%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT157^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 07:48:26 AM UTC 2026
% Result : Theorem 0.85s 0.55s
% Output : Refutation 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT157^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 18:00:41 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.29 Running higher-order theorem proving
% 0.26/0.37 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/0.55 % (3731214)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.85/0.55 % (3731223)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1436110346:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.85/0.55 % (3731219)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=365975389:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.85/0.55 % (3731225)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.85/0.55 % (3731225)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
% 0.85/0.55 % (3731223)Instruction limit reached!
% 0.85/0.55 % (3731223)------------------------------
% 0.85/0.55 % (3731223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731223)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731223)Termination reason: Instruction limit
% 0.85/0.55 % (3731223)Termination phase: Property scanning
% 0.85/0.55 % (3731223)Time elapsed: 0.011 s
% 0.85/0.55 % (3731223)Peak memory usage: 10 MB
% 0.85/0.55 % (3731223)Instructions burned: 25 (million)
% 0.85/0.55 % (3731222)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=3979487946: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)
% 0.85/0.55 % (3731224)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1185678256:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.85/0.55 % (3731225)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=2009979675:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.85/0.55 % (3731220)lrs+10_16_si=on:nwc=1.5:random_seed=3588260348:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.85/0.55 % (3731221)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=84441353:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.85/0.55 % (3731221)Instruction limit reached!
% 0.85/0.55 % (3731221)------------------------------
% 0.85/0.55 % (3731221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731221)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731221)Termination reason: Instruction limit
% 0.85/0.55 % (3731221)Termination phase: shuffling
% 0.85/0.55 % (3731221)Time elapsed: 0.004 s
% 0.85/0.55 % (3731221)Peak memory usage: 10 MB
% 0.85/0.55 % (3731221)Instructions burned: 4 (million)
% 0.85/0.55 % (3731228)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2601832342:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.85/0.55 % (3731220)Instruction limit reached!
% 0.85/0.55 % (3731220)------------------------------
% 0.85/0.55 % (3731220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731220)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731220)Termination reason: Instruction limit
% 0.85/0.55 % (3731220)Termination phase: Property scanning
% 0.85/0.55 % (3731220)Time elapsed: 0.016 s
% 0.85/0.55 % (3731220)Peak memory usage: 10 MB
% 0.85/0.55 % (3731220)Instructions burned: 18 (million)
% 0.85/0.55 % (3731228)Instruction limit reached!
% 0.85/0.55 % (3731228)------------------------------
% 0.85/0.55 % (3731228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731228)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731228)Termination reason: Instruction limit
% 0.85/0.55 % (3731228)Termination phase: shuffling
% 0.85/0.55 % (3731228)Time elapsed: 0.002 s
% 0.85/0.55 % (3731228)Peak memory usage: 10 MB
% 0.85/0.55 % (3731228)Instructions burned: 4 (million)
% 0.85/0.55 % (3731236)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.55 % (3731236)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2076604512:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.85/0.55 % (3731236)Instruction limit reached!
% 0.85/0.55 % (3731236)------------------------------
% 0.85/0.55 % (3731236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731236)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731236)Termination reason: Instruction limit
% 0.85/0.55 % (3731236)Termination phase: shuffling
% 0.85/0.55 % (3731236)Time elapsed: 0.003 s
% 0.85/0.55 % (3731236)Peak memory usage: 10 MB
% 0.85/0.55 % (3731236)Instructions burned: 7 (million)
% 0.85/0.55 % (3731234)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4070585123:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.85/0.55 % (3731234)Instruction limit reached!
% 0.85/0.55 % (3731234)------------------------------
% 0.85/0.55 % (3731234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731234)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731234)Termination reason: Instruction limit
% 0.85/0.55 % (3731234)Termination phase: shuffling
% 0.85/0.55 % (3731234)Time elapsed: 0.005 s
% 0.85/0.55 % (3731234)Peak memory usage: 10 MB
% 0.85/0.55 % (3731234)Instructions burned: 5 (million)
% 0.85/0.55 % (3731237)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3534016393:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.85/0.55 % (3731219)Instruction limit reached!
% 0.85/0.55 % (3731219)------------------------------
% 0.85/0.55 % (3731219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731219)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731219)Termination reason: Instruction limit
% 0.85/0.55 % (3731219)Termination phase: Saturation
% 0.85/0.55 % (3731219)Time elapsed: 0.064 s
% 0.85/0.55 % (3731219)Peak memory usage: 12 MB
% 0.85/0.55 % (3731219)Instructions burned: 88 (million)
% 0.85/0.55 % (3731240)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
% 0.85/0.55 % (3731240)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.55 % (3731240)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4127967186:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 0.85/0.55 % (3731237)Instruction limit reached!
% 0.85/0.55 % (3731237)------------------------------
% 0.85/0.55 % (3731237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731237)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731237)Termination reason: Instruction limit
% 0.85/0.55 % (3731237)Termination phase: shuffling
% 0.85/0.55 % (3731237)Time elapsed: 0.011 s
% 0.85/0.55 % (3731237)Peak memory usage: 10 MB
% 0.85/0.55 % (3731237)Instructions burned: 12 (million)
% 0.85/0.55 % (3731224)Instruction limit reached!
% 0.85/0.55 % (3731224)------------------------------
% 0.85/0.55 % (3731224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731224)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731224)Termination reason: Instruction limit
% 0.85/0.55 % (3731224)Termination phase: Property scanning
% 0.85/0.55 % (3731224)Time elapsed: 0.063 s
% 0.85/0.55 % (3731224)Peak memory usage: 12 MB
% 0.85/0.55 % (3731224)Instructions burned: 75 (million)
% 0.85/0.55 % (3731243)lrs+10_1_si=on:cs=on:random_seed=1791451954:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.85/0.55 % (3731240)Instruction limit reached!
% 0.85/0.55 % (3731240)------------------------------
% 0.85/0.55 % (3731240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731240)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731240)Termination reason: Instruction limit
% 0.85/0.55 % (3731240)Termination phase: Property scanning
% 0.85/0.55 % (3731240)Time elapsed: 0.013 s
% 0.85/0.55 % (3731240)Peak memory usage: 10 MB
% 0.85/0.55 % (3731240)Instructions burned: 30 (million)
% 0.85/0.55 % (3731243)Instruction limit reached!
% 0.85/0.55 % (3731243)------------------------------
% 0.85/0.55 % (3731243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731243)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731243)Termination reason: Instruction limit
% 0.85/0.55 % (3731243)Termination phase: shuffling
% 0.85/0.55 % (3731243)Time elapsed: 0.005 s
% 0.85/0.55 % (3731243)Peak memory usage: 10 MB
% 0.85/0.55 % (3731243)Instructions burned: 9 (million)
% 0.85/0.55 % (3731241)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=3658186566:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.85/0.55 % (3731245)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.85/0.55 % (3731245)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=1421948106:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.85/0.55 % (3731246)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=86592464:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.85/0.55 % (3731245)Instruction limit reached!
% 0.85/0.55 % (3731245)------------------------------
% 0.85/0.55 % (3731245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731245)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731245)Termination reason: Instruction limit
% 0.85/0.55 % (3731245)Termination phase: shuffling
% 0.85/0.55 % (3731245)Time elapsed: 0.002 s
% 0.85/0.55 % (3731245)Peak memory usage: 10 MB
% 0.85/0.55 % (3731245)Instructions burned: 2 (million)
% 0.85/0.55 % (3731222) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3731214-3731222"...
% 0.85/0.55 % (3731249)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2711544904:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.85/0.55 % (3731225) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3731214-3731225"...
% 0.85/0.55 % (3731222)...printing done.
% 0.85/0.55 % (3731222)Refutation found. Thanks to Tanya!
% 0.85/0.55 % SZS status Theorem for theBenchmark
% 0.85/0.55 % SZS output start Proof for theBenchmark
% 0.85/0.55 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.85/0.55 thf(type_def_6, type, list: $tType > $tType).
% 0.85/0.55 thf(type_def_7, type, set: $tType > $tType).
% 0.85/0.55 thf(type_def_8, type, itself: $tType > $tType).
% 0.85/0.55 thf(type_def_9, type, a: $tType).
% 0.85/0.55 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.85/0.55 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.85/0.55 thf(func_def_1, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.85/0.55 thf(func_def_2, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.85/0.55 thf(func_def_3, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.85/0.55 thf(func_def_4, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.85/0.55 thf(func_def_5, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_6, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.85/0.55 thf(func_def_7, type, coinductive_lsorted: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.85/0.55 thf(func_def_8, type, condit2040224947_above: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.85/0.55 thf(func_def_9, type, condit1201339847_below: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.85/0.55 thf(func_def_10, type, finite_folding: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > $o))).
% 0.85/0.55 thf(func_def_11, type, semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.85/0.55 thf(func_def_12, type, hammin1328233080lmerge: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_13, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.85/0.55 thf(func_def_14, type, semilattice: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.85/0.55 thf(func_def_15, type, lattic1693879045er_set: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.85/0.55 thf(func_def_16, type, insort_key: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > list @ X1 > list @ X1))).
% 0.85/0.55 thf(func_def_17, type, least: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_18, type, min: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 0.85/0.55 thf(func_def_19, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.85/0.55 thf(func_def_20, type, antimono: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > $o))).
% 0.85/0.55 thf(func_def_21, type, mono: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > $o))).
% 0.85/0.55 thf(func_def_22, type, strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > $o))).
% 0.85/0.55 thf(func_def_23, type, ordering: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.85/0.55 thf(func_def_24, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.85/0.55 thf(func_def_25, type, transp: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.85/0.55 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.85/0.55 thf(func_def_27, type, set_atLeast: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_28, type, set_atLeastAtMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_29, type, set_atLeastLessThan: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_30, type, set_atMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_31, type, set_greaterThan: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_32, type, set_gr323396891AtMost: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_33, type, set_gr1161524159ssThan: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_34, type, set_lessThan: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.85/0.55 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.85/0.55 thf(func_def_36, type, less: (a > a > $o)).
% 0.85/0.55 thf(func_def_37, type, less_eq: (a > a > $o)).
% 0.85/0.55 thf(func_def_38, type, thesis: $o).
% 0.85/0.55 thf(func_def_39, type, x: a).
% 0.85/0.55 thf(func_def_40, type, x2: a).
% 0.85/0.55 thf(func_def_41, type, xsa: coinductive_llist @ a).
% 0.85/0.55 thf(func_def_42, type, ysa: coinductive_llist @ a).
% 0.85/0.55 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.85/0.55 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.85/0.55 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.85/0.55 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.85/0.55 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.85/0.55 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.85/0.55 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 0.85/0.55 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.85/0.55 thf(func_def_54, type, sP0: (a > a > a > $o)).
% 0.85/0.55 thf(func_def_55, type, sP1: (a > a > a > $o)).
% 0.85/0.55 thf(func_def_56, type, sK2: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_57, type, sK3: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.85/0.55 thf(func_def_58, type, sK4: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_59, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_60, type, sK6: a).
% 0.85/0.55 thf(func_def_61, type, sK7: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_62, type, sK8: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_63, type, sK9: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_64, type, sK10: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_65, type, sK11: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_66, type, sK12: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_67, type, sK13: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_68, type, sK14: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_69, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.85/0.55 thf(func_def_70, type, sK16: (a > set @ a > a)).
% 0.85/0.55 thf(func_def_71, type, sK17: (set @ a > a)).
% 0.85/0.55 thf(func_def_72, type, sK18: (a > set @ a > a)).
% 0.85/0.55 thf(func_def_73, type, sK19: ((a > $o) > a > a)).
% 0.85/0.55 thf(func_def_74, type, sK20: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_75, type, sK21: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_76, type, sK22: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_77, type, sK23: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_78, type, sK24: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_79, type, sK25: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_80, type, sK26: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.85/0.55 thf(func_def_81, type, sK27: (set @ a > a > a)).
% 0.85/0.55 thf(func_def_82, type, sK28: ((a > a > $o) > a)).
% 0.85/0.55 thf(func_def_83, type, sK29: ((a > a > $o) > a)).
% 0.85/0.55 thf(func_def_84, type, sK30: ((a > a > $o) > a)).
% 0.85/0.55 thf(func_def_85, type, sK31: ((a > a > $o) > a)).
% 0.85/0.55 thf(func_def_86, type, sK32: (a > (a > $o) > a)).
% 0.85/0.55 thf(func_def_87, type, sK33: ((a > $o) > (a > $o) > a)).
% 0.85/0.55 thf(func_def_88, type, sK34: (a > coinductive_llist @ a > a)).
% 0.85/0.55 thf(func_def_89, type, sK35: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_90, type, sK36: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_91, type, sK37: (a > set @ a > a)).
% 0.85/0.55 thf(func_def_92, type, sK38: (set @ a > a)).
% 0.85/0.55 thf(func_def_93, type, sK39: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_94, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_95, type, sK41: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_96, type, sK42: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_97, type, sK43: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_98, type, sK44: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.85/0.55 thf(func_def_99, type, sK45: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.85/0.55 thf(func_def_100, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_101, type, sK47: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.85/0.55 thf(func_def_102, type, sK48: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_103, type, sK49: !>[X0: $tType]:(((a > X0) > a))).
% 0.85/0.55 thf(func_def_104, type, vNOT: ($o > $o)).
% 0.85/0.55 thf(f44,axiom,(
% 0.85/0.55 ? [X0 : a] : ((less_eq @ x @ X0) & (member @ a @ X0 @ (coinductive_lset @ a @ ysa)))),
% 0.85/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_step_Oprems_I3_J)).
% 0.85/0.55 thf(f261,axiom,(
% 0.85/0.55 ! [X0 : a] : ((member @ a @ X0 @ (coinductive_lset @ a @ ysa)) => ((less_eq @ x @ X0) => thesis))),
% 0.85/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.85/0.55 thf(f262,conjecture,(
% 0.85/0.55 thesis),
% 0.85/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.85/0.55 thf(f263,negated_conjecture,(
% 0.85/0.55 ~thesis),
% 0.85/0.55 inference(negated_conjecture,[status(cth)],[f262])).
% 0.85/0.55 thf(f391,plain,(
% 0.85/0.55 ~thesis),
% 0.85/0.55 inference(rectify,[],[f263])).
% 0.85/0.55 thf(f392,plain,(
% 0.85/0.55 ~ (thesis = $true)),
% 0.85/0.55 inference(fool_elimination,[],[f391])).
% 0.85/0.55 thf(f578,plain,(
% 0.85/0.55 ! [X0 : a] : ((member @ a @ X0 @ (coinductive_lset @ a @ ysa)) => ((less_eq @ x @ X0) => thesis))),
% 0.85/0.55 inference(rectify,[],[f261])).
% 0.85/0.55 thf(f579,plain,(
% 0.85/0.55 ! [X0 : a] : ((((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) = $true) => ((((less_eq @ x @ X0)) = $true) => (thesis = $true)))),
% 0.85/0.55 inference(fool_elimination,[],[f578])).
% 0.85/0.55 thf(f624,plain,(
% 0.85/0.55 ? [X0 : a] : ((less_eq @ x @ X0) & (member @ a @ X0 @ (coinductive_lset @ a @ ysa)))),
% 0.85/0.55 inference(rectify,[],[f44])).
% 0.85/0.55 thf(f625,plain,(
% 0.85/0.55 ? [X0 : a] : ((((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) = $true) & (((less_eq @ x @ X0)) = $true))),
% 0.85/0.55 inference(fool_elimination,[],[f624])).
% 0.85/0.55 thf(f730,plain,(
% 0.85/0.55 (thesis != $true)),
% 0.85/0.55 inference(flattening,[],[f392])).
% 0.85/0.55 thf(f799,plain,(
% 0.85/0.55 ! [X0 : a] : (((thesis = $true) | (((less_eq @ x @ X0)) != $true)) | (((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) != $true))),
% 0.85/0.55 inference(ennf_transformation,[],[f579])).
% 0.85/0.55 thf(f800,plain,(
% 0.85/0.55 ! [X0 : a] : ((((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) != $true) | (((less_eq @ x @ X0)) != $true) | (thesis = $true))),
% 0.85/0.55 inference(flattening,[],[f799])).
% 0.85/0.55 thf(f996,plain,(
% 0.85/0.55 (((member @ a @ sK6 @ (coinductive_lset @ a @ ysa))) = $true) & ($true = ((less_eq @ x @ sK6)))),
% 0.85/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f625])).
% 0.85/0.55 thf(f1248,plain,(
% 0.85/0.55 ($true = ((less_eq @ x @ sK6)))),
% 0.85/0.55 inference(cnf_transformation,[],[f996])).
% 0.85/0.55 thf(f1249,plain,(
% 0.85/0.55 (((member @ a @ sK6 @ (coinductive_lset @ a @ ysa))) = $true)),
% 0.85/0.55 inference(cnf_transformation,[],[f996])).
% 0.85/0.55 thf(f1543,plain,(
% 0.85/0.55 (thesis != $true)),
% 0.85/0.55 inference(cnf_transformation,[],[f730])).
% 0.85/0.55 thf(f1572,plain,(
% 0.85/0.55 ( ! [X0 : a] : ((((less_eq @ x @ X0)) != $true) | (thesis = $true) | (((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) != $true)) )),
% 0.85/0.55 inference(cnf_transformation,[],[f800])).
% 0.85/0.55 thf(f1716,definition,(
% 0.85/0.55 spl50_1 <=> ($true = ((less_eq @ x @ sK6)))),
% 0.85/0.55 introduced(definition,[new_symbols(definition,[spl50_1])],[avatar_definition])).
% 0.85/0.55 thf(f1718,plain,(
% 0.85/0.55 ($true = ((less_eq @ x @ sK6))) | ~spl50_1),
% 0.85/0.55 inference(avatar_component_clause,[],[f1716])).
% 0.85/0.55 thf(f1719,plain,(
% 0.85/0.55 spl50_1),
% 0.85/0.55 inference(avatar_split_clause,[],[f1248,f1716])).
% 0.85/0.55 thf(f1731,definition,(
% 0.85/0.55 spl50_4 <=> (((member @ a @ sK6 @ (coinductive_lset @ a @ ysa))) = $true)),
% 0.85/0.55 introduced(definition,[new_symbols(definition,[spl50_4])],[avatar_definition])).
% 0.85/0.55 thf(f1733,plain,(
% 0.85/0.55 (((member @ a @ sK6 @ (coinductive_lset @ a @ ysa))) = $true) | ~spl50_4),
% 0.85/0.55 inference(avatar_component_clause,[],[f1731])).
% 0.85/0.55 thf(f1734,plain,(
% 0.85/0.55 spl50_4),
% 0.85/0.55 inference(avatar_split_clause,[],[f1249,f1731])).
% 0.85/0.55 thf(f1766,definition,(
% 0.85/0.55 spl50_11 <=> (thesis = $true)),
% 0.85/0.55 introduced(definition,[new_symbols(definition,[spl50_11])],[avatar_definition])).
% 0.85/0.55 thf(f1769,plain,(
% 0.85/0.55 ~spl50_11),
% 0.85/0.55 inference(avatar_split_clause,[],[f1543,f1766])).
% 0.85/0.55 thf(f1807,definition,(
% 0.85/0.55 spl50_20 <=> ! [X0 : a] : ((((less_eq @ x @ X0)) != $true) | (((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) != $true))),
% 0.85/0.55 introduced(definition,[new_symbols(definition,[spl50_20])],[avatar_definition])).
% 0.85/0.55 thf(f1808,plain,(
% 0.85/0.55 ( ! [X0 : a] : ((((member @ a @ X0 @ (coinductive_lset @ a @ ysa))) != $true) | (((less_eq @ x @ X0)) != $true)) ) | ~spl50_20),
% 0.85/0.55 inference(avatar_component_clause,[],[f1807])).
% 0.85/0.55 thf(f1809,plain,(
% 0.85/0.55 spl50_11 | spl50_20),
% 0.85/0.55 inference(avatar_split_clause,[],[f1572,f1807,f1766])).
% 0.85/0.55 thf(f1828,plain,(
% 0.85/0.55 ($true != ((less_eq @ x @ sK6))) | ($true != $true) | (~spl50_4 | ~spl50_20)),
% 0.85/0.55 inference(superposition,[],[f1808,f1733])).
% 0.85/0.55 thf(f1829,plain,(
% 0.85/0.55 ($true != ((less_eq @ x @ sK6))) | (~spl50_4 | ~spl50_20)),
% 0.85/0.55 inference(trivial_inequality_removal,[],[f1828])).
% 0.85/0.55 thf(f1830,plain,(
% 0.85/0.55 $false | (~spl50_1 | ~spl50_4 | ~spl50_20)),
% 0.85/0.55 inference(forward_subsumption_resolution,[],[f1829,f1718])).
% 0.85/0.55 thf(f1831,plain,(
% 0.85/0.55 ~spl50_1 | ~spl50_4 | ~spl50_20),
% 0.85/0.55 inference(avatar_contradiction_clause,[],[f1830])).
% 0.85/0.55 cnf(s1, plain, spl50_1, inference(sat_conversion,[],[f1719])).
% 0.85/0.55 cnf(s4, plain, spl50_4, inference(sat_conversion,[],[f1734])).
% 0.85/0.55 cnf(s11, plain, ~spl50_11, inference(sat_conversion,[],[f1769])).
% 0.85/0.55 cnf(s19, plain, spl50_11 | spl50_20, inference(sat_conversion,[],[f1809])).
% 0.85/0.55 cnf(s24, plain, ~spl50_1 | ~spl50_4 | ~spl50_20, inference(sat_conversion,[],[f1831])).
% 0.85/0.55 cnf(s26, plain, spl50_20, inference(rat,[],[s19,s11])).
% 0.85/0.55 cnf(s27, plain, ~spl50_1, inference(rat,[],[s24,s26,s4])).
% 0.85/0.55 cnf(s28, plain, $false, inference(rat,[],[s1,s27])).
% 0.85/0.55 thf(f1832,plain,(
% 0.85/0.55 $false),
% 0.85/0.55 inference(avatar_sat_refutation,[],[s28])).
% 0.85/0.55 % SZS output end Proof for theBenchmark
% 0.85/0.55 % (3731222)------------------------------
% 0.85/0.55 % (3731222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.55 % (3731222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.55 % (3731222)CaDiCaL version: 2.1.3
% 0.85/0.55 % (3731222)Termination reason: Refutation
% 0.85/0.55 % (3731222)Time elapsed: 0.101 s
% 0.85/0.55 % (3731222)Peak memory usage: 14 MB
% 0.85/0.55 % (3731222)Instructions burned: 118 (million)
% 0.85/0.55 % (3731214)Success in time 0.165 s
% 0.85/0.55 % Vampire exiting
%------------------------------------------------------------------------------