%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP123^2 : 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 : 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 08:08:27 AM UTC 2026
% Result : Theorem 0.52s 0.40s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP123^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n006.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 19:56:39 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.26 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
% 0.52/0.40 % (1230970)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.52/0.40 % (1230997)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4092251547:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.52/0.40 % (1230998)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.52/0.40 % (1230998)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
% 0.52/0.40 % (1230992)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3081346096:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.52/0.40 % (1230996)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3458308590:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.52/0.40 % (1230993)lrs+10_16_si=on:nwc=1.5:random_seed=193804852:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.52/0.40 % (1230994)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3246384536:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.52/0.40 % (1230995)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=582903519: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)
% 0.52/0.40 % (1230998)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=1286265831:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.52/0.40 % (1230994)Instruction limit reached!
% 0.52/0.40 % (1230994)------------------------------
% 0.52/0.40 % (1230994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1230994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1230994)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1230994)Termination reason: Instruction limit
% 0.52/0.40 % (1230994)Termination phase: shuffling
% 0.52/0.40 % (1230994)Time elapsed: 0.002 s
% 0.52/0.40 % (1230994)Peak memory usage: 10 MB
% 0.52/0.40 % (1230994)Instructions burned: 4 (million)
% 0.52/0.40 % (1230996)Instruction limit reached!
% 0.52/0.40 % (1230996)------------------------------
% 0.52/0.40 % (1230996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1230996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1230996)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1230996)Termination reason: Instruction limit
% 0.52/0.40 % (1230996)Termination phase: Unused predicate definition removal
% 0.52/0.40 % (1230996)Time elapsed: 0.011 s
% 0.52/0.40 % (1230996)Peak memory usage: 10 MB
% 0.52/0.40 % (1230996)Instructions burned: 26 (million)
% 0.52/0.40 % (1230993)Instruction limit reached!
% 0.52/0.40 % (1230993)------------------------------
% 0.52/0.40 % (1230993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1230993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1230993)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1230993)Termination reason: Instruction limit
% 0.52/0.40 % (1230993)Termination phase: Preprocessing 1
% 0.52/0.40 % (1230993)Time elapsed: 0.012 s
% 0.52/0.40 % (1230993)Peak memory usage: 10 MB
% 0.52/0.40 % (1230993)Instructions burned: 26 (million)
% 0.52/0.40 % (1230997)Instruction limit reached!
% 0.52/0.40 % (1230997)------------------------------
% 0.52/0.40 % (1230997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1230997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1230997)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1230997)Termination reason: Instruction limit
% 0.52/0.40 % (1230997)Termination phase: Saturation
% 0.52/0.40 % (1230997)Time elapsed: 0.019 s
% 0.52/0.40 % (1230997)Peak memory usage: 12 MB
% 0.52/0.40 % (1230997)Instructions burned: 77 (million)
% 0.52/0.40 % (1231021)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1810663656:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.52/0.40 % (1231015)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1076198018:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.40 % (1231021)Instruction limit reached!
% 0.52/0.40 % (1231021)------------------------------
% 0.52/0.40 % (1231021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231021)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231021)Termination reason: Instruction limit
% 0.52/0.40 % (1231021)Termination phase: shuffling
% 0.52/0.40 % (1231021)Time elapsed: 0.002 s
% 0.52/0.40 % (1231021)Peak memory usage: 10 MB
% 0.52/0.40 % (1231021)Instructions burned: 7 (million)
% 0.52/0.40 % (1231015)Instruction limit reached!
% 0.52/0.40 % (1231015)------------------------------
% 0.52/0.40 % (1231015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231015)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231015)Termination reason: Instruction limit
% 0.52/0.40 % (1231015)Termination phase: shuffling
% 0.52/0.40 % (1231015)Time elapsed: 0.002 s
% 0.52/0.40 % (1231015)Peak memory usage: 10 MB
% 0.52/0.40 % (1231015)Instructions burned: 3 (million)
% 0.52/0.40 % (1231022)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.40 % (1231023)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=922437456:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.52/0.40 % (1231022)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2854339733:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.52/0.40 % (1231031)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
% 0.52/0.40 % (1231031)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.40 % (1231031)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1628604359:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.52/0.40 % (1231022)Instruction limit reached!
% 0.52/0.40 % (1231022)------------------------------
% 0.52/0.40 % (1231022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231022)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231022)Termination reason: Instruction limit
% 0.52/0.40 % (1231022)Termination phase: shuffling
% 0.52/0.40 % (1231022)Time elapsed: 0.004 s
% 0.52/0.40 % (1231022)Peak memory usage: 10 MB
% 0.52/0.40 % (1231022)Instructions burned: 8 (million)
% 0.52/0.40 % (1231023)Instruction limit reached!
% 0.52/0.40 % (1231023)------------------------------
% 0.52/0.40 % (1231023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231023)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231023)Termination reason: Instruction limit
% 0.52/0.40 % (1231023)Termination phase: shuffling
% 0.52/0.40 % (1231023)Time elapsed: 0.006 s
% 0.52/0.40 % (1231023)Peak memory usage: 10 MB
% 0.52/0.40 % (1231023)Instructions burned: 13 (million)
% 0.52/0.40 % (1230992)Instruction limit reached!
% 0.52/0.40 % (1230992)------------------------------
% 0.52/0.40 % (1230992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1230992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1230992)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1230992)Termination reason: Instruction limit
% 0.52/0.40 % (1230992)Termination phase: Saturation
% 0.52/0.40 % (1230992)Time elapsed: 0.041 s
% 0.52/0.40 % (1230992)Peak memory usage: 13 MB
% 0.52/0.40 % (1230992)Instructions burned: 88 (million)
% 0.52/0.40 % (1231031)Instruction limit reached!
% 0.52/0.40 % (1231031)------------------------------
% 0.52/0.40 % (1231031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231031)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231031)Termination reason: Instruction limit
% 0.52/0.40 % (1231031)Termination phase: Property scanning
% 0.52/0.40 % (1231031)Time elapsed: 0.007 s
% 0.52/0.40 % (1231031)Peak memory usage: 11 MB
% 0.52/0.40 % (1231031)Instructions burned: 29 (million)
% 0.52/0.40 % (1231033)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=70115716:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.52/0.40 % (1231045)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.52/0.40 % (1231048)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1468383028:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.52/0.40 % (1231044)lrs+10_1_si=on:cs=on:random_seed=2476880058:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.52/0.40 % (1231045)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=4106814642:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.40 % (1231045)Instruction limit reached!
% 0.52/0.40 % (1231045)------------------------------
% 0.52/0.40 % (1231045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231045)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231045)Termination reason: Instruction limit
% 0.52/0.40 % (1231045)Termination phase: shuffling
% 0.52/0.40 % (1231045)Time elapsed: 0.002 s
% 0.52/0.40 % (1231045)Peak memory usage: 10 MB
% 0.52/0.40 % (1231045)Instructions burned: 4 (million)
% 0.52/0.40 % (1231047)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1140410641:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.52/0.40 % (1231044)Instruction limit reached!
% 0.52/0.40 % (1231044)------------------------------
% 0.52/0.40 % (1231044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231044)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231044)Termination reason: Instruction limit
% 0.52/0.40 % (1231044)Termination phase: shuffling
% 0.52/0.40 % (1231044)Time elapsed: 0.004 s
% 0.52/0.40 % (1231044)Peak memory usage: 10 MB
% 0.52/0.40 % (1231044)Instructions burned: 8 (million)
% 0.52/0.40 % (1231048) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1230970-1231048"...
% 0.52/0.40 % (1231048)...printing done.
% 0.52/0.40 % (1231048)Refutation found. Thanks to Tanya!
% 0.52/0.40 % SZS status Theorem for theBenchmark
% 0.52/0.40 % SZS output start Proof for theBenchmark
% 0.52/0.40 thf(type_def_5, type, set: $tType > $tType).
% 0.52/0.40 thf(type_def_6, type, a: $tType).
% 0.52/0.40 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.52/0.40 thf(func_def_0, type, condit2040224947_above: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.52/0.40 thf(func_def_1, type, condit1201339847_below: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.52/0.40 thf(func_def_2, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > $o))).
% 0.52/0.40 thf(func_def_3, type, abel_semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.52/0.40 thf(func_def_4, type, semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.52/0.40 thf(func_def_5, type, lattice: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > (X0 > X0 > X0) > $o))).
% 0.52/0.40 thf(func_def_6, type, semilattice: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.52/0.40 thf(func_def_7, type, semilattice_order: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_8, type, lattices_is_arg_max: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > $o) > X1 > $o))).
% 0.52/0.40 thf(func_def_9, type, lattices_is_arg_min: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > $o) > X1 > $o))).
% 0.52/0.40 thf(func_def_10, type, lattic1693879045er_set: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_11, type, lattic35693393ce_set: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.52/0.40 thf(func_def_12, type, modula1618706180attice: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_13, type, modula1192512645attice: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_14, type, modula105138637_a_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_15, type, modula477145868_b_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_16, type, modula849153099_c_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_17, type, modula1221160330_d_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_18, type, modula1593167561_e_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_19, type, modula1937309406incomp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_20, type, modula141148890istrib: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_21, type, least: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.52/0.40 thf(func_def_22, type, max: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_23, type, min: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 0.52/0.40 thf(func_def_24, type, greatest: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.52/0.40 thf(func_def_25, type, ordering: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.52/0.40 thf(func_def_27, type, set_gr1161524159ssThan: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.52/0.40 thf(func_def_28, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.52/0.40 thf(func_def_29, type, inf: (a > a > a)).
% 0.52/0.40 thf(func_def_30, type, less: (a > a > $o)).
% 0.52/0.40 thf(func_def_31, type, less_eq: (a > a > $o)).
% 0.52/0.40 thf(func_def_32, type, sup: (a > a > a)).
% 0.52/0.40 thf(func_def_33, type, x: a).
% 0.52/0.40 thf(func_def_34, type, y: a).
% 0.52/0.40 thf(func_def_35, type, z: a).
% 0.52/0.40 thf(func_def_39, type, vAND: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_40, type, vNOT: ($o > $o)).
% 0.52/0.40 thf(func_def_41, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_42, type, db0: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.52/0.40 thf(func_def_44, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_45, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_46, type, vIMP: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_47, type, db1: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_48, type, vOR: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_50, type, db4: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_51, type, db3: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_52, type, sK0: a).
% 0.52/0.40 thf(func_def_53, type, sK1: a).
% 0.52/0.40 thf(func_def_54, type, sK2: a).
% 0.52/0.40 thf(func_def_55, type, sK3: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_56, type, sK4: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_57, type, sK5: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_58, type, sK6: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_59, type, sK7: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_60, type, sK8: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_61, type, sK9: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_62, type, sK10: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_63, type, sK11: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_64, type, sK12: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_65, type, sK13: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_66, type, sK14: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_67, type, sK15: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_68, type, sK16: ((a > a > a) > a)).
% 0.52/0.40 thf(func_def_69, type, sK17: a).
% 0.52/0.40 thf(func_def_70, type, sK18: a).
% 0.52/0.40 thf(func_def_71, type, sK19: a).
% 0.52/0.40 thf(func_def_72, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.52/0.40 thf(f40,axiom,(
% 0.52/0.40 ! [X1 : a,X0 : a] : (((sup @ X0 @ X1)) = ((sup @ X1 @ X0)))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_local_Osup_Ocommute)).
% 0.52/0.40 thf(f54,axiom,(
% 0.52/0.40 ! [X0 : a,X1 : a] : ((less @ X0 @ X1) => (less_eq @ X0 @ X1))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_local_Odual__order_Ostrict__implies__order)).
% 0.52/0.40 thf(f111,axiom,(
% 0.52/0.40 ! [X2 : a,X0 : a,X1 : a] : ((less_eq @ X0 @ X1) => (less_eq @ X0 @ (sup @ X2 @ X1)))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_local_Osup_OcoboundedI2)).
% 0.52/0.40 thf(f131,axiom,(
% 0.52/0.40 ! [X1 : a,X2 : a,X0 : a] : ((less @ (sup @ X0 @ X1) @ X2) => ~((less @ X0 @ X2) => ~(less @ X1 @ X2)))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_local_Osup_Ostrict__boundedE)).
% 0.52/0.40 thf(f260,axiom,(
% 0.52/0.40 (less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)).
% 0.52/0.40 thf(f261,conjecture,(
% 0.52/0.40 (less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4)).
% 0.52/0.40 thf(f262,negated_conjecture,(
% 0.52/0.40 ~(less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))),
% 0.52/0.40 inference(negated_conjecture,[status(cth)],[f261])).
% 0.52/0.40 thf(f279,plain,(
% 0.52/0.40 ~(less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))),
% 0.52/0.40 inference(rectify,[],[f262])).
% 0.52/0.40 thf(f280,plain,(
% 0.52/0.40 ~ (((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))) = $true)),
% 0.52/0.40 inference(fool_elimination,[],[f279])).
% 0.52/0.40 thf(f311,plain,(
% 0.52/0.40 (less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))),
% 0.52/0.40 inference(rectify,[],[f260])).
% 0.52/0.40 thf(f312,plain,(
% 0.52/0.40 (((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))) = $true)),
% 0.52/0.40 inference(fool_elimination,[],[f311])).
% 0.52/0.40 thf(f582,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a] : ((less @ X0 @ X1) => (less_eq @ X0 @ X1))),
% 0.52/0.40 inference(rectify,[],[f54])).
% 0.52/0.40 thf(f583,plain,(
% 0.52/0.40 ! [X1 : a,X0 : a] : ((((less @ X0 @ X1)) = $true) => (((less_eq @ X0 @ X1)) = $true))),
% 0.52/0.40 inference(fool_elimination,[],[f582])).
% 0.52/0.40 thf(f588,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a,X2 : a] : ((less @ (sup @ X2 @ X0) @ X1) => ~((less @ X2 @ X1) => ~(less @ X0 @ X1)))),
% 0.52/0.40 inference(rectify,[],[f131])).
% 0.52/0.40 thf(f589,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a,X2 : a] : ((((less @ (sup @ X2 @ X0) @ X1)) = $true) => ~((((less @ X2 @ X1)) = $true) => ~ (((less @ X0 @ X1)) = $true)))),
% 0.52/0.40 inference(fool_elimination,[],[f588])).
% 0.52/0.40 thf(f609,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ X1 @ X2) => (less_eq @ X1 @ (sup @ X0 @ X2)))),
% 0.52/0.40 inference(rectify,[],[f111])).
% 0.52/0.40 thf(f610,plain,(
% 0.52/0.40 ! [X0 : a,X2 : a,X1 : a] : ((((less_eq @ X1 @ X2)) = $true) => (((less_eq @ X1 @ (sup @ X0 @ X2))) = $true))),
% 0.52/0.40 inference(fool_elimination,[],[f609])).
% 0.52/0.40 thf(f660,plain,(
% 0.52/0.40 (((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))) != $true)),
% 0.52/0.40 inference(flattening,[],[f280])).
% 0.52/0.40 thf(f678,plain,(
% 0.52/0.40 ! [X2 : a,X1 : a,X0 : a] : ((((less @ (sup @ X2 @ X0) @ X1)) = $true) => ~((((less @ X2 @ X1)) = $true) => (((less @ X0 @ X1)) != $true)))),
% 0.52/0.40 inference(flattening,[],[f589])).
% 0.52/0.40 thf(f697,plain,(
% 0.52/0.40 ! [X1 : a,X2 : a,X0 : a] : (((((less @ X0 @ X1)) = $true) & (((less @ X2 @ X1)) = $true)) | (((less @ (sup @ X2 @ X0) @ X1)) != $true))),
% 0.52/0.40 inference(ennf_transformation,[],[f678])).
% 0.52/0.40 thf(f755,plain,(
% 0.52/0.40 ! [X0 : a,X2 : a,X1 : a] : ((((less_eq @ X1 @ X2)) != $true) | (((less_eq @ X1 @ (sup @ X0 @ X2))) = $true))),
% 0.52/0.40 inference(ennf_transformation,[],[f610])).
% 0.52/0.40 thf(f808,plain,(
% 0.52/0.40 ! [X1 : a,X0 : a] : ((((less_eq @ X0 @ X1)) = $true) | (((less @ X0 @ X1)) != $true))),
% 0.52/0.40 inference(ennf_transformation,[],[f583])).
% 0.52/0.40 thf(f820,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a] : ((((less_eq @ X1 @ X0)) = $true) | (((less @ X1 @ X0)) != $true))),
% 0.52/0.40 inference(rectify,[],[f808])).
% 0.52/0.40 thf(f830,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a,X2 : a] : (((((less @ X2 @ X0)) = $true) & (((less @ X1 @ X0)) = $true)) | (((less @ (sup @ X1 @ X2) @ X0)) != $true))),
% 0.52/0.40 inference(rectify,[],[f697])).
% 0.52/0.40 thf(f858,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a] : (((sup @ X0 @ X1)) = ((sup @ X1 @ X0)))),
% 0.52/0.40 inference(rectify,[],[f40])).
% 0.52/0.40 thf(f867,plain,(
% 0.52/0.40 ! [X0 : a,X1 : a,X2 : a] : ((((less_eq @ X2 @ X1)) != $true) | ($true = ((less_eq @ X2 @ (sup @ X0 @ X1)))))),
% 0.52/0.40 inference(rectify,[],[f755])).
% 0.52/0.40 thf(f914,plain,(
% 0.52/0.40 ( ! [X0 : a,X1 : a] : ((((less_eq @ X1 @ X0)) = $true) | (((less @ X1 @ X0)) != $true)) )),
% 0.52/0.40 inference(cnf_transformation,[],[f820])).
% 0.52/0.40 thf(f925,plain,(
% 0.52/0.40 ( ! [X2 : a,X0 : a,X1 : a] : ((((less @ (sup @ X1 @ X2) @ X0)) != $true) | (((less @ X1 @ X0)) = $true)) )),
% 0.52/0.40 inference(cnf_transformation,[],[f830])).
% 0.52/0.40 thf(f973,plain,(
% 0.52/0.40 ( ! [X0 : a,X1 : a] : ((((sup @ X0 @ X1)) = ((sup @ X1 @ X0)))) )),
% 0.52/0.40 inference(cnf_transformation,[],[f858])).
% 0.52/0.40 thf(f985,plain,(
% 0.52/0.40 (((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))) != $true)),
% 0.52/0.40 inference(cnf_transformation,[],[f660])).
% 0.52/0.40 thf(f986,plain,(
% 0.52/0.40 ( ! [X2 : a,X0 : a,X1 : a] : (($true = ((less_eq @ X2 @ (sup @ X0 @ X1)))) | (((less_eq @ X2 @ X1)) != $true)) )),
% 0.52/0.40 inference(cnf_transformation,[],[f867])).
% 0.52/0.40 thf(f1025,plain,(
% 0.52/0.40 (((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))) = $true)),
% 0.52/0.40 inference(cnf_transformation,[],[f312])).
% 0.52/0.40 thf(f1057,plain,(
% 0.52/0.40 (((less_eq @ x @ (sup @ z @ (inf @ y @ (sup @ x @ z))))) != $true)),
% 0.52/0.40 inference(forward_demodulation,[],[f985,f973])).
% 0.52/0.40 thf(f1075,plain,(
% 0.52/0.40 (((less_eq @ x @ (inf @ y @ (sup @ x @ z)))) != $true) | ($true != $true)),
% 0.52/0.40 inference(superposition,[],[f1057,f986])).
% 0.52/0.40 thf(f1087,plain,(
% 0.52/0.40 (((less_eq @ x @ (inf @ y @ (sup @ x @ z)))) != $true)),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f1075])).
% 0.52/0.40 thf(f1233,plain,(
% 0.52/0.40 ($true != $true) | (((less @ x @ (inf @ y @ (sup @ x @ z)))) = $true)),
% 0.52/0.40 inference(superposition,[],[f925,f1025])).
% 0.52/0.40 thf(f1244,plain,(
% 0.52/0.40 (((less @ x @ (inf @ y @ (sup @ x @ z)))) = $true)),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f1233])).
% 0.52/0.40 thf(f1437,plain,(
% 0.52/0.40 ($true != $true) | (((less @ x @ (inf @ y @ (sup @ x @ z)))) != $true)),
% 0.52/0.40 inference(superposition,[],[f1087,f914])).
% 0.52/0.40 thf(f1446,plain,(
% 0.52/0.40 (((less @ x @ (inf @ y @ (sup @ x @ z)))) != $true)),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f1437])).
% 0.52/0.40 thf(f1458,plain,(
% 0.52/0.40 $false),
% 0.52/0.40 inference(forward_subsumption_resolution,[],[f1446,f1244])).
% 0.52/0.40 % SZS output end Proof for theBenchmark
% 0.52/0.40 % (1231048)------------------------------
% 0.52/0.40 % (1231048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (1231048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (1231048)CaDiCaL version: 2.1.3
% 0.52/0.40 % (1231048)Termination reason: Refutation
% 0.52/0.40 % (1231048)Time elapsed: 0.019 s
% 0.52/0.40 % (1231048)Peak memory usage: 13 MB
% 0.52/0.40 % (1231048)Instructions burned: 73 (million)
% 0.52/0.40 % (1230970)Success in time 0.129 s
% 0.52/0.40 % Vampire exiting
%------------------------------------------------------------------------------