%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV512^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:46 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV512^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:56:04 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.31 % (1218556)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (1218572)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3766449491:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (1218575)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (1218575)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (1218568)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4261561075:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (1218569)lrs+10_16_si=on:nwc=1.5:random_seed=654765096:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (1218571)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1482119522:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (1218573)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4199502594:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (1218574)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1997742973:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (1218575)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=234776076:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (1218571)Instruction limit reached!
% 0.22/0.31 % (1218571)------------------------------
% 0.22/0.31 % (1218571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1218571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1218571)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1218571)Termination reason: Instruction limit
% 0.22/0.31 % (1218571)Termination phase: Property scanning
% 0.22/0.31 % (1218571)Time elapsed: 0.002 s
% 0.22/0.31 % (1218571)Peak memory usage: 10 MB
% 0.22/0.31 % (1218571)Instructions burned: 3 (million)
% 0.22/0.31 % (1218569)Instruction limit reached!
% 0.22/0.31 % (1218569)------------------------------
% 0.22/0.31 % (1218569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1218569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1218569)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1218569)Termination reason: Instruction limit
% 0.22/0.31 % (1218569)Termination phase: Saturation
% 0.22/0.31 % (1218569)Time elapsed: 0.012 s
% 0.22/0.31 % (1218569)Peak memory usage: 12 MB
% 0.22/0.31 % (1218569)Instructions burned: 19 (million)
% 0.22/0.31 % (1218573)Instruction limit reached!
% 0.22/0.31 % (1218573)------------------------------
% 0.22/0.31 % (1218573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1218573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1218573)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1218573)Termination reason: Instruction limit
% 0.22/0.32 % (1218573)Termination phase: Saturation
% 0.22/0.32 % (1218573)Time elapsed: 0.015 s
% 0.22/0.32 % (1218573)Peak memory usage: 12 MB
% 0.22/0.32 % (1218573)Instructions burned: 25 (million)
% 0.22/0.32 % (1218590)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=351264728:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (1218590)Instruction limit reached!
% 0.22/0.32 % (1218590)------------------------------
% 0.22/0.32 % (1218590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1218590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1218590)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1218590)Termination reason: Instruction limit
% 0.22/0.32 % (1218590)Termination phase: Saturation
% 0.22/0.32 % (1218590)Time elapsed: 0.002 s
% 0.22/0.32 % (1218590)Peak memory usage: 11 MB
% 0.22/0.32 % (1218590)Instructions burned: 3 (million)
% 0.22/0.32 % (1218595)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.32 % (1218594)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2399502420:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.32 % (1218595)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2453173270:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.32 % (1218594)Instruction limit reached!
% 0.22/0.32 % (1218594)------------------------------
% 0.22/0.32 % (1218594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1218594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1218594)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1218594)Termination reason: Instruction limit
% 0.22/0.32 % (1218594)Termination phase: Saturation
% 0.22/0.32 % (1218594)Time elapsed: 0.003 s
% 0.22/0.32 % (1218594)Peak memory usage: 11 MB
% 0.22/0.32 % (1218594)Instructions burned: 5 (million)
% 0.22/0.32 % (1218568) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1218556-1218568"...
% 0.22/0.32 % (1218595)Instruction limit reached!
% 0.22/0.32 % (1218595)------------------------------
% 0.22/0.32 % (1218595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1218595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1218595)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1218595)Termination reason: Instruction limit
% 0.22/0.32 % (1218595)Termination phase: Saturation
% 0.22/0.32 % (1218595)Time elapsed: 0.004 s
% 0.22/0.32 % (1218595)Peak memory usage: 12 MB
% 0.22/0.32 % (1218595)Instructions burned: 7 (million)
% 0.22/0.32 % (1218568)...printing done.
% 0.22/0.32 % (1218568)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/0.32 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.22/0.32 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(type_def_8, type, sK2: $tType).
% 0.22/0.32 thf(type_def_9, type, sK3: $tType).
% 0.22/0.32 thf(func_def_0, type, 'const/trivia/o': !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X1 > X0) > X1 > X2))).
% 0.22/0.32 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_2, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X1 > $o))).
% 0.22/0.32 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_4, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.22/0.32 thf(func_def_5, type, 'const/realax/real_add': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.22/0.32 thf(func_def_6, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.22/0.32 thf(func_def_7, type, 'const/nums/_0': 'type/nums/num').
% 0.22/0.32 thf(func_def_8, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.22/0.32 thf(func_def_9, type, 'const/iterate/neutral': !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.22/0.32 thf(func_def_10, type, 'const/iterate/monoidal': !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.22/0.32 thf(func_def_11, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:(((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1))).
% 0.22/0.32 thf(func_def_15, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > $o) > (X1 > X2) > (X2 > X0) > (X0 > X0 > X0) > X1))).
% 0.22/0.32 thf(func_def_16, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > $o) > (X1 > X2) > (X2 > X0) > (X0 > X0 > X0) > X1))).
% 0.22/0.32 thf(func_def_17, type, sK4: (sK2 > sK3)).
% 0.22/0.32 thf(func_def_18, type, sK5: (sK3 > 'type/realax/real')).
% 0.22/0.32 thf(func_def_19, type, sK6: (sK2 > $o)).
% 0.22/0.32 thf(func_def_20, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_21, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_22, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(f1,axiom,(
% 0.22/0.32 ! [X2 : $tType,X0 : $tType,X1 : $tType,X3 : (X2 > X2 > X2)] : (('const/iterate/monoidal' @ X2 @ X3) => ! [X4 : (X0 > X2),X6 : (X1 > $o),X5 : (X1 > X0)] : ((('const/sets/FINITE' @ X1 @ X6) & ! [X7 : X1,X8 : X1] : ((('const/sets/IN' @ X1 @ X8 @ X6) & (X7 != X8) & ('const/sets/IN' @ X1 @ X7 @ X6) & (((X5 @ X7)) = ((X5 @ X8)))) => (((X4 @ (X5 @ X7))) = (('const/iterate/neutral' @ X2 @ X3))))) => ((('const/iterate/iterate' @ X0 @ X2 @ X3 @ ('const/sets/IMAGE' @ X1 @ X0 @ X5 @ X6) @ X4)) = (('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ ('const/trivia/o' @ X0 @ X1 @ X2 @ X4 @ X5))))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_IMAGE_NONZERO_')).
% 0.22/0.32 thf(f2,axiom,(
% 0.22/0.32 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.22/0.32 thf(f4,axiom,(
% 0.22/0.32 ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_REAL_ADD_')).
% 0.22/0.32 thf(f5,conjecture,(
% 0.22/0.32 ! [X0 : $tType,X1 : $tType,X3 : (X0 > X1),X2 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X4) & ! [X5 : X0,X6 : X0] : ((('const/sets/IN' @ X0 @ X5 @ X4) & (((X3 @ X5)) = ((X3 @ X6))) & (X5 != X6) & ('const/sets/IN' @ X0 @ X6 @ X4)) => (((X2 @ (X3 @ X5))) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))) => ((('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2)) = (('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3)))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_IMAGE_NONZERO_')).
% 0.22/0.32 thf(f6,negated_conjecture,(
% 0.22/0.32 ~ ! [X0 : $tType,X1 : $tType,X3 : (X0 > X1),X2 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X4) & ! [X5 : X0,X6 : X0] : ((('const/sets/IN' @ X0 @ X5 @ X4) & (((X3 @ X5)) = ((X3 @ X6))) & (X5 != X6) & ('const/sets/IN' @ X0 @ X6 @ X4)) => (((X2 @ (X3 @ X5))) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))) => ((('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2)) = (('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3)))))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f5])).
% 0.22/0.32 thf(f7,plain,(
% 0.22/0.32 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X3) => ! [X4 : (X1 > X0),X5 : (X2 > $o),X6 : (X2 > X1)] : ((('const/sets/FINITE' @ X2 @ X5) & ! [X7 : X2,X8 : X2] : ((('const/sets/IN' @ X2 @ X8 @ X5) & (X7 != X8) & ('const/sets/IN' @ X2 @ X7 @ X5) & (((X6 @ X8)) = ((X6 @ X7)))) => ((('const/iterate/neutral' @ X0 @ X3)) = ((X4 @ (X6 @ X7)))))) => ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ ('const/sets/IMAGE' @ X2 @ X1 @ X6 @ X5) @ X4)) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ X5 @ ('const/trivia/o' @ X1 @ X2 @ X0 @ X4 @ X6))))))),
% 0.22/0.32 inference(rectify,[],[f1])).
% 0.22/0.32 thf(f8,plain,(
% 0.22/0.32 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X3)) = $true) => ! [X5 : (X2 > $o),X4 : (X1 > X0),X6 : (X2 > X1)] : ((! [X8 : X2,X7 : X2] : (((((X6 @ X8)) = ((X6 @ X7))) & ((('const/sets/IN' @ X2 @ X8 @ X5)) = $true) & (X7 != X8) & ((('const/sets/IN' @ X2 @ X7 @ X5)) = $true)) => ((('const/iterate/neutral' @ X0 @ X3)) = ((X4 @ (X6 @ X7))))) & ((('const/sets/FINITE' @ X2 @ X5)) = $true)) => ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ ('const/sets/IMAGE' @ X2 @ X1 @ X6 @ X5) @ X4)) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ X5 @ ('const/trivia/o' @ X1 @ X2 @ X0 @ X4 @ X6))))))),
% 0.22/0.32 inference(fool_elimination,[],[f7])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X4) & ! [X5 : X0,X6 : X0] : ((('const/sets/IN' @ X0 @ X5 @ X4) & (((X2 @ X5)) = ((X2 @ X6))) & (X5 != X6) & ('const/sets/IN' @ X0 @ X6 @ X4)) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X3 @ (X2 @ X5)))))) => ((('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X3 @ X2))) = (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4) @ X3))))),
% 0.22/0.32 inference(rectify,[],[f6])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : ((! [X5 : X0,X6 : X0] : (((X5 != X6) & ((('const/sets/IN' @ X0 @ X5 @ X4)) = $true) & (((X2 @ X5)) = ((X2 @ X6))) & ((('const/sets/IN' @ X0 @ X6 @ X4)) = $true)) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X3 @ (X2 @ X5))))) & ((('const/sets/FINITE' @ X0 @ X4)) = $true)) => ((('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X3 @ X2))) = (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4) @ X3))))),
% 0.22/0.32 inference(fool_elimination,[],[f9])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.22/0.32 inference(fool_elimination,[],[f11])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X0 > X0 > X0)] : (! [X5 : (X2 > $o),X4 : (X1 > X0),X6 : (X2 > X1)] : (((('const/iterate/iterate' @ X1 @ X0 @ X3 @ ('const/sets/IMAGE' @ X2 @ X1 @ X6 @ X5) @ X4)) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ X5 @ ('const/trivia/o' @ X1 @ X2 @ X0 @ X4 @ X6)))) | (? [X8 : X2,X7 : X2] : (((('const/iterate/neutral' @ X0 @ X3)) != ((X4 @ (X6 @ X7)))) & ((((X6 @ X8)) = ((X6 @ X7))) & ((('const/sets/IN' @ X2 @ X8 @ X5)) = $true) & (X7 != X8) & ((('const/sets/IN' @ X2 @ X7 @ X5)) = $true))) | ((('const/sets/FINITE' @ X2 @ X5)) != $true))) | ((('const/iterate/monoidal' @ X0 @ X3)) != $true))),
% 0.22/0.32 inference(ennf_transformation,[],[f8])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 ! [X0 : $tType,X2 : $tType,X1 : $tType,X3 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ! [X4 : (X1 > X0),X6 : (X2 > X1),X5 : (X2 > $o)] : (((('const/sets/FINITE' @ X2 @ X5)) != $true) | ? [X8 : X2,X7 : X2] : (((('const/sets/IN' @ X2 @ X8 @ X5)) = $true) & (((X6 @ X8)) = ((X6 @ X7))) & ((('const/sets/IN' @ X2 @ X7 @ X5)) = $true) & ((('const/iterate/neutral' @ X0 @ X3)) != ((X4 @ (X6 @ X7)))) & (X7 != X8)) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ ('const/sets/IMAGE' @ X2 @ X1 @ X6 @ X5) @ X4)) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ X5 @ ('const/trivia/o' @ X1 @ X2 @ X0 @ X4 @ X6))))))),
% 0.22/0.32 inference(flattening,[],[f13])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : (((('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X3 @ X2))) != (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4) @ X3))) & (! [X5 : X0,X6 : X0] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X3 @ (X2 @ X5)))) | ((X5 = X6) | ((('const/sets/IN' @ X0 @ X5 @ X4)) != $true) | (((X2 @ X5)) != ((X2 @ X6))) | ((('const/sets/IN' @ X0 @ X6 @ X4)) != $true))) & ((('const/sets/FINITE' @ X0 @ X4)) = $true)))),
% 0.22/0.32 inference(ennf_transformation,[],[f10])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > 'type/realax/real'),X4 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X4)) = $true) & ((('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X3 @ X2))) != (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4) @ X3))) & ! [X5 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X4)) != $true) | (((X2 @ X5)) != ((X2 @ X6))) | (X5 = X6) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X3 @ (X2 @ X5)))) | ((('const/sets/IN' @ X0 @ X5 @ X4)) != $true)))),
% 0.22/0.32 inference(flattening,[],[f15])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ! [X4 : (X2 > X0),X5 : (X1 > X2),X6 : (X1 > $o)] : (((('const/sets/FINITE' @ X1 @ X6)) != $true) | ? [X7 : X1,X8 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X6)) = $true) & (((X5 @ X8)) = ((X5 @ X7))) & ((('const/sets/IN' @ X1 @ X8 @ X6)) = $true) & ((('const/iterate/neutral' @ X0 @ X3)) != ((X4 @ (X5 @ X8)))) & (X7 != X8)) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4)))))),
% 0.22/0.32 inference(rectify,[],[f14])).
% 0.22/0.32 thf(f18,plain,(
% 0.22/0.32 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ! [X4 : (X2 > X0),X5 : (X1 > X2),X6 : (X1 > $o)] : (((('const/sets/FINITE' @ X1 @ X6)) != $true) | (((('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) = $true) & (((X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) = ((X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)))) & ((('const/sets/IN' @ X1 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) = $true) & ((('const/iterate/neutral' @ X0 @ X3)) != ((X4 @ (X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))))) & (((sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) != ((sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)))) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4)))))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X8,sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3),skolemize(X8,sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)],[f17])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 ((('const/sets/FINITE' @ sK2 @ sK6)) = $true) & ((('const/iterate/sum' @ sK3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5)) != (('const/iterate/sum' @ sK2 @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4)))) & ! [X5 : sK2,X6 : sK2] : (((('const/sets/IN' @ sK2 @ X6 @ sK6)) != $true) | (((sK4 @ X5)) != ((sK4 @ X6))) | (X5 = X6) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X5)))) | ((('const/sets/IN' @ sK2 @ X5 @ sK6)) != $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X4,sK6)],[f16])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X0 > X0),X6 : (X1 > $o),X4 : (X2 > X0),X5 : (X1 > X2)] : ((((sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) != ((sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4))) | ((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X1 @ X6)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f18])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X0 > X0),X6 : (X1 > $o),X4 : (X2 > X0),X5 : (X1 > X2)] : (((('const/iterate/neutral' @ X0 @ X3)) != ((X4 @ (X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))))) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4))) | ((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X1 @ X6)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f18])).
% 0.22/0.32 thf(f22,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X0 > X0),X6 : (X1 > $o),X4 : (X2 > X0),X5 : (X1 > X2)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4))) | ((('const/sets/IN' @ X1 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) = $true) | ((('const/sets/FINITE' @ X1 @ X6)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f18])).
% 0.22/0.32 thf(f23,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X0 > X0),X6 : (X1 > $o),X4 : (X2 > X0),X5 : (X1 > X2)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4))) | ((('const/sets/FINITE' @ X1 @ X6)) != $true) | (((X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) = ((X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f18])).
% 0.22/0.32 thf(f24,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X0 > X0),X6 : (X1 > $o),X4 : (X2 > X0),X5 : (X1 > X2)] : (((('const/iterate/monoidal' @ X0 @ X3)) != $true) | ((('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) = $true) | ((('const/sets/FINITE' @ X1 @ X6)) != $true) | ((('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) = (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f18])).
% 0.22/0.32 thf(f25,plain,(
% 0.22/0.32 ( ! [X6 : sK2,X5 : sK2] : (((('const/sets/IN' @ sK2 @ X6 @ sK6)) != $true) | (((sK4 @ X5)) != ((sK4 @ X6))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X5)))) | ((('const/sets/IN' @ sK2 @ X5 @ sK6)) != $true) | (X5 = X6)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f19])).
% 0.22/0.32 thf(f26,plain,(
% 0.22/0.32 ((('const/iterate/sum' @ sK3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5)) != (('const/iterate/sum' @ sK2 @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))))),
% 0.22/0.32 inference(cnf_transformation,[],[f19])).
% 0.22/0.32 thf(f27,plain,(
% 0.22/0.32 ((('const/sets/FINITE' @ sK2 @ sK6)) = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f19])).
% 0.22/0.32 thf(f28,plain,(
% 0.22/0.32 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f3])).
% 0.22/0.32 thf(f29,plain,(
% 0.22/0.32 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f12])).
% 0.22/0.32 thf(f30,plain,(
% 0.22/0.32 ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.22/0.32 inference(cnf_transformation,[],[f4])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) != (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5)))),
% 0.22/0.32 inference(definition_unfolding,[],[f26,f28,f28])).
% 0.22/0.32 thf(f34,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : $tType,X3 : (X2 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > X2)] : (((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ ('const/trivia/o' @ X2 @ X0 @ 'type/realax/real' @ X3 @ X4))) = (('const/iterate/iterate' @ X2 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X2 @ X4 @ X1) @ X3))) | ((('const/sets/FINITE' @ X0 @ X1)) != $true) | ($true != $true) | ((('const/sets/IN' @ X0 @ (sK1 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add') @ X1)) = $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f22,f29])).
% 0.22/0.32 thf(f35,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : $tType,X3 : (X2 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > X2)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ ('const/trivia/o' @ X2 @ X0 @ 'type/realax/real' @ X3 @ X4))) = (('const/iterate/iterate' @ X2 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X2 @ X4 @ X1) @ X3))) | ((('const/sets/IN' @ X0 @ (sK1 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add') @ X1)) = $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f34])).
% 0.22/0.32 thf(f36,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (sK2 > X0),X1 : (X0 > 'type/realax/real')] : (((('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X2 @ X1 @ 'const/realax/real_add') @ sK6)) = $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X1 @ X2))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X2 @ sK6) @ X1))) | ($true != $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f35,f27])).
% 0.22/0.32 thf(f37,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (sK2 > X0),X1 : (X0 > 'type/realax/real')] : (((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X1 @ X2))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X2 @ sK6) @ X1))) | ((('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X2 @ X1 @ 'const/realax/real_add') @ sK6)) = $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f36])).
% 0.22/0.32 thf(f41,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X0 > X1),X4 : (X1 > 'type/realax/real')] : (((('const/sets/IN' @ X0 @ (sK0 @ 'type/realax/real' @ X0 @ X1 @ X2 @ X3 @ X4 @ 'const/realax/real_add') @ X2)) = $true) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X2 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X4 @ X3))) = (('const/iterate/iterate' @ X1 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X2) @ X4))) | ($true != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f24,f29])).
% 0.22/0.32 thf(f42,plain,(
% 0.22/0.32 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X0 > X1),X4 : (X1 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ (sK0 @ 'type/realax/real' @ X0 @ X1 @ X2 @ X3 @ X4 @ 'const/realax/real_add') @ X2)) = $true) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X2 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X4 @ X3))) = (('const/iterate/iterate' @ X1 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X2) @ X4)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f41])).
% 0.22/0.32 thf(f43,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (sK2 > X0)] : (((('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add') @ sK6)) = $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | ($true != $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f42,f27])).
% 0.22/0.32 thf(f44,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (sK2 > X0)] : (((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | ((('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add') @ sK6)) = $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f43])).
% 0.22/0.32 thf(f45,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : sK2,X1 : (sK2 > X0)] : ((((sK4 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))) != ((sK4 @ X3))) | ($true != $true) | ((('const/sets/IN' @ sK2 @ X3 @ sK6)) != $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X3)))) | (((sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add')) = X3)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f25,f44])).
% 0.22/0.32 thf(f46,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : sK2,X1 : (sK2 > X0)] : ((((sK4 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))) != ((sK4 @ X3))) | ((('const/sets/IN' @ sK2 @ X3 @ sK6)) != $true) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X3)))) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | (((sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add')) = X3)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.32 thf(f84,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : $tType,X3 : (X2 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > X2)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | ($true != $true) | (((X4 @ (sK0 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add'))) = ((X4 @ (sK1 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add')))) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ ('const/trivia/o' @ X2 @ X0 @ 'type/realax/real' @ X3 @ X4))) = (('const/iterate/iterate' @ X2 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X2 @ X4 @ X1) @ X3)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f23,f29])).
% 0.22/0.32 thf(f85,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : $tType,X3 : (X2 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > X2)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | (((X4 @ (sK0 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add'))) = ((X4 @ (sK1 @ 'type/realax/real' @ X0 @ X2 @ X1 @ X4 @ X3 @ 'const/realax/real_add')))) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ ('const/trivia/o' @ X2 @ X0 @ 'type/realax/real' @ X3 @ X4))) = (('const/iterate/iterate' @ X2 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ X0 @ X2 @ X4 @ X1) @ X3)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.32 thf(f86,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (sK2 > X0)] : (($true != $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | (((X1 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))) = ((X1 @ (sK1 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f85,f27])).
% 0.22/0.32 thf(f87,plain,(
% 0.22/0.32 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (sK2 > X0)] : (((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ X0 @ sK2 @ 'type/realax/real' @ X2 @ X1))) = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK6) @ X2))) | (((X1 @ (sK0 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))) = ((X1 @ (sK1 @ 'type/realax/real' @ sK2 @ X0 @ sK6 @ X1 @ X2 @ 'const/realax/real_add'))))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f86])).
% 0.22/0.32 thf(f99,plain,(
% 0.22/0.32 ( ! [X0 : (sK3 > 'type/realax/real'),X1 : sK2] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X1)))) | ((('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ X0)) = (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ X0 @ sK4)))) | ((('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ X0)) = (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ X0 @ sK4)))) | ((('const/sets/IN' @ sK2 @ X1 @ sK6)) != $true) | (((sK4 @ X1)) != ((sK4 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')))) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')) = X1)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f46,f87])).
% 0.22/0.32 thf(f100,plain,(
% 0.22/0.32 ( ! [X0 : (sK3 > 'type/realax/real'),X1 : sK2] : ((((sK4 @ X1)) != ((sK4 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')))) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')) = X1) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ X1)))) | ((('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ X0)) = (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ X0 @ sK4)))) | ((('const/sets/IN' @ sK2 @ X1 @ sK6)) != $true)) )),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f99])).
% 0.22/0.32 thf(f104,plain,(
% 0.22/0.32 ( ! [X0 : (sK3 > 'type/realax/real')] : (((('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ X0)) = (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ X0 @ sK4)))) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')) = ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add'))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add'))))) | ((('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add') @ sK6)) != $true)) )),
% 0.22/0.32 inference(equality_resolution,[],[f100])).
% 0.22/0.32 thf(f106,plain,(
% 0.22/0.32 ( ! [X0 : (sK3 > 'type/realax/real')] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((sK5 @ (sK4 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add'))))) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add')) = ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ X0 @ 'const/realax/real_add'))) | ((('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ X0)) = (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ X0 @ sK4))))) )),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f104,f37])).
% 0.22/0.32 thf(f125,plain,(
% 0.22/0.32 ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ((('const/sets/FINITE' @ sK2 @ sK6)) != $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) = (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5))) | ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ sK5 @ 'const/realax/real_add')) = ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ sK5 @ 'const/realax/real_add'))) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) = (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5)))),
% 0.22/0.32 inference(constrained_superposition,[],[f21,f106])).
% 0.22/0.32 thf(f126,plain,(
% 0.22/0.32 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true) | ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | (((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ sK5 @ 'const/realax/real_add')) = ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK4 @ sK5 @ 'const/realax/real_add'))) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) = (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5))) | ((('const/sets/FINITE' @ sK2 @ sK6)) != $true)),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f125])).
% 0.22/0.32 thf(f127,plain,(
% 0.22/0.32 ((('const/sets/FINITE' @ sK2 @ sK6)) != $true) | ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) = (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5))) | ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true) | ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f126,f20])).
% 0.22/0.32 thf(f128,plain,(
% 0.22/0.32 ((('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK5 @ sK4))) = (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK4 @ sK6) @ sK5))) | ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f127,f27])).
% 0.22/0.32 thf(f129,plain,(
% 0.22/0.32 ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add')) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f128,f33])).
% 0.22/0.32 thf(f130,plain,(
% 0.22/0.32 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) != $true)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f129,f30])).
% 0.22/0.32 thf(f131,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f130,f29])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (1218568)------------------------------
% 0.22/0.32 % (1218568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1218568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1218568)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1218568)Termination reason: Refutation
% 0.22/0.32 % (1218568)Time elapsed: 0.041 s
% 0.22/0.32 % (1218568)Peak memory usage: 13 MB
% 0.22/0.32 % (1218568)Instructions burned: 73 (million)
% 0.22/0.32 % (1218556)Success in time 0.074 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------