%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT144^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 07:48:25 AM UTC 2026
% Result : Theorem 0.50s 0.40s
% Output : Refutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT144^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n007.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 17:58:56 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.40 % (3726164)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.40 % (3726181)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=208325991:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.40 % (3726182)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.40 % (3726182)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
% 0.50/0.40 % (3726176)lrs+10_16_si=on:nwc=1.5:random_seed=2308113198:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.40 % (3726175)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=616344752:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.40 % (3726178)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=1923386381: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)
% 0.50/0.40 % (3726180)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=456314187:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.40 % (3726182)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=3790273025:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.40 % (3726177)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2017608930:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.40 % (3726177)Instruction limit reached!
% 0.50/0.40 % (3726177)------------------------------
% 0.50/0.40 % (3726177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726177)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726177)Termination reason: Instruction limit
% 0.50/0.40 % (3726177)Termination phase: shuffling
% 0.50/0.40 % (3726177)Time elapsed: 0.002 s
% 0.50/0.40 % (3726177)Peak memory usage: 10 MB
% 0.50/0.40 % (3726177)Instructions burned: 3 (million)
% 0.50/0.40 % (3726176)Instruction limit reached!
% 0.50/0.40 % (3726176)------------------------------
% 0.50/0.40 % (3726176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726176)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726176)Termination reason: Instruction limit
% 0.50/0.40 % (3726176)Termination phase: Property scanning
% 0.50/0.40 % (3726176)Time elapsed: 0.009 s
% 0.50/0.40 % (3726176)Peak memory usage: 10 MB
% 0.50/0.40 % (3726176)Instructions burned: 19 (million)
% 0.50/0.40 % (3726181)Instruction limit reached!
% 0.50/0.40 % (3726181)------------------------------
% 0.50/0.40 % (3726181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726181)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726181)Termination reason: Instruction limit
% 0.50/0.40 % (3726181)Termination phase: Property scanning
% 0.50/0.40 % (3726181)Time elapsed: 0.020 s
% 0.50/0.40 % (3726180)Instruction limit reached!
% 0.50/0.40 % (3726180)------------------------------
% 0.50/0.40 % (3726180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726180)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726180)Termination reason: Instruction limit
% 0.50/0.40 % (3726180)Termination phase: Property scanning
% 0.50/0.40 % (3726180)Time elapsed: 0.012 s
% 0.50/0.40 % (3726180)Peak memory usage: 10 MB
% 0.50/0.40 % (3726180)Instructions burned: 25 (million)
% 0.50/0.40 % (3726181)Peak memory usage: 12 MB
% 0.50/0.40 % (3726181)Instructions burned: 78 (million)
% 0.50/0.40 % (3726205)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.40 % (3726205)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1576420581:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.40 % (3726199)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3965040162:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.40 % (3726205)Instruction limit reached!
% 0.50/0.40 % (3726205)------------------------------
% 0.50/0.40 % (3726205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726205)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726205)Termination reason: Instruction limit
% 0.50/0.40 % (3726205)Termination phase: shuffling
% 0.50/0.40 % (3726205)Time elapsed: 0.002 s
% 0.50/0.40 % (3726205)Peak memory usage: 10 MB
% 0.50/0.40 % (3726205)Instructions burned: 9 (million)
% 0.50/0.40 % (3726202)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3489674199:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.40 % (3726199)Instruction limit reached!
% 0.50/0.40 % (3726199)------------------------------
% 0.50/0.40 % (3726199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726199)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726199)Termination reason: Instruction limit
% 0.50/0.40 % (3726199)Termination phase: shuffling
% 0.50/0.40 % (3726199)Time elapsed: 0.002 s
% 0.50/0.40 % (3726199)Peak memory usage: 10 MB
% 0.50/0.40 % (3726199)Instructions burned: 3 (million)
% 0.50/0.40 % (3726202)Instruction limit reached!
% 0.50/0.40 % (3726202)------------------------------
% 0.50/0.40 % (3726202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726202)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726202)Termination reason: Instruction limit
% 0.50/0.40 % (3726202)Termination phase: shuffling
% 0.50/0.40 % (3726202)Time elapsed: 0.003 s
% 0.50/0.40 % (3726202)Peak memory usage: 10 MB
% 0.50/0.40 % (3726202)Instructions burned: 6 (million)
% 0.50/0.40 % (3726206)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=954338313:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.40 % (3726216)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
% 0.50/0.40 % (3726216)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.40 % (3726216)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3405988266:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.40 % (3726206)Instruction limit reached!
% 0.50/0.40 % (3726206)------------------------------
% 0.50/0.40 % (3726206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726206)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726206)Termination reason: Instruction limit
% 0.50/0.40 % (3726206)Termination phase: shuffling
% 0.50/0.40 % (3726206)Time elapsed: 0.006 s
% 0.50/0.40 % (3726206)Peak memory usage: 10 MB
% 0.50/0.40 % (3726206)Instructions burned: 13 (million)
% 0.50/0.40 % (3726175)Instruction limit reached!
% 0.50/0.40 % (3726175)------------------------------
% 0.50/0.40 % (3726175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726175)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726175)Termination reason: Instruction limit
% 0.50/0.40 % (3726175)Termination phase: Property scanning
% 0.50/0.40 % (3726175)Time elapsed: 0.042 s
% 0.50/0.40 % (3726175)Peak memory usage: 12 MB
% 0.50/0.40 % (3726175)Instructions burned: 88 (million)
% 0.50/0.40 % (3726216)Instruction limit reached!
% 0.50/0.40 % (3726216)------------------------------
% 0.50/0.40 % (3726216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726216)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726216)Termination reason: Instruction limit
% 0.50/0.40 % (3726216)Termination phase: Property scanning
% 0.50/0.40 % (3726216)Time elapsed: 0.007 s
% 0.50/0.40 % (3726216)Peak memory usage: 11 MB
% 0.50/0.40 % (3726216)Instructions burned: 31 (million)
% 0.50/0.40 % (3726219)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=351310827:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.40 % (3726221)lrs+10_1_si=on:cs=on:random_seed=1271929374:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.40 % (3726223)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.50/0.40 % (3726221)Instruction limit reached!
% 0.50/0.40 % (3726221)------------------------------
% 0.50/0.40 % (3726221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726221)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726221)Termination reason: Instruction limit
% 0.50/0.40 % (3726221)Termination phase: shuffling
% 0.50/0.40 % (3726221)Time elapsed: 0.004 s
% 0.50/0.40 % (3726221)Peak memory usage: 10 MB
% 0.50/0.40 % (3726221)Instructions burned: 8 (million)
% 0.50/0.40 % (3726225)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2072145573:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.50/0.40 % (3726223)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=420377331:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.40 % (3726223)Instruction limit reached!
% 0.50/0.40 % (3726223)------------------------------
% 0.50/0.40 % (3726223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726223)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726223)Termination reason: Instruction limit
% 0.50/0.40 % (3726223)Termination phase: shuffling
% 0.50/0.40 % (3726223)Time elapsed: 0.002 s
% 0.50/0.40 % (3726223)Peak memory usage: 10 MB
% 0.50/0.40 % (3726223)Instructions burned: 3 (million)
% 0.50/0.40 % (3726224)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1783131848:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.50/0.40 % (3726178) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3726164-3726178"...
% 0.50/0.40 % (3726225) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3726164-3726225"...
% 0.50/0.40 % (3726225)...printing done.
% 0.50/0.40 % (3726178)...printing done.
% 0.50/0.40 % (3726225)Refutation found. Thanks to Tanya!
% 0.50/0.40 % SZS status Theorem for theBenchmark
% 0.50/0.40 % SZS output start Proof for theBenchmark
% 0.50/0.40 thf(type_def_5, type, extended_enat: $tType).
% 0.50/0.40 thf(type_def_6, type, real: $tType).
% 0.50/0.40 thf(type_def_7, type, set: $tType > $tType).
% 0.50/0.40 thf(type_def_8, type, num: $tType).
% 0.50/0.40 thf(type_def_9, type, nat: $tType).
% 0.50/0.40 thf(type_def_10, type, int: $tType).
% 0.50/0.40 thf(type_def_11, type, itself: $tType > $tType).
% 0.50/0.40 thf(type_def_12, type, a: $tType).
% 0.50/0.40 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.50/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_1, type, ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_3, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_7, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_8, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_9, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_10, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_11, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_12, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_13, type, archim1727834104eiling: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_14, type, topolo47006728_space: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_15, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_16, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_17, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.50/0.40 thf(func_def_18, type, archimedean_ceiling: !>[X0: $tType]:((X0 > int))).
% 0.50/0.40 thf(func_def_19, type, archim2085082626_floor: !>[X0: $tType]:((X0 > int))).
% 0.50/0.40 thf(func_def_20, type, archimedean_round: !>[X0: $tType]:((X0 > int))).
% 0.50/0.40 thf(func_def_21, type, bNF_pred_DEADID: !>[X0: $tType]:((X0 > $o))).
% 0.50/0.40 thf(func_def_22, type, bNF_Grp: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0 > X1 > $o))).
% 0.50/0.40 thf(func_def_23, type, bNF_eq_onp: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > $o))).
% 0.50/0.40 thf(func_def_24, type, extended_enat2: (nat > extended_enat)).
% 0.50/0.40 thf(func_def_25, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.50/0.40 thf(func_def_26, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.50/0.40 thf(func_def_27, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_28, type, undefined: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_29, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.50/0.40 thf(func_def_30, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.50/0.40 thf(func_def_31, type, nat2: (int > nat)).
% 0.50/0.40 thf(func_def_32, type, neg: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > $o))).
% 0.50/0.40 thf(func_def_33, type, pos: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > $o))).
% 0.50/0.40 thf(func_def_34, type, quotient: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > (X0 > X1 > $o) > $o))).
% 0.50/0.40 thf(func_def_35, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.50/0.40 thf(func_def_36, type, nat_tr1645093318rphism: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > $o))).
% 0.50/0.40 thf(func_def_37, type, nat_tsub: (int > int > int)).
% 0.50/0.40 thf(func_def_38, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 0.50/0.40 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.40 thf(func_def_40, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.50/0.40 thf(func_def_41, type, top_top: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_42, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.50/0.40 thf(func_def_43, type, domainp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > $o))).
% 0.50/0.40 thf(func_def_44, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.50/0.40 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.50/0.40 thf(func_def_46, type, topological_monoseq: !>[X0: $tType]:(((nat > X0) > $o))).
% 0.50/0.40 thf(func_def_47, type, topolo406746546ounded: !>[X0: $tType]:((set @ X0 > $o))).
% 0.50/0.40 thf(func_def_48, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.50/0.40 thf(func_def_49, type, p: (a > $o)).
% 0.50/0.40 thf(func_def_50, type, x: a).
% 0.50/0.40 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.50/0.40 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.40 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.50/0.40 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.50/0.40 thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 0.50/0.40 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.50/0.40 thf(func_def_63, type, vNOT: ($o > $o)).
% 0.50/0.40 thf(func_def_64, type, db3: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_65, type, vOR: ($o > $o > $o)).
% 0.50/0.40 thf(func_def_66, type, db5: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_67, type, db4: !>[X0: $tType]:(X0)).
% 0.50/0.40 thf(func_def_68, type, sK0: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.50/0.40 thf(func_def_69, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.50/0.40 thf(func_def_70, type, sK2: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.50/0.40 thf(func_def_71, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.50/0.40 thf(func_def_72, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.50/0.40 thf(f4,axiom,(
% 0.50/0.40 ! [X0 : $tType,X1 : (X0 > $o),X2 : X0] : (((bNF_eq_onp @ X0 @ X1 @ X2 @ X2)) = ((X1 @ X2)))),
% 0.50/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_eq__onp__same__args)).
% 0.50/0.40 thf(f318,axiom,(
% 0.50/0.40 (p @ x)),
% 0.50/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.50/0.40 thf(f319,conjecture,(
% 0.50/0.40 (bNF_eq_onp @ a @ p @ x @ x)),
% 0.50/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.50/0.40 thf(f320,negated_conjecture,(
% 0.50/0.40 ~(bNF_eq_onp @ a @ p @ x @ x)),
% 0.50/0.40 inference(negated_conjecture,[status(cth)],[f319])).
% 0.50/0.40 thf(f456,plain,(
% 0.50/0.40 (p @ x)),
% 0.50/0.40 inference(rectify,[],[f318])).
% 0.50/0.40 thf(f457,plain,(
% 0.50/0.40 (((p @ x)) = $true)),
% 0.50/0.40 inference(fool_elimination,[],[f456])).
% 0.50/0.40 thf(f719,plain,(
% 0.50/0.40 ~(bNF_eq_onp @ a @ p @ x @ x)),
% 0.50/0.40 inference(rectify,[],[f320])).
% 0.50/0.40 thf(f720,plain,(
% 0.50/0.40 ~ (((bNF_eq_onp @ a @ p @ x @ x)) = $true)),
% 0.50/0.40 inference(fool_elimination,[],[f719])).
% 0.50/0.40 thf(f911,plain,(
% 0.50/0.40 (((bNF_eq_onp @ a @ p @ x @ x)) != $true)),
% 0.50/0.40 inference(flattening,[],[f720])).
% 0.50/0.40 thf(f954,plain,(
% 0.50/0.40 (((p @ x)) = $true)),
% 0.50/0.40 inference(cnf_transformation,[],[f457])).
% 0.50/0.40 thf(f958,plain,(
% 0.50/0.40 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((((bNF_eq_onp @ X0 @ X1 @ X2 @ X2)) = ((X1 @ X2)))) )),
% 0.50/0.40 inference(cnf_transformation,[],[f4])).
% 0.50/0.40 thf(f961,plain,(
% 0.50/0.40 (((bNF_eq_onp @ a @ p @ x @ x)) != $true)),
% 0.50/0.40 inference(cnf_transformation,[],[f911])).
% 0.50/0.40 thf(f971,plain,(
% 0.50/0.40 (((p @ x)) != $true)),
% 0.50/0.40 inference(forward_demodulation,[],[f961,f958])).
% 0.50/0.40 thf(f972,plain,(
% 0.50/0.40 $false),
% 0.50/0.40 inference(forward_subsumption_resolution,[],[f971,f954])).
% 0.50/0.40 % SZS output end Proof for theBenchmark
% 0.50/0.40 % (3726225)------------------------------
% 0.50/0.40 % (3726225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.40 % (3726225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.40 % (3726225)CaDiCaL version: 2.1.3
% 0.50/0.40 % (3726225)Termination reason: Refutation
% 0.50/0.40 % (3726225)Time elapsed: 0.011 s
% 0.50/0.40 % (3726225)Peak memory usage: 13 MB
% 0.50/0.40 % (3726225)Instructions burned: 42 (million)
% 0.50/0.40 % (3726164)Success in time 0.114 s
% 0.50/0.40 % Vampire exiting
%------------------------------------------------------------------------------