TSTP Solution File: SEV513^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV513^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 : Tue May 21 04:14:03 EDT 2024
% Result : Theorem 0.17s 0.36s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEV513^1 : TPTP v8.2.0. Released v7.0.0.
% 0.02/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 18:52:52 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH1_THM_EQU_NAR problem
% 0.11/0.32 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % (24971)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34 % (24972)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.11/0.34 % (24973)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.11/0.34 % (24974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34 % (24975)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34 % (24976)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.11/0.34 % (24977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34 % (24978)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.34 % Exception at run slice level
% 0.11/0.34 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.11/0.34 % (24974)Instruction limit reached!
% 0.11/0.34 % (24974)------------------------------
% 0.11/0.34 % (24974)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24974)Termination reason: Unknown
% 0.11/0.34 % (24974)Termination phase: Preprocessing 3
% 0.11/0.34
% 0.11/0.34 % (24974)Memory used [KB]: 1023
% 0.11/0.34 % (24974)Time elapsed: 0.003 s
% 0.11/0.34 % (24974)Instructions burned: 3 (million)
% 0.11/0.34 % (24974)------------------------------
% 0.11/0.34 % (24974)------------------------------
% 0.11/0.34 % (24978)Instruction limit reached!
% 0.11/0.34 % (24978)------------------------------
% 0.11/0.34 % (24978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24978)Termination reason: Unknown
% 0.11/0.34 % (24978)Termination phase: Property scanning
% 0.11/0.34
% 0.11/0.34 % (24978)Memory used [KB]: 1023
% 0.11/0.34 % (24978)Time elapsed: 0.003 s
% 0.11/0.34 % (24978)Instructions burned: 3 (million)
% 0.11/0.34 % (24978)------------------------------
% 0.11/0.34 % (24978)------------------------------
% 0.11/0.34 % (24972)Instruction limit reached!
% 0.11/0.34 % (24972)------------------------------
% 0.11/0.34 % (24972)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24972)Termination reason: Unknown
% 0.11/0.34 % (24972)Termination phase: Saturation
% 0.11/0.34
% 0.11/0.34 % (24972)Memory used [KB]: 5500
% 0.11/0.34 % (24972)Time elapsed: 0.004 s
% 0.11/0.34 % (24972)Instructions burned: 5 (million)
% 0.11/0.34 % (24972)------------------------------
% 0.11/0.34 % (24972)------------------------------
% 0.11/0.34 % (24976)Refutation not found, incomplete strategy
% 0.11/0.34 % (24976)------------------------------
% 0.11/0.34 % (24976)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24976)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.34
% 0.11/0.34
% 0.11/0.34 % (24976)Memory used [KB]: 5500
% 0.11/0.34 % (24976)Time elapsed: 0.005 s
% 0.11/0.34 % (24976)Instructions burned: 7 (million)
% 0.11/0.34 % (24976)------------------------------
% 0.11/0.34 % (24976)------------------------------
% 0.11/0.34 % (24973)Refutation not found, incomplete strategy
% 0.11/0.34 % (24973)------------------------------
% 0.11/0.34 % (24973)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24973)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.34
% 0.11/0.34
% 0.11/0.34 % (24973)Memory used [KB]: 5628
% 0.11/0.34 % (24973)Time elapsed: 0.008 s
% 0.11/0.34 % (24973)Instructions burned: 12 (million)
% 0.11/0.34 % (24973)------------------------------
% 0.11/0.34 % (24973)------------------------------
% 0.11/0.35 % (24977)Instruction limit reached!
% 0.11/0.35 % (24977)------------------------------
% 0.11/0.35 % (24977)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (24977)Termination reason: Unknown
% 0.11/0.35 % (24977)Termination phase: Saturation
% 0.11/0.35
% 0.11/0.35 % (24977)Memory used [KB]: 5628
% 0.11/0.35 % (24977)Time elapsed: 0.011 s
% 0.11/0.35 % (24977)Instructions burned: 18 (million)
% 0.11/0.35 % (24977)------------------------------
% 0.11/0.35 % (24977)------------------------------
% 0.17/0.35 % (24979)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.17/0.35 % (24980)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.17/0.35 % (24981)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.35 % (24982)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.17/0.35 % (24981)Instruction limit reached!
% 0.17/0.35 % (24981)------------------------------
% 0.17/0.35 % (24981)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (24981)Termination reason: Unknown
% 0.17/0.35 % (24981)Termination phase: Property scanning
% 0.17/0.35
% 0.17/0.35 % (24981)Memory used [KB]: 1023
% 0.17/0.35 % (24981)Time elapsed: 0.003 s
% 0.17/0.35 % (24981)Instructions burned: 3 (million)
% 0.17/0.35 % (24981)------------------------------
% 0.17/0.35 % (24981)------------------------------
% 0.17/0.35 % (24983)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.36 % (24980)First to succeed.
% 0.17/0.36 % (24984)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.17/0.36 % (24983)Instruction limit reached!
% 0.17/0.36 % (24983)------------------------------
% 0.17/0.36 % (24983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (24983)Termination reason: Unknown
% 0.17/0.36 % (24983)Termination phase: Saturation
% 0.17/0.36
% 0.17/0.36 % (24983)Memory used [KB]: 1023
% 0.17/0.36 % (24983)Time elapsed: 0.005 s
% 0.17/0.36 % (24983)Instructions burned: 7 (million)
% 0.17/0.36 % (24983)------------------------------
% 0.17/0.36 % (24983)------------------------------
% 0.17/0.36 % (24985)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.36 % (24980)Refutation found. Thanks to Tanya!
% 0.17/0.36 % SZS status Theorem for theBenchmark
% 0.17/0.36 % SZS output start Proof for theBenchmark
% 0.17/0.36 thf(type_def_6, type, 'type/realax/real': $tType).
% 0.17/0.36 thf(type_def_7, type, sK0: $tType).
% 0.17/0.36 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.17/0.36 thf(func_def_1, type, 'const/sets/SETSPEC': !>[X0: $tType]:(X0 > $o > X0 > $o)).
% 0.17/0.36 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.17/0.36 thf(func_def_3, type, 'const/sets/GSPEC': !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 0.17/0.36 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.17/0.36 thf(func_def_5, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 0.17/0.36 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 0.17/0.36 thf(func_def_7, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 0.17/0.36 thf(func_def_8, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 0.17/0.36 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 0.17/0.36 thf(func_def_19, type, sK1: sK0 > $o).
% 0.17/0.36 thf(func_def_20, type, sK2: sK0 > $o).
% 0.17/0.36 thf(func_def_21, type, sK3: sK0 > 'type/realax/real').
% 0.17/0.36 thf(func_def_22, type, sK4: sK0 > 'type/realax/real').
% 0.17/0.36 thf(func_def_24, type, ph6: !>[X0: $tType]:(X0)).
% 0.17/0.36 thf(f41,plain,(
% 0.17/0.36 $false),
% 0.17/0.36 inference(avatar_sat_refutation,[],[f27,f32,f40])).
% 0.17/0.36 thf(f40,plain,(
% 0.17/0.36 ~spl5_1 | spl5_2),
% 0.17/0.36 inference(avatar_contradiction_clause,[],[f39])).
% 0.17/0.36 thf(f39,plain,(
% 0.17/0.36 $false | (~spl5_1 | spl5_2)),
% 0.17/0.36 inference(subsumption_resolution,[],[f38,f21])).
% 0.17/0.36 thf(f21,plain,(
% 0.17/0.36 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.17/0.36 inference(cnf_transformation,[],[f10])).
% 0.17/0.36 thf(f10,plain,(
% 0.17/0.36 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.17/0.36 inference(fool_elimination,[],[f9])).
% 0.17/0.36 thf(f9,plain,(
% 0.17/0.36 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.17/0.36 inference(rectify,[],[f2])).
% 0.17/0.36 thf(f2,axiom,(
% 0.17/0.36 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.17/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.17/0.36 thf(f38,plain,(
% 0.17/0.36 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | (~spl5_1 | spl5_2)),
% 0.17/0.36 inference(subsumption_resolution,[],[f37,f26])).
% 0.17/0.36 thf(f26,plain,(
% 0.17/0.36 (('const/sets/FINITE' @ sK0 @ sK1) = $true) | ~spl5_1),
% 0.17/0.36 inference(avatar_component_clause,[],[f24])).
% 0.17/0.36 thf(f24,plain,(
% 0.17/0.36 spl5_1 <=> (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 0.17/0.36 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
% 0.17/0.36 thf(f37,plain,(
% 0.17/0.36 (('const/sets/FINITE' @ sK0 @ sK1) != $true) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | spl5_2),
% 0.17/0.36 inference(trivial_inequality_removal,[],[f36])).
% 0.17/0.36 thf(f36,plain,(
% 0.17/0.36 (('const/sets/FINITE' @ sK0 @ sK1) != $true) | (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | spl5_2),
% 0.17/0.36 inference(superposition,[],[f31,f20])).
% 0.17/0.36 thf(f20,plain,(
% 0.17/0.36 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > $o,X6 : X0 > X1,X4 : X0 > $o,X5 : X0 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true) | ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))))) )),
% 0.17/0.36 inference(cnf_transformation,[],[f13])).
% 0.17/0.36 thf(f13,plain,(
% 0.17/0.36 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) != $true) | ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : (((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0))))) | (('const/sets/FINITE' @ X0 @ X3) != $true)))),
% 0.17/0.36 inference(ennf_transformation,[],[f8])).
% 0.17/0.36 thf(f8,plain,(
% 0.17/0.36 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) = $true) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X3) = $true) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))))))),
% 0.17/0.36 inference(fool_elimination,[],[f7])).
% 0.17/0.36 thf(f7,plain,(
% 0.17/0.36 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[X7 : X0] : ('const/class/COND' @ X1 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X8 : X0] : (? [X9 : X0] : ('const/sets/SETSPEC' @ X0 @ X8 @ ('const/sets/IN' @ X0 @ X9 @ X3) & (X4 @ X9) @ X9)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X10 : X0] : (? [X11 : X0] : ('const/sets/SETSPEC' @ X0 @ X10 @ ('const/sets/IN' @ X0 @ X11 @ X3) & ~(X4 @ X11) @ X11)))) @ X6)))))),
% 0.17/0.36 inference(rectify,[],[f1])).
% 0.17/0.36 thf(f1,axiom,(
% 0.17/0.36 ! [X0 : $tType,X2 : $tType,X1 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X1) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X2,X6 : X0 > X2] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/iterate' @ X0 @ X2 @ X1 @ X3 @ (^[X7 : X0] : ('const/class/COND' @ X2 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))) = (X1 @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X3) & (X4 @ X8) @ X8)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X3) & ~(X4 @ X8) @ X8)))) @ X6)))))),
% 0.17/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CASES_')).
% 0.17/0.36 thf(f31,plain,(
% 0.17/0.36 (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) | spl5_2),
% 0.17/0.36 inference(avatar_component_clause,[],[f29])).
% 0.17/0.36 thf(f29,plain,(
% 0.17/0.36 spl5_2 <=> (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) = ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 0.17/0.36 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
% 0.17/0.36 thf(f32,plain,(
% 0.17/0.36 ~spl5_2),
% 0.17/0.36 inference(avatar_split_clause,[],[f22,f29])).
% 0.17/0.36 thf(f22,plain,(
% 0.17/0.36 (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 0.17/0.36 inference(definition_unfolding,[],[f18,f19,f19,f19])).
% 0.17/0.36 thf(f19,plain,(
% 0.17/0.36 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 0.17/0.36 inference(cnf_transformation,[],[f3])).
% 0.17/0.36 thf(f3,axiom,(
% 0.17/0.36 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 0.17/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.17/0.36 thf(f18,plain,(
% 0.17/0.36 (('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)))),
% 0.17/0.36 inference(cnf_transformation,[],[f16])).
% 0.17/0.36 thf(f16,plain,(
% 0.17/0.36 (('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 0.17/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f14,f15])).
% 0.17/0.36 thf(f15,plain,(
% 0.17/0.36 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4)) != ('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) & (('const/sets/FINITE' @ X0 @ X1) = $true)) => ((('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true))),
% 0.17/0.36 introduced(choice_axiom,[])).
% 0.17/0.36 thf(f14,plain,(
% 0.17/0.36 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4)) != ('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) & (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 0.17/0.36 inference(ennf_transformation,[],[f12])).
% 0.17/0.36 thf(f12,plain,(
% 0.17/0.36 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) = $true) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4)) = ('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))))),
% 0.17/0.36 inference(fool_elimination,[],[f11])).
% 0.17/0.36 thf(f11,plain,(
% 0.17/0.36 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ('const/sets/IN' @ X0 @ X6 @ X1) & (X2 @ X6) @ X6)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X1) & ~(X2 @ X8) @ X8)))) @ X4)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X9 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X2 @ X9) @ (X3 @ X9) @ (X4 @ X9))))))),
% 0.17/0.36 inference(rectify,[],[f5])).
% 0.17/0.36 thf(f5,negated_conjecture,(
% 0.17/0.36 ~! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & (X4 @ X7) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & ~(X4 @ X7) @ X7)))) @ X5)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6))))))),
% 0.17/0.36 inference(negated_conjecture,[],[f4])).
% 0.17/0.36 thf(f4,conjecture,(
% 0.17/0.36 ! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & (X4 @ X7) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & ~(X4 @ X7) @ X7)))) @ X5)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6))))))),
% 0.17/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CASES_')).
% 0.17/0.36 thf(f27,plain,(
% 0.17/0.36 spl5_1),
% 0.17/0.36 inference(avatar_split_clause,[],[f17,f24])).
% 0.17/0.36 thf(f17,plain,(
% 0.17/0.36 (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 0.17/0.36 inference(cnf_transformation,[],[f16])).
% 0.17/0.36 % SZS output end Proof for theBenchmark
% 0.17/0.36 % (24980)------------------------------
% 0.17/0.36 % (24980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (24980)Termination reason: Refutation
% 0.17/0.36
% 0.17/0.36 % (24980)Memory used [KB]: 5756
% 0.17/0.36 % (24980)Time elapsed: 0.009 s
% 0.17/0.36 % (24980)Instructions burned: 8 (million)
% 0.17/0.36 % (24980)------------------------------
% 0.17/0.36 % (24980)------------------------------
% 0.17/0.36 % (24970)Success in time 0.043 s
% 0.17/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------