%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP154^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:08:35 AM UTC 2026
% Result : Theorem 0.60s 0.40s
% Output : Refutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP154^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.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 20:02:46 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
% 0.09/0.25 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
% 0.60/0.40 % (572433)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.60/0.40 % (572442)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=393956652:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.60/0.40 % (572444)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.60/0.40 % (572444)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
% 0.60/0.40 % (572439)lrs+10_16_si=on:nwc=1.5:random_seed=2945469231:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.60/0.40 % (572438)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=423092923:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.60/0.40 % (572440)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4163908531:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.60/0.40 % (572442)Instruction limit reached!
% 0.60/0.40 % (572442)------------------------------
% 0.60/0.40 % (572442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572442)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572442)Termination reason: Instruction limit
% 0.60/0.40 % (572442)Termination phase: Property scanning
% 0.60/0.40 % (572442)Time elapsed: 0.007 s
% 0.60/0.40 % (572442)Peak memory usage: 10 MB
% 0.60/0.40 % (572442)Instructions burned: 27 (million)
% 0.60/0.40 % (572441)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=669210224: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)
% 0.60/0.40 % (572443)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3202150748:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.60/0.40 % (572444)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=2588675129:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.60/0.40 % (572440)Instruction limit reached!
% 0.60/0.40 % (572440)------------------------------
% 0.60/0.40 % (572440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572440)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572440)Termination reason: Instruction limit
% 0.60/0.40 % (572440)Termination phase: shuffling
% 0.60/0.40 % (572440)Time elapsed: 0.002 s
% 0.60/0.40 % (572440)Peak memory usage: 10 MB
% 0.60/0.40 % (572440)Instructions burned: 4 (million)
% 0.60/0.40 % (572439)Instruction limit reached!
% 0.60/0.40 % (572439)------------------------------
% 0.60/0.40 % (572439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572439)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572439)Termination reason: Instruction limit
% 0.60/0.40 % (572439)Termination phase: shuffling
% 0.60/0.40 % (572439)Time elapsed: 0.009 s
% 0.60/0.40 % (572439)Peak memory usage: 10 MB
% 0.60/0.40 % (572439)Instructions burned: 19 (million)
% 0.60/0.40 % (572452)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1720902870:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.40 % (572452)Instruction limit reached!
% 0.60/0.40 % (572452)------------------------------
% 0.60/0.40 % (572452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572452)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572452)Termination reason: Instruction limit
% 0.60/0.40 % (572452)Termination phase: shuffling
% 0.60/0.40 % (572452)Time elapsed: 0.004 s
% 0.60/0.40 % (572452)Peak memory usage: 10 MB
% 0.60/0.40 % (572452)Instructions burned: 15 (million)
% 0.60/0.40 % (572455)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.40 % (572455)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=696359843:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.60/0.40 % (572455)Instruction limit reached!
% 0.60/0.40 % (572455)------------------------------
% 0.60/0.40 % (572455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572455)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572455)Termination reason: Instruction limit
% 0.60/0.40 % (572455)Termination phase: shuffling
% 0.60/0.40 % (572455)Time elapsed: 0.002 s
% 0.60/0.40 % (572455)Peak memory usage: 10 MB
% 0.60/0.40 % (572455)Instructions burned: 9 (million)
% 0.60/0.40 % (572453)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3432487041:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.60/0.40 % (572453)Instruction limit reached!
% 0.60/0.40 % (572453)------------------------------
% 0.60/0.40 % (572453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572453)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572453)Termination reason: Instruction limit
% 0.60/0.40 % (572453)Termination phase: shuffling
% 0.60/0.40 % (572453)Time elapsed: 0.002 s
% 0.60/0.40 % (572453)Peak memory usage: 10 MB
% 0.60/0.40 % (572453)Instructions burned: 7 (million)
% 0.60/0.40 % (572443)Instruction limit reached!
% 0.60/0.40 % (572443)------------------------------
% 0.60/0.40 % (572443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572443)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572443)Termination reason: Instruction limit
% 0.60/0.40 % (572443)Termination phase: Property scanning
% 0.60/0.40 % (572443)Time elapsed: 0.038 s
% 0.60/0.40 % (572443)Peak memory usage: 12 MB
% 0.60/0.40 % (572443)Instructions burned: 77 (million)
% 0.60/0.40 % (572458)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
% 0.60/0.40 % (572458)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.40 % (572458)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=287973488:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.60/0.40 % (572438)Instruction limit reached!
% 0.60/0.40 % (572438)------------------------------
% 0.60/0.40 % (572438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572438)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572438)Termination reason: Instruction limit
% 0.60/0.40 % (572438)Termination phase: Function definition elimination
% 0.60/0.40 % (572438)Time elapsed: 0.043 s
% 0.60/0.40 % (572438)Peak memory usage: 12 MB
% 0.60/0.40 % (572438)Instructions burned: 89 (million)
% 0.60/0.40 % (572456)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4071865566:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.60/0.40 % (572458)Instruction limit reached!
% 0.60/0.40 % (572458)------------------------------
% 0.60/0.40 % (572458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572458)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572458)Termination reason: Instruction limit
% 0.60/0.40 % (572458)Termination phase: shuffling
% 0.60/0.40 % (572458)Time elapsed: 0.007 s
% 0.60/0.40 % (572458)Peak memory usage: 10 MB
% 0.60/0.40 % (572458)Instructions burned: 29 (million)
% 0.60/0.40 % (572460)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=2340171821:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.60/0.40 % (572456)Instruction limit reached!
% 0.60/0.40 % (572456)------------------------------
% 0.60/0.40 % (572456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572456)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572456)Termination reason: Instruction limit
% 0.60/0.40 % (572456)Termination phase: shuffling
% 0.60/0.40 % (572456)Time elapsed: 0.007 s
% 0.60/0.40 % (572456)Peak memory usage: 10 MB
% 0.60/0.40 % (572456)Instructions burned: 14 (million)
% 0.60/0.40 % (572463)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.60/0.40 % (572461)lrs+10_1_si=on:cs=on:random_seed=2660900913:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.60/0.40 % (572463)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=3235352824:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.40 % (572461)Instruction limit reached!
% 0.60/0.40 % (572461)------------------------------
% 0.60/0.40 % (572461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572461)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572461)Termination reason: Instruction limit
% 0.60/0.40 % (572461)Termination phase: shuffling
% 0.60/0.40 % (572461)Time elapsed: 0.005 s
% 0.60/0.40 % (572461)Peak memory usage: 10 MB
% 0.60/0.40 % (572461)Instructions burned: 9 (million)
% 0.60/0.40 % (572463)Instruction limit reached!
% 0.60/0.40 % (572463)------------------------------
% 0.60/0.40 % (572463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572463)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572463)Termination reason: Instruction limit
% 0.60/0.40 % (572463)Termination phase: shuffling
% 0.60/0.40 % (572463)Time elapsed: 0.003 s
% 0.60/0.40 % (572463)Peak memory usage: 10 MB
% 0.60/0.40 % (572463)Instructions burned: 5 (million)
% 0.60/0.40 % (572465)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=746099106:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.60/0.40 % (572444)Instruction limit reached!
% 0.60/0.40 % (572444)------------------------------
% 0.60/0.40 % (572444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572444)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572444)Termination reason: Instruction limit
% 0.60/0.40 % (572444)Termination phase: Saturation
% 0.60/0.40 % (572444)Time elapsed: 0.072 s
% 0.60/0.40 % (572444)Peak memory usage: 14 MB
% 0.60/0.40 % (572444)Instructions burned: 159 (million)
% 0.60/0.40 % (572467)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2427651251:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.60/0.40 % (572441) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-572433-572441"...
% 0.60/0.40 % (572460)Instruction limit reached!
% 0.60/0.40 % (572460)------------------------------
% 0.60/0.40 % (572460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572460)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572460)Termination reason: Instruction limit
% 0.60/0.40 % (572460)Termination phase: Preprocessing 3
% 0.60/0.40 % (572460)Time elapsed: 0.021 s
% 0.60/0.40 % (572460)Peak memory usage: 11 MB
% 0.60/0.40 % (572460)Instructions burned: 90 (million)
% 0.60/0.40 % (572441)...printing done.
% 0.60/0.40 % (572441)Refutation found. Thanks to Tanya!
% 0.60/0.40 % SZS status Theorem for theBenchmark
% 0.60/0.40 % SZS output start Proof for theBenchmark
% 0.60/0.40 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.60/0.40 thf(type_def_6, type, set: $tType > $tType).
% 0.60/0.40 thf(type_def_7, type, a: $tType).
% 0.60/0.40 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.60/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_1, type, inf: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_2, type, sup: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_3, type, bot: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_6, type, lattice: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_7, type, finite_finite: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_8, type, linorder: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_9, type, preorder: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_10, type, order_bot: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_11, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_12, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.60/0.40 thf(func_def_13, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.60/0.40 thf(func_def_14, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.60/0.40 thf(func_def_15, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_16, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_17, type, lattic929149872er_Max: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_18, type, lattic929674654er_Min: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_19, type, lattic1704895705min_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_20, type, lattic2065218050nf_fin: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_21, type, lattic477160up_fin: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_22, type, order_preorder_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_23, type, order_under: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > set @ X0))).
% 0.60/0.40 thf(func_def_24, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.60/0.40 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.60/0.40 thf(func_def_26, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_27, type, prefer951318096ood_as: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.60/0.40 thf(func_def_28, type, prefer310429814s_good: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.60/0.40 thf(func_def_29, type, prefer1532642881r_than: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.60/0.40 thf(func_def_30, type, prefer199794634erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_31, type, prefer1997167224erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_32, type, prefer1801827867axioms: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_33, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.60/0.40 thf(func_def_34, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.60/0.40 thf(func_def_35, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.60/0.40 thf(func_def_36, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.60/0.40 thf(func_def_37, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_38, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_39, type, trans: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.60/0.40 thf(func_def_40, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.60/0.40 thf(func_def_41, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.60/0.40 thf(func_def_42, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.60/0.40 thf(func_def_43, type, carrier: set @ a).
% 0.60/0.40 thf(func_def_44, type, relation: set @ product_prod @ a @ a).
% 0.60/0.40 thf(func_def_45, type, x: a).
% 0.60/0.40 thf(func_def_46, type, y: a).
% 0.60/0.40 thf(func_def_50, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.60/0.40 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.60/0.40 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 0.60/0.40 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.60/0.40 thf(func_def_54, type, db2: !>[X0: $tType]:(X0)).
% 0.60/0.40 thf(func_def_55, type, db3: !>[X0: $tType]:(X0)).
% 0.60/0.40 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 0.60/0.40 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.60/0.40 thf(func_def_58, type, vNOT: ($o > $o)).
% 0.60/0.40 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 0.60/0.40 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.60/0.40 thf(func_def_61, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.60/0.40 thf(func_def_62, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.60/0.40 thf(func_def_63, type, sK2: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_64, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_65, type, sK4: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_66, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_67, type, sK6: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_68, type, sK7: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_69, type, sK8: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_70, type, sK9: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_71, type, sK10: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_72, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_73, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.60/0.40 thf(func_def_74, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.60/0.40 thf(func_def_75, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X3))).
% 0.60/0.40 thf(func_def_76, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.60/0.40 thf(func_def_77, type, sK16: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_78, type, sK17: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_79, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X1))).
% 0.60/0.40 thf(func_def_80, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X0))).
% 0.60/0.40 thf(func_def_81, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X4))).
% 0.60/0.40 thf(func_def_82, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X3))).
% 0.60/0.40 thf(func_def_83, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X2))).
% 0.60/0.40 thf(func_def_84, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X0 > X5))).
% 0.60/0.40 thf(func_def_85, type, sK24: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_86, type, sK25: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_87, type, sK26: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_88, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_89, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.60/0.40 thf(func_def_90, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.60/0.40 thf(func_def_91, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X6))).
% 0.60/0.40 thf(func_def_92, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.60/0.40 thf(func_def_93, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.60/0.40 thf(func_def_94, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.60/0.40 thf(func_def_95, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X5))).
% 0.60/0.40 thf(func_def_96, type, sK35: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.60/0.40 thf(func_def_97, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.60/0.40 thf(func_def_98, type, sK37: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_99, type, sK38: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.60/0.40 thf(func_def_100, type, sK39: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.60/0.40 thf(func_def_101, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.60/0.40 thf(func_def_102, type, sK41: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0 > $o) > X1))).
% 0.60/0.40 thf(func_def_103, type, sK42: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_104, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_105, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X4 > $o) > X3))).
% 0.60/0.40 thf(func_def_106, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X4 > $o) > X2))).
% 0.60/0.40 thf(func_def_107, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X4 > $o) > X1))).
% 0.60/0.40 thf(func_def_108, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X4 > $o) > X0))).
% 0.60/0.40 thf(func_def_109, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X4 > $o) > X4))).
% 0.60/0.40 thf(func_def_110, type, sK49: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_111, type, sK50: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_112, type, sK51: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_113, type, sK52: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_114, type, sK53: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_115, type, sK54: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_116, type, sK55: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_117, type, sK56: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.60/0.40 thf(func_def_118, type, sK57: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.60/0.40 thf(func_def_119, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X2))).
% 0.60/0.40 thf(func_def_120, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X4))).
% 0.60/0.40 thf(func_def_121, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X1))).
% 0.60/0.40 thf(func_def_122, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X0))).
% 0.60/0.40 thf(func_def_123, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X3))).
% 0.60/0.40 thf(func_def_124, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X6))).
% 0.60/0.40 thf(func_def_125, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ X5 > X5))).
% 0.60/0.40 thf(func_def_126, type, sK65: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.60/0.40 thf(func_def_127, type, sK66: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_128, type, sK67: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_129, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_130, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > X0 > X1))).
% 0.60/0.40 thf(func_def_131, type, sK70: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_132, type, sK71: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_133, type, sK72: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_134, type, sK73: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.60/0.40 thf(func_def_135, type, sK74: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.60/0.40 thf(func_def_136, type, sK75: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_137, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X1))).
% 0.60/0.40 thf(func_def_138, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X5))).
% 0.60/0.40 thf(func_def_139, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X2))).
% 0.60/0.40 thf(func_def_140, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X3))).
% 0.60/0.40 thf(func_def_141, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X4))).
% 0.60/0.40 thf(func_def_142, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > $o) > X0))).
% 0.60/0.40 thf(func_def_143, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.60/0.40 thf(func_def_144, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.60/0.40 thf(func_def_145, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.60/0.40 thf(func_def_146, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > X0))).
% 0.60/0.40 thf(func_def_147, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > X2))).
% 0.60/0.40 thf(func_def_148, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > X1))).
% 0.60/0.40 thf(func_def_149, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > X3))).
% 0.60/0.40 thf(func_def_150, type, sK89: !>[X0: $tType]:((set @ X0 > product_prod @ X0 @ X0 > X0))).
% 0.60/0.40 thf(func_def_151, type, sK90: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.60/0.40 thf(func_def_152, type, sK91: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.60/0.40 thf(func_def_153, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_154, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X0))).
% 0.60/0.40 thf(func_def_155, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X3))).
% 0.60/0.40 thf(func_def_156, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X2))).
% 0.60/0.40 thf(func_def_157, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X1))).
% 0.60/0.40 thf(func_def_158, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X4))).
% 0.60/0.40 thf(func_def_159, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.60/0.40 thf(func_def_160, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.60/0.40 thf(func_def_161, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_162, type, sK101: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_163, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.60/0.40 thf(func_def_164, type, sK103: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_165, type, sK104: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_166, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.60/0.40 thf(func_def_167, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.60/0.40 thf(func_def_168, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.60/0.40 thf(func_def_169, type, sK108: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_170, type, sK109: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_171, type, sK110: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_172, type, sK111: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_173, type, sK112: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_174, type, sK113: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_175, type, sK114: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_176, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_177, type, sK116: !>[X0: $tType]:((set @ X0 > X0))).
% 0.60/0.40 thf(func_def_178, type, sK117: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_179, type, sK118: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_180, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.60/0.40 thf(func_def_181, type, sK120: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.60/0.40 thf(func_def_182, type, sK121: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_183, type, sK122: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.60/0.40 thf(func_def_184, type, sK123: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.60/0.40 thf(func_def_185, type, sK124: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.60/0.40 thf(func_def_186, type, sK125: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_187, type, sK126: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.60/0.40 thf(func_def_188, type, sK127: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_189, type, sK128: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_190, type, sK129: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_191, type, sK130: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(func_def_192, type, sK131: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.60/0.40 thf(f75,axiom,(
% 0.60/0.40 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ X1)),
% 0.60/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_subset__refl)).
% 0.60/0.40 thf(f302,conjecture,(
% 0.60/0.40 (ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation)) | (ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))),
% 0.60/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.60/0.40 thf(f303,negated_conjecture,(
% 0.60/0.40 ~((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation)) | (ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation)))),
% 0.60/0.40 inference(negated_conjecture,[status(cth)],[f302])).
% 0.60/0.40 thf(f326,plain,(
% 0.60/0.40 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ X1)),
% 0.60/0.40 inference(rectify,[],[f75])).
% 0.60/0.40 thf(f327,plain,(
% 0.60/0.40 ! [X0 : $tType,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X1)) = $true)),
% 0.60/0.40 inference(fool_elimination,[],[f326])).
% 0.60/0.40 thf(f555,plain,(
% 0.60/0.40 ~((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation)) | (ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation)))),
% 0.60/0.40 inference(rectify,[],[f303])).
% 0.60/0.40 thf(f556,plain,(
% 0.60/0.40 ~((((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) = $true) | (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) = $true))),
% 0.60/0.40 inference(fool_elimination,[],[f555])).
% 0.60/0.40 thf(f1190,plain,(
% 0.60/0.40 (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) != $true) & (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) != $true)),
% 0.60/0.40 inference(ennf_transformation,[],[f556])).
% 0.60/0.40 thf(f1794,plain,(
% 0.60/0.40 (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) != $true)),
% 0.60/0.40 inference(cnf_transformation,[],[f1190])).
% 0.60/0.40 thf(f1912,plain,(
% 0.60/0.40 ( ! [X0 : $tType,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X1)) = $true)) )),
% 0.60/0.40 inference(cnf_transformation,[],[f327])).
% 0.60/0.40 thf(f2125,definition,(
% 0.60/0.40 spl132_13 <=> (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) = $true)),
% 0.60/0.40 introduced(definition,[new_symbols(definition,[spl132_13])],[avatar_definition])).
% 0.60/0.40 thf(f2127,plain,(
% 0.60/0.40 (((ord_less_eq @ set @ a @ (prefer1532642881r_than @ a @ x @ carrier @ relation) @ (prefer1532642881r_than @ a @ x @ carrier @ relation))) != $true) | spl132_13),
% 0.60/0.40 inference(avatar_component_clause,[],[f2125])).
% 0.60/0.40 thf(f2128,plain,(
% 0.60/0.40 ~spl132_13),
% 0.60/0.40 inference(avatar_split_clause,[],[f1794,f2125])).
% 0.60/0.40 thf(f2188,plain,(
% 0.60/0.40 ($true != $true) | spl132_13),
% 0.60/0.40 inference(superposition,[],[f2127,f1912])).
% 0.60/0.40 thf(f2189,plain,(
% 0.60/0.40 $false | spl132_13),
% 0.60/0.40 inference(trivial_inequality_removal,[],[f2188])).
% 0.60/0.40 thf(f2190,plain,(
% 0.60/0.40 spl132_13),
% 0.60/0.40 inference(avatar_contradiction_clause,[],[f2189])).
% 0.60/0.40 cnf(s12, plain, ~spl132_13, inference(sat_conversion,[],[f2128])).
% 0.60/0.40 cnf(s26, plain, spl132_13, inference(sat_conversion,[],[f2190])).
% 0.60/0.40 cnf(s27, plain, $false, inference(rat,[],[s12,s26])).
% 0.60/0.40 thf(f2191,plain,(
% 0.60/0.40 $false),
% 0.60/0.40 inference(avatar_sat_refutation,[],[s27])).
% 0.60/0.40 % SZS output end Proof for theBenchmark
% 0.60/0.40 % (572441)------------------------------
% 0.60/0.40 % (572441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (572441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (572441)CaDiCaL version: 2.1.3
% 0.60/0.40 % (572441)Termination reason: Refutation
% 0.60/0.40 % (572441)Time elapsed: 0.077 s
% 0.60/0.40 % (572441)Peak memory usage: 14 MB
% 0.60/0.40 % (572441)Instructions burned: 157 (million)
% 0.60/0.40 % (572433)Success in time 0.135 s
% 0.60/0.40 % Vampire exiting
%------------------------------------------------------------------------------