TSTP Solution File: SEV513^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV513^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n020.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 : Mon Jun 24 16:04:12 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV513^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n020.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:00:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.35 This is a TH1_THM_EQU_NAR problem
% 0.20/0.35 Running higher-order theorem proving
% 0.20/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.37 % (28933)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (28935)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)
% 0.20/0.37 % (28934)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)
% 0.20/0.37 % (28937)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)
% 0.20/0.37 % (28936)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (28938)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)
% 0.20/0.37 % (28939)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % Exception at run slice level
% 0.20/0.37 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
% 0.20/0.38 % (28936)Instruction limit reached!
% 0.20/0.38 % (28936)------------------------------
% 0.20/0.38 % (28936)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (28936)Termination reason: Unknown
% 0.20/0.38 % (28936)Termination phase: Preprocessing 3
% 0.20/0.38
% 0.20/0.38 % (28936)Memory used [KB]: 1023
% 0.20/0.38 % (28936)Time elapsed: 0.004 s
% 0.20/0.38 % (28936)Instructions burned: 2 (million)
% 0.20/0.38 % (28936)------------------------------
% 0.20/0.38 % (28936)------------------------------
% 0.20/0.38 % (28934)Instruction limit reached!
% 0.20/0.38 % (28934)------------------------------
% 0.20/0.38 % (28934)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (28934)Termination reason: Unknown
% 0.20/0.38 % (28934)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (28934)Memory used [KB]: 1023
% 0.20/0.38 % (28934)Time elapsed: 0.005 s
% 0.20/0.38 % (28934)Instructions burned: 4 (million)
% 0.20/0.38 % (28934)------------------------------
% 0.20/0.38 % (28934)------------------------------
% 0.20/0.38 % (28938)Refutation not found, incomplete strategy
% 0.20/0.38 % (28938)------------------------------
% 0.20/0.38 % (28938)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (28938)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (28938)Memory used [KB]: 5500
% 0.20/0.38 % (28938)Time elapsed: 0.006 s
% 0.20/0.38 % (28938)Instructions burned: 5 (million)
% 0.20/0.38 % (28938)------------------------------
% 0.20/0.38 % (28938)------------------------------
% 0.20/0.38 % (28935)First to succeed.
% 0.20/0.39 % (28939)Instruction limit reached!
% 0.20/0.39 % (28939)------------------------------
% 0.20/0.39 % (28939)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (28935)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% 0.20/0.39 thf(type_def_6, type, 'type/realax/real': $tType).
% 0.20/0.39 thf(type_def_7, type, sK0: $tType).
% 0.20/0.39 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.20/0.39 thf(func_def_1, type, 'const/sets/SETSPEC': !>[X0: $tType]:(X0 > $o > X0 > $o)).
% 0.20/0.39 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.20/0.39 thf(func_def_3, type, 'const/sets/GSPEC': !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 0.20/0.39 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.20/0.39 thf(func_def_5, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 0.20/0.39 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 0.20/0.39 thf(func_def_7, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 0.20/0.39 thf(func_def_8, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 0.20/0.39 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 0.20/0.39 thf(func_def_11, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.20/0.39 thf(func_def_20, type, sK1: sK0 > $o).
% 0.20/0.39 thf(func_def_21, type, sK2: sK0 > $o).
% 0.20/0.39 thf(func_def_22, type, sK3: sK0 > 'type/realax/real').
% 0.20/0.39 thf(func_def_23, type, sK4: sK0 > 'type/realax/real').
% 0.20/0.39 thf(func_def_25, type, ph6: !>[X0: $tType]:(X0)).
% 0.20/0.39 thf(f28,plain,(
% 0.20/0.39 $false),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f27])).
% 0.20/0.39 thf(f27,plain,(
% 0.20/0.39 (('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)))))),
% 0.20/0.39 inference(superposition,[],[f22,f26])).
% 0.20/0.39 thf(f26,plain,(
% 0.20/0.39 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > $o,X1 : sK0 > 'type/realax/real'] : ((('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 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))) @ X1) @ ('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 @ ((~ (X0 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ X2)) = ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (X0 @ Y0) @ (X1 @ Y0) @ (X2 @ Y0)))))) )),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f25])).
% 0.20/0.39 thf(f25,plain,(
% 0.20/0.39 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > $o,X1 : sK0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))) @ X1) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (X0 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ X2)) = ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (X0 @ Y0) @ (X1 @ Y0) @ (X2 @ Y0))))) | ($true != $true)) )),
% 0.20/0.39 inference(superposition,[],[f24,f20])).
% 0.20/0.39 thf(f20,plain,(
% 0.20/0.39 ($true = ('const/sets/FINITE' @ sK0 @ sK1))),
% 0.20/0.39 inference(cnf_transformation,[],[f16])).
% 0.20/0.39 thf(f16,plain,(
% 0.20/0.39 ($true = ('const/sets/FINITE' @ sK0 @ sK1)) & (('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 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ 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)))),
% 0.20/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f14,f15])).
% 0.20/0.39 thf(f15,plain,(
% 0.20/0.39 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4)) != ('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))))) => (($true = ('const/sets/FINITE' @ sK0 @ sK1)) & (('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 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ 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))))),
% 0.20/0.39 introduced(choice_axiom,[])).
% 0.20/0.39 thf(f14,plain,(
% 0.20/0.39 ? [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 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ 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))))))),
% 0.20/0.39 inference(ennf_transformation,[],[f12])).
% 0.20/0.39 thf(f12,plain,(
% 0.20/0.39 ~! [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 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ 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))))))),
% 0.20/0.39 inference(fool_elimination,[],[f11])).
% 0.20/0.39 thf(f11,plain,(
% 0.20/0.39 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/iterate/sum' @ X0 @ X1 @ (^[X5 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X2 @ X5) @ (X3 @ X5) @ (X4 @ X5)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ (X2 @ X7) & ('const/sets/IN' @ X0 @ X7 @ X1) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X8 : X0] : (? [X9 : X0] : ('const/sets/SETSPEC' @ X0 @ X8 @ ('const/sets/IN' @ X0 @ X9 @ X1) & ~(X2 @ X9) @ X9)))) @ X4))))),
% 0.20/0.39 inference(rectify,[],[f5])).
% 0.20/0.39 thf(f5,negated_conjecture,(
% 0.20/0.39 ~! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ (X4 @ X7) & ('const/sets/IN' @ X0 @ X7 @ X1) @ 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))))),
% 0.20/0.39 inference(negated_conjecture,[],[f4])).
% 0.20/0.39 thf(f4,conjecture,(
% 0.20/0.39 ! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ (X4 @ X7) & ('const/sets/IN' @ X0 @ X7 @ X1) @ 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))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CASES_')).
% 0.20/0.39 thf(f24,plain,(
% 0.20/0.39 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X1 : X0 > $o,X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/realax/real_add' @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('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/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))))) )),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f23])).
% 0.20/0.39 thf(f23,plain,(
% 0.20/0.39 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X1 : X0 > $o,X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | ($true != $true) | (('const/realax/real_add' @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('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/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))))) )),
% 0.20/0.39 inference(superposition,[],[f21,f17])).
% 0.20/0.39 thf(f17,plain,(
% 0.20/0.39 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.20/0.39 inference(cnf_transformation,[],[f8])).
% 0.20/0.39 thf(f8,plain,(
% 0.20/0.39 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.20/0.39 inference(fool_elimination,[],[f7])).
% 0.20/0.39 thf(f7,plain,(
% 0.20/0.39 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.20/0.39 inference(rectify,[],[f2])).
% 0.20/0.39 thf(f2,axiom,(
% 0.20/0.39 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.20/0.39 thf(f21,plain,(
% 0.20/0.39 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > $o,X6 : X0 > X1,X4 : X0 > $o,X5 : X0 > X1] : (($true != ('const/iterate/monoidal' @ X1 @ X2)) | (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ 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/sets/FINITE' @ X0 @ X3) != $true)) )),
% 0.20/0.39 inference(cnf_transformation,[],[f13])).
% 0.20/0.39 thf(f13,plain,(
% 0.20/0.39 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (($true != ('const/iterate/monoidal' @ X1 @ X2)) | ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ 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)))))),
% 0.20/0.39 inference(ennf_transformation,[],[f10])).
% 0.20/0.39 thf(f10,plain,(
% 0.20/0.39 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (($true = ('const/iterate/monoidal' @ X1 @ X2)) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X3) = $true) => (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ 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)))))),
% 0.20/0.39 inference(fool_elimination,[],[f9])).
% 0.20/0.39 thf(f9,plain,(
% 0.20/0.39 ! [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) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ (X4 @ X8) & ('const/sets/IN' @ X0 @ X8 @ X3) @ X8)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X9 : X0] : (? [X10 : X0] : ('const/sets/SETSPEC' @ X0 @ X9 @ ('const/sets/IN' @ X0 @ X10 @ X3) & ~(X4 @ X10) @ X10)))) @ X6)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[X11 : X0] : ('const/class/COND' @ X1 @ (X4 @ X11) @ (X5 @ X11) @ (X6 @ X11)))))))),
% 0.20/0.39 inference(rectify,[],[f1])).
% 0.20/0.39 thf(f1,axiom,(
% 0.20/0.39 ! [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) => ((X1 @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ (X4 @ X8) & ('const/sets/IN' @ X0 @ X8 @ X3) @ 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)) = ('const/iterate/iterate' @ X0 @ X2 @ X1 @ X3 @ (^[X7 : X0] : ('const/class/COND' @ X2 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CASES_')).
% 0.20/0.39 thf(f22,plain,(
% 0.20/0.39 (('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/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 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ 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)))),
% 0.20/0.39 inference(definition_unfolding,[],[f19,f18,f18,f18])).
% 0.20/0.39 thf(f18,plain,(
% 0.20/0.39 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 0.20/0.39 inference(cnf_transformation,[],[f3])).
% 0.20/0.39 thf(f3,axiom,(
% 0.20/0.39 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.20/0.39 thf(f19,plain,(
% 0.20/0.39 (('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 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ 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)))),
% 0.20/0.39 inference(cnf_transformation,[],[f16])).
% 0.20/0.39 % SZS output end Proof for theBenchmark
% 0.20/0.39 % (28935)------------------------------
% 0.20/0.39 % (28935)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (28935)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (28935)Memory used [KB]: 5756
% 0.20/0.39 % (28935)Time elapsed: 0.013 s
% 0.20/0.39 % (28935)Instructions burned: 11 (million)
% 0.20/0.39 % (28935)------------------------------
% 0.20/0.39 % (28935)------------------------------
% 0.20/0.39 % (28932)Success in time 0.036 s
%------------------------------------------------------------------------------