%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV513^1 : 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 : n019.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 08:38:47 AM UTC 2026
% Result : Theorem 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV513^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:55:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.35 % (960747)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.35 % (960756)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1985507712:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.35 % (960758)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.35 % (960758)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
% 0.21/0.35 % (960752)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=189535485:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.35 % (960753)lrs+10_16_si=on:nwc=1.5:random_seed=896154588:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.35 % (960754)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4058075460:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.35 % (960755)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=1061270917: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)
% 0.21/0.35 % (960757)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=208475103:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.35 % (960758)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=739345441:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.35 % (960756)Instruction limit reached!
% 0.21/0.35 % (960756)------------------------------
% 0.21/0.35 % (960756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960756)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960756)Termination reason: Instruction limit
% 0.21/0.35 % (960756)Termination phase: Saturation
% 0.21/0.35 % (960756)Time elapsed: 0.008 s
% 0.21/0.35 % (960756)Peak memory usage: 12 MB
% 0.21/0.35 % (960756)Instructions burned: 25 (million)
% 0.21/0.35 % (960754)Instruction limit reached!
% 0.21/0.35 % (960754)------------------------------
% 0.21/0.35 % (960754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960754)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960754)Termination reason: Instruction limit
% 0.21/0.35 % (960754)Termination phase: Property scanning
% 0.21/0.35 % (960754)Time elapsed: 0.002 s
% 0.21/0.35 % (960754)Peak memory usage: 10 MB
% 0.21/0.35 % (960754)Instructions burned: 3 (million)
% 0.21/0.35 % (960752)Refutation not found, incomplete strategy
% 0.21/0.35 % (960752)------------------------------
% 0.21/0.35 % (960752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960752)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960752)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.35 % (960752)Time elapsed: 0.004 s
% 0.21/0.35 % (960752)Peak memory usage: 12 MB
% 0.21/0.35 % (960752)Instructions burned: 6 (million)
% 0.21/0.35 % (960752)------------------------------
% 0.21/0.35 % (960752)------------------------------
% 0.21/0.35 % (960753)Instruction limit reached!
% 0.21/0.35 % (960753)------------------------------
% 0.21/0.35 % (960753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960753)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960753)Termination reason: Instruction limit
% 0.21/0.35 % (960753)Termination phase: Saturation
% 0.21/0.35 % (960753)Time elapsed: 0.010 s
% 0.21/0.35 % (960753)Peak memory usage: 12 MB
% 0.21/0.35 % (960753)Instructions burned: 18 (million)
% 0.21/0.35 % (960766)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1079352846:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (960766)Instruction limit reached!
% 0.21/0.35 % (960766)------------------------------
% 0.21/0.35 % (960766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960766)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960766)Termination reason: Instruction limit
% 0.21/0.35 % (960766)Termination phase: Saturation
% 0.21/0.35 % (960766)Time elapsed: 0.001 s
% 0.21/0.35 % (960766)Peak memory usage: 12 MB
% 0.21/0.35 % (960766)Instructions burned: 4 (million)
% 0.21/0.35 % (960768)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.35 % (960767)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=367282131:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.35 % (960771)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
% 0.21/0.35 % (960771)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.35 % (960768)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1539515193:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.35 % (960771)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3981202157:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.35 % (960767)Instruction limit reached!
% 0.21/0.35 % (960767)------------------------------
% 0.21/0.35 % (960767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960767)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960767)Termination reason: Instruction limit
% 0.21/0.35 % (960767)Termination phase: Saturation
% 0.21/0.35 % (960767)Time elapsed: 0.003 s
% 0.21/0.35 % (960767)Peak memory usage: 12 MB
% 0.21/0.35 % (960767)Instructions burned: 5 (million)
% 0.21/0.35 % (960768)Instruction limit reached!
% 0.21/0.35 % (960768)------------------------------
% 0.21/0.35 % (960768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960768)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960768)Termination reason: Instruction limit
% 0.21/0.35 % (960768)Termination phase: Saturation
% 0.21/0.35 % (960768)Time elapsed: 0.004 s
% 0.21/0.35 % (960768)Peak memory usage: 12 MB
% 0.21/0.35 % (960768)Instructions burned: 7 (million)
% 0.21/0.35 % (960769)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2300590981:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.35 % (960771)Instruction limit reached!
% 0.21/0.35 % (960771)------------------------------
% 0.21/0.35 % (960771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960771)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960771)Termination reason: Instruction limit
% 0.21/0.35 % (960771)Termination phase: Saturation
% 0.21/0.35 % (960771)Time elapsed: 0.008 s
% 0.21/0.35 % (960771)Peak memory usage: 12 MB
% 0.21/0.35 % (960771)Instructions burned: 30 (million)
% 0.21/0.35 % (960769)Instruction limit reached!
% 0.21/0.35 % (960769)------------------------------
% 0.21/0.35 % (960769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960769)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960769)Termination reason: Instruction limit
% 0.21/0.35 % (960769)Termination phase: Saturation
% 0.21/0.35 % (960769)Time elapsed: 0.008 s
% 0.21/0.35 % (960769)Peak memory usage: 12 MB
% 0.21/0.35 % (960769)Instructions burned: 12 (million)
% 0.21/0.35 % (960757)Instruction limit reached!
% 0.21/0.35 % (960757)------------------------------
% 0.21/0.35 % (960757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960757)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960757)Termination reason: Instruction limit
% 0.21/0.35 % (960757)Termination phase: Saturation
% 0.21/0.35 % (960757)Time elapsed: 0.036 s
% 0.21/0.35 % (960757)Peak memory usage: 12 MB
% 0.21/0.35 % (960757)Instructions burned: 77 (million)
% 0.21/0.35 % (960778)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.35 % (960778)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1942804405:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (960775)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1806027870:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.35 % (960778)Instruction limit reached!
% 0.21/0.35 % (960778)------------------------------
% 0.21/0.35 % (960778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960778)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960778)Termination reason: Instruction limit
% 0.21/0.35 % (960778)Termination phase: Preprocessing 1
% 0.21/0.35 % (960778)Time elapsed: 0.0000 s
% 0.21/0.35 % (960778)Peak memory usage: 10 MB
% 0.21/0.35 % (960778)Instructions burned: 2 (million)
% 0.21/0.35 % (960777)lrs+10_1_si=on:cs=on:random_seed=3107244272:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.35 % (960783)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3761121081:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.21/0.35 % (960779)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2754008086:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.35 % (960780)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2297869004:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.35 % (960780)Refutation not found, incomplete strategy
% 0.21/0.35 % (960780)------------------------------
% 0.21/0.35 % (960780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960780)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960780)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.35 % (960780)Time elapsed: 0.003 s
% 0.21/0.35 % (960780)Peak memory usage: 12 MB
% 0.21/0.35 % (960780)Instructions burned: 5 (million)
% 0.21/0.35 % (960777)Instruction limit reached!
% 0.21/0.35 % (960777)------------------------------
% 0.21/0.35 % (960777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960777)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960777)Termination reason: Instruction limit
% 0.21/0.35 % (960777)Termination phase: Saturation
% 0.21/0.35 % (960777)Time elapsed: 0.012 s
% 0.21/0.35 % (960777)Peak memory usage: 12 MB
% 0.21/0.35 % (960777)Instructions burned: 8 (million)
% 0.21/0.35 % (960780)------------------------------
% 0.21/0.35 % (960780)------------------------------
% 0.21/0.35 % (960779) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-960747-960779"...
% 0.21/0.35 % (960783)Instruction limit reached!
% 0.21/0.35 % (960783)------------------------------
% 0.21/0.35 % (960783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960783)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960783)Termination reason: Instruction limit
% 0.21/0.35 % (960783)Termination phase: Saturation
% 0.21/0.35 % (960783)Time elapsed: 0.008 s
% 0.21/0.35 % (960783)Peak memory usage: 12 MB
% 0.21/0.35 % (960783)Instructions burned: 26 (million)
% 0.21/0.35 % (960779)...printing done.
% 0.21/0.35 % (960779)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Theorem for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% 0.21/0.35 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.35 thf(type_def_7, type, sK0: $tType).
% 0.21/0.35 thf(func_def_0, type, 'const/sets/SETSPEC': !>[X0: $tType]:((X0 > $o > X0 > $o))).
% 0.21/0.35 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.35 thf(func_def_2, type, 'const/sets/GSPEC': !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.21/0.35 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.35 thf(func_def_4, type, 'const/realax/real_add': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.21/0.35 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.21/0.35 thf(func_def_6, type, 'const/iterate/monoidal': !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.21/0.35 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:(((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1))).
% 0.21/0.35 thf(func_def_8, type, 'const/class/COND': !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.35 thf(func_def_14, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.35 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 0.21/0.35 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.21/0.35 thf(func_def_18, type, sK1: (sK0 > $o)).
% 0.21/0.35 thf(func_def_19, type, sK2: (sK0 > $o)).
% 0.21/0.35 thf(func_def_20, type, sK3: (sK0 > 'type/realax/real')).
% 0.21/0.35 thf(func_def_21, type, sK4: (sK0 > 'type/realax/real')).
% 0.21/0.35 thf(f1,axiom,(
% 0.21/0.35 ! [X2 : $tType,X0 : $tType,X1 : (X2 > X2 > X2)] : (('const/iterate/monoidal' @ X2 @ X1) => ! [X4 : (X0 > $o),X5 : (X0 > X2),X6 : (X0 > X2),X3 : (X0 > $o)] : (('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))))))),
% 0.21/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CASES_')).
% 0.21/0.35 thf(f2,axiom,(
% 0.21/0.35 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.21/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.21/0.35 thf(f3,axiom,(
% 0.21/0.35 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))),
% 0.21/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.21/0.35 thf(f4,conjecture,(
% 0.21/0.35 ! [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 @ (^[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 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ('const/sets/IN' @ X0 @ X6 @ X1) & ~(X2 @ X6) @ X6)))) @ X4)))))),
% 0.21/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CASES_')).
% 0.21/0.35 thf(f5,negated_conjecture,(
% 0.21/0.35 ~ ! [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 @ (^[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 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ('const/sets/IN' @ X0 @ X6 @ X1) & ~(X2 @ X6) @ X6)))) @ X4)))))),
% 0.21/0.35 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.35 thf(f6,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X2) => ! [X3 : (X1 > $o),X4 : (X1 > X0),X5 : (X1 > X0),X6 : (X1 > $o)] : (('const/sets/FINITE' @ X1 @ X6) => ((('const/iterate/iterate' @ X1 @ X0 @ X2 @ X6 @ (^[X7 : X1] : (('const/class/COND' @ X0 @ (X3 @ X7) @ (X4 @ X7) @ (X5 @ X7)))))) = ((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[X8 : X1] : (? [X9 : X1] : ('const/sets/SETSPEC' @ X1 @ X8 @ ('const/sets/IN' @ X1 @ X9 @ X6) & (X3 @ X9) @ X9)))) @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[X10 : X1] : (? [X11 : X1] : ('const/sets/SETSPEC' @ X1 @ X10 @ ('const/sets/IN' @ X1 @ X11 @ X6) & ~(X3 @ X11) @ X11)))) @ X5))))))),
% 0.21/0.35 inference(rectify,[],[f1])).
% 0.21/0.35 thf(f7,plain,(
% 0.21/0.35 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X0 > X0)] : (($true = (('const/iterate/monoidal' @ X0 @ X2))) => ! [X3 : (X1 > $o),X5 : (X1 > X0),X4 : (X1 > X0),X6 : (X1 > $o)] : (($true = (('const/sets/FINITE' @ X1 @ X6))) => (((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[Y0 : X1]: (?? @ X1 @ (^[Y1 : X1]: ('const/sets/SETSPEC' @ X1 @ Y0 @ ((X3 @ Y1) & ('const/sets/IN' @ X1 @ Y1 @ X6)) @ Y1))))) @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[Y0 : X1]: (?? @ X1 @ (^[Y1 : X1]: ('const/sets/SETSPEC' @ X1 @ Y0 @ ((~ (X3 @ Y1)) & ('const/sets/IN' @ X1 @ Y1 @ X6)) @ Y1))))) @ X5))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ X6 @ (^[Y0 : X1]: ('const/class/COND' @ X0 @ (X3 @ Y0) @ (X4 @ Y0) @ (X5 @ Y0))))))))),
% 0.21/0.35 inference(fool_elimination,[],[f6])).
% 0.21/0.35 thf(f8,plain,(
% 0.21/0.35 ~ ! [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 @ ('const/sets/IN' @ X0 @ X7 @ X1) & (X2 @ X7) @ 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)))))),
% 0.21/0.35 inference(rectify,[],[f5])).
% 0.21/0.35 thf(f9,plain,(
% 0.21/0.35 ~ ! [X0 : $tType,X3 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X4 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : (((('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)))))))),
% 0.21/0.35 inference(fool_elimination,[],[f8])).
% 0.21/0.35 thf(f10,plain,(
% 0.21/0.35 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.21/0.35 inference(rectify,[],[f2])).
% 0.21/0.35 thf(f11,plain,(
% 0.21/0.35 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.21/0.35 inference(fool_elimination,[],[f10])).
% 0.21/0.35 thf(f12,plain,(
% 0.21/0.35 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X0 > X0)] : (! [X4 : (X1 > X0),X3 : (X1 > $o),X6 : (X1 > $o),X5 : (X1 > X0)] : ((((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[Y0 : X1]: (?? @ X1 @ (^[Y1 : X1]: ('const/sets/SETSPEC' @ X1 @ Y0 @ ((X3 @ Y1) & ('const/sets/IN' @ X1 @ Y1 @ X6)) @ Y1))))) @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/GSPEC' @ X1 @ (^[Y0 : X1]: (?? @ X1 @ (^[Y1 : X1]: ('const/sets/SETSPEC' @ X1 @ Y0 @ ((~ (X3 @ Y1)) & ('const/sets/IN' @ X1 @ Y1 @ X6)) @ Y1))))) @ X5))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ X6 @ (^[Y0 : X1]: ('const/class/COND' @ X0 @ (X3 @ Y0) @ (X4 @ Y0) @ (X5 @ Y0)))))) | ($true != (('const/sets/FINITE' @ X1 @ X6)))) | ($true != (('const/iterate/monoidal' @ X0 @ X2))))),
% 0.21/0.35 inference(ennf_transformation,[],[f7])).
% 0.21/0.35 thf(f13,plain,(
% 0.21/0.35 ? [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X4 : (X0 > 'type/realax/real'),X3 : (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)))))))),
% 0.21/0.35 inference(ennf_transformation,[],[f9])).
% 0.21/0.35 thf(f14,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (! [X3 : (X0 > X1),X4 : (X0 > $o),X5 : (X0 > $o),X6 : (X0 > X1)] : (((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X3 @ Y0) @ (X6 @ Y0))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X5)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X5)) @ Y1))))) @ X6)))) | ($true != (('const/sets/FINITE' @ X0 @ X5)))) | ($true != (('const/iterate/monoidal' @ X1 @ X2))))),
% 0.21/0.35 inference(rectify,[],[f12])).
% 0.21/0.35 thf(f15,plain,(
% 0.21/0.35 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) & ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X1 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X2)) @ Y1))))) @ X4) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X1 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X2)) @ Y1))))) @ X3))) != (('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X1 @ Y0) @ (X4 @ Y0) @ (X3 @ Y0)))))))),
% 0.21/0.35 inference(rectify,[],[f13])).
% 0.21/0.35 thf(f16,plain,(
% 0.21/0.35 ((('const/sets/FINITE' @ sK0 @ sK2)) = $true) & ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK1 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK4) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK1 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK3))) != (('const/iterate/sum' @ sK0 @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK1 @ Y0) @ (sK4 @ Y0) @ (sK3 @ Y0))))))),
% 0.21/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f15])).
% 0.21/0.35 thf(f17,plain,(
% 0.21/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X1 > X1),X3 : (X0 > X1),X6 : (X0 > X1),X4 : (X0 > $o),X5 : (X0 > $o)] : (((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X3 @ Y0) @ (X6 @ Y0))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X5)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X5)) @ Y1))))) @ X6)))) | ($true != (('const/iterate/monoidal' @ X1 @ X2))) | ($true != (('const/sets/FINITE' @ X0 @ X5)))) )),
% 0.21/0.35 inference(cnf_transformation,[],[f14])).
% 0.21/0.35 thf(f18,plain,(
% 0.21/0.35 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.21/0.35 inference(cnf_transformation,[],[f11])).
% 0.21/0.35 thf(f19,plain,(
% 0.21/0.35 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))) )),
% 0.21/0.35 inference(cnf_transformation,[],[f3])).
% 0.21/0.35 thf(f20,plain,(
% 0.21/0.35 ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK1 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK4) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK1 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK3))) != (('const/iterate/sum' @ sK0 @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK1 @ Y0) @ (sK4 @ Y0) @ (sK3 @ Y0))))))),
% 0.21/0.35 inference(cnf_transformation,[],[f16])).
% 0.21/0.35 thf(f21,plain,(
% 0.21/0.35 ((('const/sets/FINITE' @ sK0 @ sK2)) = $true)),
% 0.21/0.35 inference(cnf_transformation,[],[f16])).
% 0.21/0.35 thf(f24,plain,(
% 0.21/0.35 ((('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 @ ((sK1 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK4) @ ('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 @ ((~ (sK1 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ Y1))))) @ sK3))) != (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK1 @ Y0) @ (sK4 @ Y0) @ (sK3 @ Y0))))))),
% 0.21/0.35 inference(definition_unfolding,[],[f20,f19,f19,f19])).
% 0.21/0.35 thf(f25,plain,(
% 0.21/0.35 ( ! [X2 : (sK0 > 'type/realax/real'),X0 : (sK0 > $o),X1 : (sK0 > 'type/realax/real')] : (((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (X0 @ Y0) @ (X1 @ Y0) @ (X2 @ 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 @ ((X0 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK2)) @ 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 @ sK2)) @ Y1))))) @ X2))))) )),
% 0.21/0.35 inference(unit_resulting_resolution,[],[f17,f21,f18])).
% 0.21/0.35 thf(f27,plain,(
% 0.21/0.35 ((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK1 @ Y0) @ (sK4 @ Y0) @ (sK3 @ Y0))))) != (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK1 @ Y0) @ (sK4 @ Y0) @ (sK3 @ Y0))))))),
% 0.21/0.35 inference(backward_demodulation,[],[f24,f25])).
% 0.21/0.35 thf(f28,plain,(
% 0.21/0.35 $false),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f27])).
% 0.21/0.35 % SZS output end Proof for theBenchmark
% 0.21/0.35 % (960779)------------------------------
% 0.21/0.35 % (960779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (960779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (960779)CaDiCaL version: 2.1.3
% 0.21/0.35 % (960779)Termination reason: Refutation
% 0.21/0.35 % (960779)Time elapsed: 0.007 s
% 0.21/0.35 % (960779)Peak memory usage: 12 MB
% 0.21/0.35 % (960779)Instructions burned: 12 (million)
% 0.21/0.35 % (960747)Success in time 0.102 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------