%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM178^1 : 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 : n006.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 07:46:24 AM UTC 2026
% Result : Theorem 0.74s 0.40s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM178^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:48:55 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.27 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
% 0.74/0.40 % (1084168)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.40 % (1084174)lrs+10_16_si=on:nwc=1.5:random_seed=4031632521:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.40 % (1084179)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.40 % (1084179)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
% 0.74/0.40 % (1084174)Instruction limit reached!
% 0.74/0.40 % (1084174)------------------------------
% 0.74/0.40 % (1084174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084174)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084174)Termination reason: Instruction limit
% 0.74/0.40 % (1084174)Termination phase: shuffling
% 0.74/0.40 % (1084174)Time elapsed: 0.005 s
% 0.74/0.40 % (1084174)Peak memory usage: 10 MB
% 0.74/0.40 % (1084174)Instructions burned: 22 (million)
% 0.74/0.40 % (1084173)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3747119535:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.40 % (1084175)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=23021695:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.40 % (1084176)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=1316606974: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)
% 0.74/0.40 % (1084177)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1886761154:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.40 % (1084178)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3056754652:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.40 % (1084179)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=3914622347:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.40 % (1084175)Instruction limit reached!
% 0.74/0.40 % (1084175)------------------------------
% 0.74/0.40 % (1084175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084175)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084175)Termination reason: Instruction limit
% 0.74/0.40 % (1084175)Termination phase: shuffling
% 0.74/0.40 % (1084175)Time elapsed: 0.003 s
% 0.74/0.40 % (1084175)Peak memory usage: 10 MB
% 0.74/0.40 % (1084175)Instructions burned: 6 (million)
% 0.74/0.40 % (1084181)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3987966659:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.40 % (1084181)Instruction limit reached!
% 0.74/0.40 % (1084181)------------------------------
% 0.74/0.40 % (1084181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084181)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084181)Termination reason: Instruction limit
% 0.74/0.40 % (1084181)Termination phase: shuffling
% 0.74/0.40 % (1084181)Time elapsed: 0.0000 s
% 0.74/0.40 % (1084181)Peak memory usage: 10 MB
% 0.74/0.40 % (1084181)Instructions burned: 2 (million)
% 0.74/0.40 % (1084177)Instruction limit reached!
% 0.74/0.40 % (1084177)------------------------------
% 0.74/0.40 % (1084177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084177)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084177)Termination reason: Instruction limit
% 0.74/0.40 % (1084177)Termination phase: Property scanning
% 0.74/0.40 % (1084177)Time elapsed: 0.011 s
% 0.74/0.40 % (1084177)Peak memory usage: 10 MB
% 0.74/0.40 % (1084177)Instructions burned: 24 (million)
% 0.74/0.40 % (1084190)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.40 % (1084190)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2379729435:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.40 % (1084188)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1142640145:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.40 % (1084190)Instruction limit reached!
% 0.74/0.40 % (1084190)------------------------------
% 0.74/0.40 % (1084190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084190)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084190)Termination reason: Instruction limit
% 0.74/0.40 % (1084190)Termination phase: shuffling
% 0.74/0.40 % (1084190)Time elapsed: 0.002 s
% 0.74/0.40 % (1084190)Peak memory usage: 10 MB
% 0.74/0.40 % (1084190)Instructions burned: 9 (million)
% 0.74/0.40 % (1084188)Instruction limit reached!
% 0.74/0.40 % (1084188)------------------------------
% 0.74/0.40 % (1084188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084188)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084188)Termination reason: Instruction limit
% 0.74/0.40 % (1084188)Termination phase: shuffling
% 0.74/0.40 % (1084188)Time elapsed: 0.004 s
% 0.74/0.40 % (1084188)Peak memory usage: 10 MB
% 0.74/0.40 % (1084188)Instructions burned: 7 (million)
% 0.74/0.40 % (1084191)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2881850164:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.40 % (1084194)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
% 0.74/0.40 % (1084194)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.40 % (1084194)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=528091530:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.40 % (1084178)Instruction limit reached!
% 0.74/0.40 % (1084178)------------------------------
% 0.74/0.40 % (1084178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084178)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084178)Termination reason: Instruction limit
% 0.74/0.40 % (1084178)Termination phase: Property scanning
% 0.74/0.40 % (1084178)Time elapsed: 0.036 s
% 0.74/0.40 % (1084178)Peak memory usage: 12 MB
% 0.74/0.40 % (1084178)Instructions burned: 75 (million)
% 0.74/0.40 % (1084191)Instruction limit reached!
% 0.74/0.40 % (1084191)------------------------------
% 0.74/0.40 % (1084191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084191)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084191)Termination reason: Instruction limit
% 0.74/0.40 % (1084191)Termination phase: shuffling
% 0.74/0.40 % (1084191)Time elapsed: 0.006 s
% 0.74/0.40 % (1084191)Peak memory usage: 10 MB
% 0.74/0.40 % (1084191)Instructions burned: 12 (million)
% 0.74/0.40 % (1084194)Instruction limit reached!
% 0.74/0.40 % (1084194)------------------------------
% 0.74/0.40 % (1084194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084194)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084194)Termination reason: Instruction limit
% 0.74/0.40 % (1084194)Termination phase: shuffling
% 0.74/0.40 % (1084194)Time elapsed: 0.008 s
% 0.74/0.40 % (1084194)Peak memory usage: 10 MB
% 0.74/0.40 % (1084194)Instructions burned: 32 (million)
% 0.74/0.40 % (1084195)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=523374218:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.40 % (1084200)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1597337830:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.40 % (1084199)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.40 % (1084198)lrs+10_1_si=on:cs=on:random_seed=3740165202:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.40 % (1084199)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=445926558:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.40 % (1084199)Instruction limit reached!
% 0.74/0.40 % (1084199)------------------------------
% 0.74/0.40 % (1084199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084199)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084199)Termination reason: Instruction limit
% 0.74/0.40 % (1084199)Termination phase: shuffling
% 0.74/0.40 % (1084199)Time elapsed: 0.003 s
% 0.74/0.40 % (1084199)Peak memory usage: 10 MB
% 0.74/0.40 % (1084199)Instructions burned: 6 (million)
% 0.74/0.40 % (1084198)Instruction limit reached!
% 0.74/0.40 % (1084198)------------------------------
% 0.74/0.40 % (1084198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084198)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084198)Termination reason: Instruction limit
% 0.74/0.40 % (1084198)Termination phase: shuffling
% 0.74/0.40 % (1084198)Time elapsed: 0.005 s
% 0.74/0.40 % (1084198)Peak memory usage: 10 MB
% 0.74/0.40 % (1084198)Instructions burned: 10 (million)
% 0.74/0.40 % (1084200)Instruction limit reached!
% 0.74/0.40 % (1084200)------------------------------
% 0.74/0.40 % (1084200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084200)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084200)Termination reason: Instruction limit
% 0.74/0.40 % (1084200)Termination phase: Preprocessing 3
% 0.74/0.40 % (1084200)Time elapsed: 0.010 s
% 0.74/0.40 % (1084200)Peak memory usage: 11 MB
% 0.74/0.40 % (1084200)Instructions burned: 41 (million)
% 0.74/0.40 % (1084207)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1256867735:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.40 % (1084179)Instruction limit reached!
% 0.74/0.40 % (1084179)------------------------------
% 0.74/0.40 % (1084179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084179)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084179)Termination reason: Instruction limit
% 0.74/0.40 % (1084179)Termination phase: Saturation
% 0.74/0.40 % (1084179)Time elapsed: 0.073 s
% 0.74/0.40 % (1084179)Peak memory usage: 14 MB
% 0.74/0.40 % (1084179)Instructions burned: 159 (million)
% 0.74/0.40 % (1084176) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1084168-1084176"...
% 0.74/0.40 % (1084207)Instruction limit reached!
% 0.74/0.40 % (1084207)------------------------------
% 0.74/0.40 % (1084207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084207)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084207)Termination reason: Instruction limit
% 0.74/0.40 % (1084207)Termination phase: shuffling
% 0.74/0.40 % (1084207)Time elapsed: 0.004 s
% 0.74/0.40 % (1084207)Peak memory usage: 10 MB
% 0.74/0.40 % (1084207)Instructions burned: 14 (million)
% 0.74/0.40 % (1084173)Instruction limit reached!
% 0.74/0.40 % (1084173)------------------------------
% 0.74/0.40 % (1084173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084173)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084173)Termination reason: Instruction limit
% 0.74/0.40 % (1084173)Termination phase: Function definition elimination
% 0.74/0.40 % (1084173)Time elapsed: 0.077 s
% 0.74/0.40 % (1084173)Peak memory usage: 12 MB
% 0.74/0.40 % (1084173)Instructions burned: 87 (million)
% 0.74/0.40 % (1084176)...printing done.
% 0.74/0.40 % (1084176)Refutation found. Thanks to Tanya!
% 0.74/0.40 % SZS status Theorem for theBenchmark
% 0.74/0.40 % SZS output start Proof for theBenchmark
% 0.74/0.40 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.74/0.40 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.74/0.40 thf(type_def_7, type, set: $tType > $tType).
% 0.74/0.40 thf(type_def_8, type, itself: $tType > $tType).
% 0.74/0.40 thf(type_def_9, type, node: $tType).
% 0.74/0.40 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.74/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.74/0.40 thf(func_def_1, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.74/0.40 thf(func_def_2, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_3, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.74/0.40 thf(func_def_4, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_5, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_6, type, coindu218763757pWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_7, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_8, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_9, type, coinductive_llexord: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_10, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_11, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.74/0.40 thf(func_def_12, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0))).
% 0.74/0.40 thf(func_def_13, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_14, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_15, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.74/0.40 thf(func_def_16, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_17, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_18, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_19, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_20, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_21, type, coinductive_lzip: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X1 > coinductive_llist @ product_prod @ X0 @ X1))).
% 0.74/0.40 thf(func_def_22, type, coinductive_lsorted: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_23, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 0.74/0.40 thf(func_def_24, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.74/0.40 thf(func_def_25, type, koenig793108494nected: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.74/0.40 thf(func_def_26, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.74/0.40 thf(func_def_28, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.74/0.40 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.74/0.40 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.74/0.40 thf(func_def_31, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.74/0.40 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.74/0.40 thf(func_def_33, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.74/0.40 thf(func_def_34, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.74/0.40 thf(func_def_35, type, f: (product_prod @ node @ set @ node > coinductive_llist @ node)).
% 0.74/0.40 thf(func_def_36, type, graph: (node > node > $o)).
% 0.74/0.40 thf(func_def_37, type, n: node).
% 0.74/0.40 thf(func_def_38, type, ns: set @ node).
% 0.74/0.40 thf(func_def_42, type, db0: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_43, type, db2: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_44, type, db1: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_45, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.74/0.40 thf(func_def_46, type, vOR: ($o > $o > $o)).
% 0.74/0.40 thf(func_def_47, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.74/0.40 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.74/0.40 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.74/0.40 thf(func_def_50, type, db5: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_51, type, db3: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_52, type, db4: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_53, type, db6: !>[X0: $tType]:(X0)).
% 0.74/0.40 thf(func_def_54, type, vIMP: ($o > $o > $o)).
% 0.74/0.40 thf(func_def_55, type, vNOT: ($o > $o)).
% 0.74/0.40 thf(func_def_56, type, sP0: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.74/0.40 thf(func_def_57, type, sK1: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_58, type, sK2: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_59, type, sK3: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_60, type, sK4: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_61, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_62, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_63, type, sK7: !>[X0: $tType]:((set @ X0 > X0))).
% 0.74/0.40 thf(func_def_64, type, sK8: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_65, type, sK9: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_66, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_67, type, sK11: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_68, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_69, type, sK13: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_70, type, sK14: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_71, type, sK15: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.74/0.40 thf(func_def_72, type, sK16: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_73, type, sK17: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_74, type, sK18: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_75, type, sK19: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_76, type, sK20: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_77, type, sK21: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_78, type, sK22: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_79, type, sK23: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_80, type, sK24: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_81, type, sK25: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.74/0.40 thf(func_def_82, type, sK26: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.74/0.40 thf(func_def_83, type, sK27: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_84, type, sK28: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_85, type, sK29: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_86, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X4 > X1))).
% 0.74/0.40 thf(func_def_87, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X4 > X0))).
% 0.74/0.40 thf(func_def_88, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X4 > X3))).
% 0.74/0.40 thf(func_def_89, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X4 > X2))).
% 0.74/0.40 thf(func_def_90, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X4 > X4))).
% 0.74/0.40 thf(func_def_91, type, sK35: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_92, type, sK36: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_93, type, sK37: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.74/0.40 thf(func_def_94, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_95, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_96, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X0))).
% 0.74/0.40 thf(func_def_97, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X1))).
% 0.74/0.40 thf(func_def_98, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X2))).
% 0.74/0.40 thf(func_def_99, type, sK43: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_100, type, sK44: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_101, type, sK45: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_102, type, sK46: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_103, type, sK47: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_104, type, sK48: !>[X0: $tType]:((set @ product_prod @ coinductive_llist @ X0 @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_105, type, sK49: !>[X0: $tType]:((set @ product_prod @ coinductive_llist @ X0 @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_106, type, sK50: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_107, type, sK51: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_108, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.74/0.40 thf(func_def_109, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1))).
% 0.74/0.40 thf(func_def_110, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X0))).
% 0.74/0.40 thf(func_def_111, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3))).
% 0.74/0.40 thf(func_def_112, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X2))).
% 0.74/0.40 thf(func_def_113, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.74/0.40 thf(func_def_114, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.74/0.40 thf(func_def_115, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.74/0.40 thf(func_def_116, type, sK60: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_117, type, sK61: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_118, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_119, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_120, type, sK64: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_121, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X4))).
% 0.74/0.40 thf(func_def_122, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X1))).
% 0.74/0.40 thf(func_def_123, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X3))).
% 0.74/0.40 thf(func_def_124, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X0))).
% 0.74/0.40 thf(func_def_125, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X5))).
% 0.74/0.40 thf(func_def_126, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ X2 > X2))).
% 0.74/0.40 thf(func_def_127, type, sK71: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_128, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X4))).
% 0.74/0.40 thf(func_def_129, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X3))).
% 0.74/0.40 thf(func_def_130, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X0))).
% 0.74/0.40 thf(func_def_131, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X1))).
% 0.74/0.40 thf(func_def_132, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X5))).
% 0.74/0.40 thf(func_def_133, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X2))).
% 0.74/0.40 thf(func_def_134, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.74/0.40 thf(func_def_135, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.74/0.40 thf(func_def_136, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.74/0.40 thf(func_def_137, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.74/0.40 thf(func_def_138, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X6))).
% 0.74/0.40 thf(func_def_139, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X0))).
% 0.74/0.40 thf(func_def_140, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X2))).
% 0.74/0.40 thf(func_def_141, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X5))).
% 0.74/0.40 thf(func_def_142, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X4))).
% 0.74/0.40 thf(func_def_143, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X3))).
% 0.74/0.40 thf(func_def_144, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ X3 > $o) > X1))).
% 0.74/0.40 thf(func_def_145, type, sK89: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_146, type, sK90: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_147, type, sK91: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_148, type, sK92: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_149, type, sK93: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_150, type, sK94: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_151, type, sK95: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_152, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_153, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.74/0.40 thf(func_def_154, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X4))).
% 0.74/0.40 thf(func_def_155, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X3))).
% 0.74/0.40 thf(func_def_156, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.74/0.40 thf(func_def_157, type, sK101: !>[X0: $tType]:((set @ X0 > X0))).
% 0.74/0.40 thf(func_def_158, type, sK102: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_159, type, sK103: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_160, type, sK104: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_161, type, sK105: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.74/0.40 thf(func_def_162, type, sK106: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.74/0.40 thf(func_def_163, type, sK107: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_164, type, sK108: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_165, type, sK109: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_166, type, sK110: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_167, type, sK111: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_168, type, sK112: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_169, type, sK113: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > coinductive_llist @ X1 > coinductive_llist @ X0 > X1))).
% 0.74/0.40 thf(func_def_170, type, sK114: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > coinductive_llist @ X1 > coinductive_llist @ X0 > coinductive_llist @ X1))).
% 0.74/0.40 thf(func_def_171, type, sK115: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > coinductive_llist @ X1 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_172, type, sK116: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X0 @ X1 > product_prod @ X0 @ X1 > coinductive_llist @ X1 > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_173, type, sK117: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_174, type, sK118: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_175, type, sK119: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_176, type, sK120: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_177, type, sK121: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_178, type, sK122: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_179, type, sK123: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.74/0.40 thf(func_def_180, type, sK124: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_181, type, sK125: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_182, type, sK126: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_183, type, sK127: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_184, type, sK128: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_185, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X5))).
% 0.74/0.40 thf(func_def_186, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X1))).
% 0.74/0.40 thf(func_def_187, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X3))).
% 0.74/0.40 thf(func_def_188, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X4))).
% 0.74/0.40 thf(func_def_189, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X0))).
% 0.74/0.40 thf(func_def_190, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X6))).
% 0.74/0.40 thf(func_def_191, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X2))).
% 0.74/0.40 thf(func_def_192, type, sK136: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_193, type, sK137: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_194, type, sK138: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_195, type, sK139: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_196, type, sK140: !>[X0: $tType]:((set @ X0 > X0))).
% 0.74/0.40 thf(func_def_197, type, sK141: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_198, type, sK142: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_199, type, sK143: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > X0))).
% 0.74/0.40 thf(func_def_200, type, sK144: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_201, type, sK145: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_202, type, sK146: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_203, type, sK147: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_204, type, sK148: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_205, type, sK149: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_206, type, sK150: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_207, type, sK151: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_208, type, sK152: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_209, type, sK153: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_210, type, sK154: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_211, type, sK155: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.74/0.40 thf(func_def_212, type, sK156: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_213, type, sK157: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.74/0.40 thf(func_def_214, type, sK158: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.74/0.40 thf(func_def_215, type, sK159: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.74/0.40 thf(f1,axiom,(
% 0.74/0.40 (member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 0.74/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062lhd_A_If_A_In_M_Ans_J_J_A_092_060in_062_Alset_A_If_A_In_M_Ans_J_J_092_060close_062)).
% 0.74/0.40 thf(f2,axiom,(
% 0.74/0.40 (ns = bot_bot @ set @ node)),
% 0.74/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ns__def)).
% 0.74/0.40 thf(f3,axiom,(
% 0.74/0.40 ! [X0 : node,X1 : set @ node] : (((coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) = X0)),
% 0.74/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_f__simps_I2_J)).
% 0.74/0.40 thf(f261,conjecture,(
% 0.74/0.40 (member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 0.74/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.74/0.40 thf(f262,negated_conjecture,(
% 0.74/0.40 ~(member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 0.74/0.40 inference(negated_conjecture,[status(cth)],[f261])).
% 0.74/0.40 thf(f378,plain,(
% 0.74/0.40 (member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 0.74/0.40 inference(rectify,[],[f1])).
% 0.74/0.40 thf(f379,plain,(
% 0.74/0.40 (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 0.74/0.40 inference(fool_elimination,[],[f378])).
% 0.74/0.40 thf(f601,plain,(
% 0.74/0.40 ~(member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 0.74/0.40 inference(rectify,[],[f262])).
% 0.74/0.40 thf(f602,plain,(
% 0.74/0.40 ~ (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 0.74/0.40 inference(fool_elimination,[],[f601])).
% 0.74/0.40 thf(f776,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) != $true)),
% 0.74/0.40 inference(flattening,[],[f602])).
% 0.74/0.40 thf(f1299,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) != $true)),
% 0.74/0.40 inference(cnf_transformation,[],[f776])).
% 0.74/0.40 thf(f1434,plain,(
% 0.74/0.40 (ns = bot_bot @ set @ node)),
% 0.74/0.40 inference(cnf_transformation,[],[f2])).
% 0.74/0.40 thf(f1508,plain,(
% 0.74/0.40 ( ! [X0 : node,X1 : set @ node] : ((((coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) = X0)) )),
% 0.74/0.40 inference(cnf_transformation,[],[f3])).
% 0.74/0.40 thf(f1728,plain,(
% 0.74/0.40 (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 0.74/0.40 inference(cnf_transformation,[],[f379])).
% 0.74/0.40 thf(f1850,definition,(
% 0.74/0.40 spl160_2 <=> (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 0.74/0.40 introduced(definition,[new_symbols(definition,[spl160_2])],[avatar_definition])).
% 0.74/0.40 thf(f1852,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) != $true) | spl160_2),
% 0.74/0.40 inference(avatar_component_clause,[],[f1850])).
% 0.74/0.40 thf(f1853,plain,(
% 0.74/0.40 ~spl160_2),
% 0.74/0.40 inference(avatar_split_clause,[],[f1299,f1850])).
% 0.74/0.40 thf(f1860,definition,(
% 0.74/0.40 spl160_4 <=> (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 0.74/0.40 introduced(definition,[new_symbols(definition,[spl160_4])],[avatar_definition])).
% 0.74/0.40 thf(f1862,plain,(
% 0.74/0.40 (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true) | ~spl160_4),
% 0.74/0.40 inference(avatar_component_clause,[],[f1860])).
% 0.74/0.40 thf(f1863,plain,(
% 0.74/0.40 spl160_4),
% 0.74/0.40 inference(avatar_split_clause,[],[f1728,f1860])).
% 0.74/0.40 thf(f1865,definition,(
% 0.74/0.40 spl160_5 <=> (ns = bot_bot @ set @ node)),
% 0.74/0.40 introduced(definition,[new_symbols(definition,[spl160_5])],[avatar_definition])).
% 0.74/0.40 thf(f1867,plain,(
% 0.74/0.40 (ns = bot_bot @ set @ node) | ~spl160_5),
% 0.74/0.40 inference(avatar_component_clause,[],[f1865])).
% 0.74/0.40 thf(f1868,plain,(
% 0.74/0.40 spl160_5),
% 0.74/0.40 inference(avatar_split_clause,[],[f1434,f1865])).
% 0.74/0.40 thf(f1885,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))))) != $true) | (spl160_2 | ~spl160_5)),
% 0.74/0.40 inference(forward_demodulation,[],[f1852,f1867])).
% 0.74/0.40 thf(f1887,definition,(
% 0.74/0.40 spl160_6 <=> (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))))) = $true)),
% 0.74/0.40 introduced(definition,[new_symbols(definition,[spl160_6])],[avatar_definition])).
% 0.74/0.40 thf(f1889,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))))) != $true) | spl160_6),
% 0.74/0.40 inference(avatar_component_clause,[],[f1887])).
% 0.74/0.40 thf(f1890,plain,(
% 0.74/0.40 ~spl160_6 | spl160_2 | ~spl160_5),
% 0.74/0.40 inference(avatar_split_clause,[],[f1885,f1865,f1850,f1887])).
% 0.74/0.40 thf(f1896,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true) | ~spl160_4),
% 0.74/0.40 inference(forward_demodulation,[],[f1862,f1508])).
% 0.74/0.40 thf(f1897,plain,(
% 0.74/0.40 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))))) = $true) | (~spl160_4 | ~spl160_5)),
% 0.74/0.40 inference(forward_demodulation,[],[f1896,f1867])).
% 0.74/0.40 thf(f1898,plain,(
% 0.74/0.40 $false | (~spl160_4 | ~spl160_5 | spl160_6)),
% 0.74/0.40 inference(forward_subsumption_resolution,[],[f1897,f1889])).
% 0.74/0.40 thf(f1899,plain,(
% 0.74/0.40 ~spl160_4 | ~spl160_5 | spl160_6),
% 0.74/0.40 inference(avatar_contradiction_clause,[],[f1898])).
% 0.74/0.40 cnf(s2, plain, ~spl160_2, inference(sat_conversion,[],[f1853])).
% 0.74/0.40 cnf(s4, plain, spl160_4, inference(sat_conversion,[],[f1863])).
% 0.74/0.40 cnf(s5, plain, spl160_5, inference(sat_conversion,[],[f1868])).
% 0.74/0.40 cnf(s6, plain, spl160_2 | ~spl160_5 | ~spl160_6, inference(sat_conversion,[],[f1890])).
% 0.74/0.40 cnf(s7, plain, ~spl160_4 | ~spl160_5 | spl160_6, inference(sat_conversion,[],[f1899])).
% 0.74/0.40 cnf(s8, plain, spl160_6, inference(rat,[],[s7,s5,s4])).
% 0.74/0.40 cnf(s9, plain, spl160_2, inference(rat,[],[s6,s5,s8])).
% 0.74/0.40 cnf(s10, plain, $false, inference(rat,[],[s2,s9])).
% 0.74/0.40 thf(f1900,plain,(
% 0.74/0.40 $false),
% 0.74/0.40 inference(avatar_sat_refutation,[],[s10])).
% 0.74/0.40 % SZS output end Proof for theBenchmark
% 0.74/0.40 % (1084176)------------------------------
% 0.74/0.40 % (1084176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (1084176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (1084176)CaDiCaL version: 2.1.3
% 0.74/0.40 % (1084176)Termination reason: Refutation
% 0.74/0.40 % (1084176)Time elapsed: 0.076 s
% 0.74/0.40 % (1084176)Peak memory usage: 14 MB
% 0.74/0.40 % (1084176)Instructions burned: 155 (million)
% 0.74/0.40 % (1084168)Success in time 0.123 s
% 0.74/0.41 % Vampire exiting
%------------------------------------------------------------------------------