 13.49/2.50 Prover 4: Warning: ignoring some quantifiers
% 13.49/2.54 Prover 6: Proving ...
% 13.87/2.58 Prover 2: Proving ...
% 13.87/2.69 Prover 4: Constructing countermodel ...
% 13.87/2.70 Prover 0: Proving ...
% 18.09/3.12 Prover 3: proved (2484ms)
% 18.09/3.12
% 18.09/3.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.09/3.12
% 18.09/3.12 Prover 2: stopped
% 18.09/3.13 Prover 5: stopped
% 18.09/3.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.09/3.15 Prover 0: stopped
% 18.09/3.16 Prover 6: stopped
% 18.47/3.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.47/3.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.47/3.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.47/3.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.47/3.22 Prover 7: Preprocessing ...
% 19.10/3.26 Prover 8: Preprocessing ...
% 19.10/3.26 Prover 13: Preprocessing ...
% 19.10/3.27 Prover 10: Preprocessing ...
% 19.37/3.29 Prover 11: Preprocessing ...
% 21.39/3.58 Prover 10: Warning: ignoring some quantifiers
% 21.39/3.60 Prover 7: Warning: ignoring some quantifiers
% 21.72/3.63 Prover 8: Warning: ignoring some quantifiers
% 21.72/3.63 Prover 10: Constructing countermodel ...
% 21.72/3.63 Prover 7: Constructing countermodel ...
% 22.00/3.68 Prover 8: Constructing countermodel ...
% 22.00/3.70 Prover 13: Warning: ignoring some quantifiers
% 22.00/3.72 Prover 13: Constructing countermodel ...
% 23.06/3.84 Prover 10: Found proof (size 21)
% 23.06/3.84 Prover 10: proved (687ms)
% 23.06/3.84 Prover 11: Warning: ignoring some quantifiers
% 23.06/3.84 Prover 1: stopped
% 23.06/3.84 Prover 13: stopped
% 23.06/3.84 Prover 8: stopped
% 23.06/3.84 Prover 7: stopped
% 23.06/3.84 Prover 4: stopped
% 23.60/3.86 Prover 11: Constructing countermodel ...
% 23.60/3.88 Prover 11: stopped
% 23.60/3.88
% 23.60/3.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.60/3.88
% 23.60/3.89 % SZS output start Proof for theBenchmark
% 23.60/3.89 Assumptions after simplification:
% 23.60/3.89 ---------------------------------
% 23.60/3.89
% 23.60/3.90 (d4_xboole_0)
% 23.82/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.82/3.92 (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.82/3.92 $i(v0) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0: $i] : ! [v1: $i] : !
% 23.82/3.92 [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v3) | ~
% 23.82/3.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) & ! [v0: $i] :
% 23.82/3.92 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 23.82/3.92 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2) |
% 23.82/3.92 in(v3, v1)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 =
% 23.82/3.92 v0 | ~ (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.82/3.92 ? [v4: $i] : ($i(v4) & ( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) &
% 23.82/3.92 (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2)))))
% 23.82/3.92
% 23.82/3.92 (d5_subset_1)
% 23.82/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 23.82/3.93 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 &
% 23.82/3.93 set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) & ~
% 23.82/3.93 element(v1, v3))))
% 23.82/3.93
% 23.82/3.93 (dt_k3_subset_1)
% 23.82/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 23.82/3.93 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~
% 23.82/3.93 element(v1, v3) | element(v2, v3))))
% 23.82/3.93
% 23.82/3.93 (t54_subset_1)
% 23.82/3.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 23.82/3.93 (subset_complement(v0, v2) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & $i(v2)
% 23.82/3.93 & $i(v1) & $i(v0) & element(v2, v3) & in(v1, v4) & in(v1, v2))
% 23.82/3.93
% 23.82/3.93 (function-axioms)
% 23.82/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & !
% 23.82/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 23.82/3.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 23.82/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 23.82/3.93 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 23.82/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.82/3.93 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 23.82/3.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 23.82/3.93 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.82/3.93 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i]
% 23.82/3.93 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 23.82/3.93 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 23.82/3.93 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 23.82/3.93
% 23.82/3.93 Further assumptions not needed in the proof:
% 23.82/3.93 --------------------------------------------
% 23.82/3.93 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 23.82/3.93 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 23.82/3.93 d1_xboole_0, d1_zfmisc_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1,
% 23.82/3.93 d3_tarski, d3_xboole_0, d4_tarski, d5_tarski, d7_xboole_0, d8_xboole_0,
% 23.82/3.93 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0,
% 23.82/3.93 dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0,
% 23.82/3.93 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 23.82/3.93 fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 23.82/3.93 involutiveness_k3_subset_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 23.82/3.93 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 23.82/3.93 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, rc1_subset_1,
% 23.82/3.93 rc1_xboole_0, rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski,
% 23.82/3.93 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1,
% 23.82/3.93 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1,
% 23.82/3.93 t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1,
% 23.82/3.93 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, t37_zfmisc_1,
% 23.82/3.93 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_xboole_0, t3_xboole_1,
% 23.82/3.93 t40_xboole_1, t43_subset_1, t45_xboole_1, t46_zfmisc_1, t48_xboole_1, t4_boole,
% 23.82/3.93 t4_xboole_0, t50_subset_1, t60_xboole_1, t63_xboole_1, t65_zfmisc_1,
% 23.82/3.93 t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1,
% 23.82/3.93 t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_tarski,
% 23.82/3.93 t9_zfmisc_1
% 23.82/3.93
% 23.82/3.93 Those formulas are unsatisfiable:
% 23.82/3.93 ---------------------------------
% 23.82/3.93
% 23.82/3.93 Begin of proof
% 23.82/3.93 |
% 23.82/3.93 | ALPHA: (d4_xboole_0) implies:
% 23.82/3.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.82/3.94 | (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 23.82/3.94 | ~ $i(v0) | ~ in(v3, v2) | ~ in(v3, v1))
% 23.82/3.94 |
% 23.82/3.94 | ALPHA: (function-axioms) implies:
% 23.82/3.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 23.82/3.94 | v1) | ~ (powerset(v2) = v0))
% 23.82/3.94 |
% 23.82/3.94 | DELTA: instantiating (t54_subset_1) with fresh symbols all_113_0, all_113_1,
% 23.82/3.94 | all_113_2, all_113_3, all_113_4 gives:
% 23.82/3.94 | (3) subset_complement(all_113_4, all_113_2) = all_113_0 &
% 23.82/3.94 | powerset(all_113_4) = all_113_1 & $i(all_113_0) & $i(all_113_1) &
% 23.82/3.94 | $i(all_113_2) & $i(all_113_3) & $i(all_113_4) & element(all_113_2,
% 23.82/3.94 | all_113_1) & in(all_113_3, all_113_0) & in(all_113_3, all_113_2)
% 23.82/3.94 |
% 23.82/3.94 | ALPHA: (3) implies:
% 23.82/3.94 | (4) in(all_113_3, all_113_2)
% 23.82/3.94 | (5) in(all_113_3, all_113_0)
% 23.82/3.94 | (6) element(all_113_2, all_113_1)
% 23.82/3.94 | (7) $i(all_113_4)
% 23.82/3.94 | (8) $i(all_113_3)
% 23.82/3.94 | (9) $i(all_113_2)
% 23.82/3.94 | (10) powerset(all_113_4) = all_113_1
% 23.82/3.94 | (11) subset_complement(all_113_4, all_113_2) = all_113_0
% 23.82/3.94 |
% 23.82/3.94 | GROUND_INST: instantiating (d5_subset_1) with all_113_4, all_113_2, all_113_0,
% 23.82/3.94 | simplifying with (7), (9), (11) gives:
% 23.82/3.94 | (12) ? [v0: $i] : ? [v1: int] : ((v1 = all_113_0 &
% 23.82/3.94 | set_difference(all_113_4, all_113_2) = all_113_0 & $i(all_113_0))
% 23.82/3.94 | | (powerset(all_113_4) = v0 & $i(v0) & ~ element(all_113_2, v0)))
% 23.82/3.94 |
% 23.82/3.94 | GROUND_INST: instantiating (dt_k3_subset_1) with all_113_4, all_113_2,
% 23.82/3.94 | all_113_0, simplifying with (7), (9), (11) gives:
% 23.82/3.94 | (13) ? [v0: $i] : (powerset(all_113_4) = v0 & $i(v0) & ( ~
% 23.82/3.94 | element(all_113_2, v0) | element(all_113_0, v0)))
% 23.82/3.94 |
% 23.82/3.94 | DELTA: instantiating (13) with fresh symbol all_139_0 gives:
% 23.82/3.94 | (14) powerset(all_113_4) = all_139_0 & $i(all_139_0) & ( ~
% 23.82/3.94 | element(all_113_2, all_139_0) | element(all_113_0, all_139_0))
% 23.82/3.94 |
% 23.82/3.94 | ALPHA: (14) implies:
% 23.82/3.94 | (15) powerset(all_113_4) = all_139_0
% 23.82/3.94 |
% 23.82/3.94 | DELTA: instantiating (12) with fresh symbols all_141_0, all_141_1 gives:
% 23.82/3.94 | (16) (all_141_0 = all_113_0 & set_difference(all_113_4, all_113_2) =
% 23.82/3.94 | all_113_0 & $i(all_113_0)) | (powerset(all_113_4) = all_141_1 &
% 23.82/3.94 | $i(all_141_1) & ~ element(all_113_2, all_141_1))
% 23.82/3.94 |
% 23.82/3.94 | GROUND_INST: instantiating (2) with all_113_1, all_139_0, all_113_4,
% 23.82/3.94 | simplifying with (10), (15) gives:
% 23.82/3.94 | (17) all_139_0 = all_113_1
% 23.82/3.94 |
% 23.82/3.94 | BETA: splitting (16) gives:
% 23.82/3.94 |
% 23.82/3.94 | Case 1:
% 23.82/3.94 | |
% 23.82/3.95 | | (18) all_141_0 = all_113_0 & set_difference(all_113_4, all_113_2) =
% 23.82/3.95 | | all_113_0 & $i(all_113_0)
% 23.82/3.95 | |
% 23.82/3.95 | | ALPHA: (18) implies:
% 23.82/3.95 | | (19) $i(all_113_0)
% 23.82/3.95 | | (20) set_difference(all_113_4, all_113_2) = all_113_0
% 23.82/3.95 | |
% 23.82/3.95 | | GROUND_INST: instantiating (1) with all_113_4, all_113_2, all_113_0,
% 23.82/3.95 | | all_113_3, simplifying with (4), (5), (7), (8), (9), (19), (20)
% 23.82/3.95 | | gives:
% 23.82/3.95 | | (21) $false
% 23.82/3.95 | |
% 23.82/3.95 | | CLOSE: (21) is inconsistent.
% 23.82/3.95 | |
% 23.82/3.95 | Case 2:
% 23.82/3.95 | |
% 23.82/3.95 | | (22) powerset(all_113_4) = all_141_1 & $i(all_141_1) & ~
% 23.82/3.95 | | element(all_113_2, all_141_1)
% 23.82/3.95 | |
% 23.82/3.95 | | ALPHA: (22) implies:
% 23.82/3.95 | | (23) ~ element(all_113_2, all_141_1)
% 23.82/3.95 | | (24) powerset(all_113_4) = all_141_1
% 23.82/3.95 | |
% 23.82/3.95 | | GROUND_INST: instantiating (2) with all_113_1, all_141_1, all_113_4,
% 23.82/3.95 | | simplifying with (10), (24) gives:
% 23.82/3.95 | | (25) all_141_1 = all_113_1
% 23.82/3.95 | |
% 23.82/3.95 | | REDUCE: (23), (25) imply:
% 23.82/3.95 | | (26) ~ element(all_113_2, all_113_1)
% 23.82/3.95 | |
% 23.82/3.95 | | PRED_UNIFY: (6), (26) imply:
% 23.82/3.95 | | (27) $false
% 23.82/3.95 | |
% 23.82/3.95 | | CLOSE: (27) is inconsistent.
% 23.82/3.95 | |
% 23.82/3.95 | End of split
% 23.82/3.95 |
% 23.82/3.95 End of proof
% 23.82/3.95 % SZS output end Proof for theBenchmark
% 23.82/3.95
% 23.82/3.95 3333ms
%------------------------------------------------------------------------------