%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP195^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:08:46 AM UTC 2026
% Result : Theorem 0.61s 0.44s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP195^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 20:12:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.23/0.27 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
% 0.61/0.42 % (583115)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.42 % (583131)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2833353588:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.42 % (583137)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.42 % (583137)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
% 0.61/0.42 % (583133)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=824517729:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.42 % (583132)lrs+10_16_si=on:nwc=1.5:random_seed=1859317481:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.42 % (583135)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1807746464:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.42 % (583137)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=1149966117:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.42 % (583134)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=3528590233: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)
% 0.61/0.42 % (583133)Instruction limit reached!
% 0.61/0.42 % (583133)------------------------------
% 0.61/0.42 % (583133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (583133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (583133)CaDiCaL version: 2.1.3
% 0.61/0.42 % (583133)Termination reason: Instruction limit
% 0.61/0.42 % (583133)Termination phase: shuffling
% 0.61/0.42 % (583133)Time elapsed: 0.002 s
% 0.61/0.42 % (583133)Peak memory usage: 10 MB
% 0.61/0.42 % (583133)Instructions burned: 3 (million)
% 0.61/0.42 % (583136)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2207760258:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.42 % (583132)Instruction limit reached!
% 0.61/0.42 % (583132)------------------------------
% 0.61/0.42 % (583132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (583132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (583132)CaDiCaL version: 2.1.3
% 0.61/0.42 % (583132)Termination reason: Instruction limit
% 0.61/0.42 % (583132)Termination phase: Property scanning
% 0.61/0.42 % (583132)Time elapsed: 0.009 s
% 0.61/0.42 % (583132)Peak memory usage: 10 MB
% 0.61/0.42 % (583132)Instructions burned: 18 (million)
% 0.61/0.42 % (583135)Instruction limit reached!
% 0.61/0.42 % (583135)------------------------------
% 0.61/0.42 % (583135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (583135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (583135)CaDiCaL version: 2.1.3
% 0.61/0.42 % (583135)Termination reason: Instruction limit
% 0.61/0.42 % (583135)Termination phase: Preprocessing 1
% 0.61/0.42 % (583135)Time elapsed: 0.012 s
% 0.61/0.42 % (583135)Peak memory usage: 10 MB
% 0.61/0.42 % (583135)Instructions burned: 25 (million)
% 0.61/0.42 % (583131)Instruction limit reached!
% 0.61/0.42 % (583131)------------------------------
% 0.61/0.42 % (583131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (583131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (583131)CaDiCaL version: 2.1.3
% 0.61/0.42 % (583131)Termination reason: Instruction limit
% 0.61/0.42 % (583131)Termination phase: Saturation
% 0.61/0.42 % (583131)Time elapsed: 0.023 s
% 0.61/0.42 % (583131)Peak memory usage: 13 MB
% 0.61/0.42 % (583131)Instructions burned: 91 (million)
% 0.61/0.42 % (583151)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1845745663:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.42 % (583151)Instruction limit reached!
% 0.61/0.42 % (583151)------------------------------
% 0.61/0.42 % (583151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583151)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583151)Termination reason: Instruction limit
% 0.61/0.44 % (583151)Termination phase: shuffling
% 0.61/0.44 % (583151)Time elapsed: 0.003 s
% 0.61/0.44 % (583151)Peak memory usage: 10 MB
% 0.61/0.44 % (583151)Instructions burned: 5 (million)
% 0.61/0.44 % (583159)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1444888503:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.44 % (583157)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.44 % (583155)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3208693825:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.44 % (583159)Instruction limit reached!
% 0.61/0.44 % (583159)------------------------------
% 0.61/0.44 % (583159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583159)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583159)Termination reason: Instruction limit
% 0.61/0.44 % (583159)Termination phase: shuffling
% 0.61/0.44 % (583159)Time elapsed: 0.003 s
% 0.61/0.44 % (583159)Peak memory usage: 10 MB
% 0.61/0.44 % (583159)Instructions burned: 12 (million)
% 0.61/0.44 % (583157)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1114081676:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.44 % (583155)Instruction limit reached!
% 0.61/0.44 % (583155)------------------------------
% 0.61/0.44 % (583155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583155)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583155)Termination reason: Instruction limit
% 0.61/0.44 % (583155)Termination phase: shuffling
% 0.61/0.44 % (583155)Time elapsed: 0.003 s
% 0.61/0.44 % (583155)Peak memory usage: 10 MB
% 0.61/0.44 % (583155)Instructions burned: 5 (million)
% 0.61/0.44 % (583157)Instruction limit reached!
% 0.61/0.44 % (583157)------------------------------
% 0.61/0.44 % (583157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583157)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583157)Termination reason: Instruction limit
% 0.61/0.44 % (583157)Termination phase: shuffling
% 0.61/0.44 % (583157)Time elapsed: 0.004 s
% 0.61/0.44 % (583157)Peak memory usage: 10 MB
% 0.61/0.44 % (583157)Instructions burned: 8 (million)
% 0.61/0.44 % (583165)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=1476918871:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.44 % (583162)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
% 0.61/0.44 % (583162)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.44 % (583162)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3685927395:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.44 % (583168)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.44 % (583167)lrs+10_1_si=on:cs=on:random_seed=2268884452:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.44 % (583168)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=3214604905:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.44 % (583167)Instruction limit reached!
% 0.61/0.44 % (583167)------------------------------
% 0.61/0.44 % (583167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583167)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583167)Termination reason: Instruction limit
% 0.61/0.44 % (583167)Termination phase: shuffling
% 0.61/0.44 % (583167)Time elapsed: 0.005 s
% 0.61/0.44 % (583167)Peak memory usage: 10 MB
% 0.61/0.44 % (583167)Instructions burned: 9 (million)
% 0.61/0.44 % (583162)Instruction limit reached!
% 0.61/0.44 % (583162)------------------------------
% 0.61/0.44 % (583162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583168)Instruction limit reached!
% 0.61/0.44 % (583168)------------------------------
% 0.61/0.44 % (583168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583162)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583162)Termination reason: Instruction limit
% 0.61/0.44 % (583162)Termination phase: Property scanning
% 0.61/0.44 % (583162)Time elapsed: 0.013 s
% 0.61/0.44 % (583162)Peak memory usage: 10 MB
% 0.61/0.44 % (583162)Instructions burned: 29 (million)
% 0.61/0.44 % (583168)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583168)Termination reason: Instruction limit
% 0.61/0.44 % (583168)Termination phase: shuffling
% 0.61/0.44 % (583168)Time elapsed: 0.002 s
% 0.61/0.44 % (583168)Peak memory usage: 10 MB
% 0.61/0.44 % (583168)Instructions burned: 4 (million)
% 0.61/0.44 % (583165)Instruction limit reached!
% 0.61/0.44 % (583165)------------------------------
% 0.61/0.44 % (583165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583165)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583165)Termination reason: Instruction limit
% 0.61/0.44 % (583165)Termination phase: Property scanning
% 0.61/0.44 % (583165)Time elapsed: 0.020 s
% 0.61/0.44 % (583165)Peak memory usage: 11 MB
% 0.61/0.44 % (583165)Instructions burned: 90 (million)
% 0.61/0.44 % (583136)Instruction limit reached!
% 0.61/0.44 % (583136)------------------------------
% 0.61/0.44 % (583136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583136)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583136)Termination reason: Instruction limit
% 0.61/0.44 % (583136)Termination phase: Property scanning
% 0.61/0.44 % (583136)Time elapsed: 0.059 s
% 0.61/0.44 % (583136)Peak memory usage: 12 MB
% 0.61/0.44 % (583136)Instructions burned: 76 (million)
% 0.61/0.44 % (583176)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=612881875:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.44 % (583173)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3407281095:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.61/0.44 % (583174)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2200042291:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.44 % (583176)Instruction limit reached!
% 0.61/0.44 % (583176)------------------------------
% 0.61/0.44 % (583176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583176)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583176)Termination reason: Instruction limit
% 0.61/0.44 % (583176)Termination phase: Property scanning
% 0.61/0.44 % (583176)Time elapsed: 0.004 s
% 0.61/0.44 % (583176)Peak memory usage: 10 MB
% 0.61/0.44 % (583176)Instructions burned: 17 (million)
% 0.61/0.44 % (583175)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3565347830:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.44 % (583137)Instruction limit reached!
% 0.61/0.44 % (583137)------------------------------
% 0.61/0.44 % (583137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583137)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583137)Termination reason: Instruction limit
% 0.61/0.44 % (583137)Termination phase: Saturation
% 0.61/0.44 % (583137)Time elapsed: 0.082 s
% 0.61/0.44 % (583137)Peak memory usage: 14 MB
% 0.61/0.44 % (583137)Instructions burned: 159 (million)
% 0.61/0.44 % (583188)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1096861768:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.44 % (583180)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1035539676:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.44 % (583188)Instruction limit reached!
% 0.61/0.44 % (583188)------------------------------
% 0.61/0.44 % (583188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583188)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583188)Termination reason: Instruction limit
% 0.61/0.44 % (583188)Termination phase: Property scanning
% 0.61/0.44 % (583188)Time elapsed: 0.004 s
% 0.61/0.44 % (583188)Peak memory usage: 10 MB
% 0.61/0.44 % (583188)Instructions burned: 16 (million)
% 0.61/0.44 % (583173)Instruction limit reached!
% 0.61/0.44 % (583173)------------------------------
% 0.61/0.44 % (583173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583173)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583173)Termination reason: Instruction limit
% 0.61/0.44 % (583173)Termination phase: Preprocessing 3
% 0.61/0.44 % (583173)Time elapsed: 0.020 s
% 0.61/0.44 % (583173)Peak memory usage: 11 MB
% 0.61/0.44 % (583173)Instructions burned: 38 (million)
% 0.61/0.44 % (583175)Instruction limit reached!
% 0.61/0.44 % (583175)------------------------------
% 0.61/0.44 % (583175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583175)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583175)Termination reason: Instruction limit
% 0.61/0.44 % (583175)Termination phase: SInE selection
% 0.61/0.44 % (583175)Time elapsed: 0.013 s
% 0.61/0.44 % (583175)Peak memory usage: 11 MB
% 0.61/0.44 % (583175)Instructions burned: 26 (million)
% 0.61/0.44 % (583134) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-583115-583134"...
% 0.61/0.44 % (583134)...printing done.
% 0.61/0.44 % (583199)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3639574068:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.61/0.44 % (583134)Refutation found. Thanks to Tanya!
% 0.61/0.44 % SZS status Theorem for theBenchmark
% 0.61/0.44 % SZS output start Proof for theBenchmark
% 0.61/0.44 thf(type_def_5, type, poly: $tType > $tType).
% 0.61/0.44 thf(type_def_6, type, real: $tType).
% 0.61/0.44 thf(type_def_7, type, set: $tType > $tType).
% 0.61/0.44 thf(type_def_8, type, nat: $tType).
% 0.61/0.44 thf(type_def_9, type, int: $tType).
% 0.61/0.44 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.44 thf(func_def_0, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_3, type, idom: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_6, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_8, type, no_bot: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_9, type, no_top: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_10, type, semiring_1: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_11, type, comm_ring_1: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_14, type, field_char_0: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_15, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_16, type, wellorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_17, type, dense_order: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_18, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_19, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_21, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_22, type, ring_n68954251visors: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_23, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_24, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_26, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_27, type, one_one: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_29, type, suc: (nat > nat)).
% 0.61/0.44 thf(func_def_30, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.61/0.44 thf(func_def_31, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_33, type, is_zero: !>[X0: $tType]:((poly @ X0 > $o))).
% 0.61/0.44 thf(func_def_34, type, order2: !>[X0: $tType]:((X0 > poly @ X0 > nat))).
% 0.61/0.44 thf(func_def_35, type, pderiv: !>[X0: $tType]:((poly @ X0 > poly @ X0))).
% 0.61/0.44 thf(func_def_36, type, poly2: !>[X0: $tType]:((poly @ X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_37, type, coeff: !>[X0: $tType]:((poly @ X0 > nat > X0))).
% 0.61/0.44 thf(func_def_38, type, poly_cutoff: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 0.61/0.44 thf(func_def_39, type, poly_shift: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 0.61/0.44 thf(func_def_40, type, reflect_poly: !>[X0: $tType]:((poly @ X0 > poly @ X0))).
% 0.61/0.44 thf(func_def_41, type, rsquarefree: !>[X0: $tType]:((poly @ X0 > $o))).
% 0.61/0.44 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.61/0.44 thf(func_def_43, type, sturm_424270202_cross: (poly @ real > real > real > int)).
% 0.61/0.44 thf(func_def_44, type, sturm_1700286437_r_pos: (poly @ real > real > $o)).
% 0.61/0.44 thf(func_def_45, type, sturm_1771227917iation: (real > real > int)).
% 0.61/0.44 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.61/0.44 thf(func_def_47, type, p: poly @ real).
% 0.61/0.44 thf(func_def_48, type, x: real).
% 0.61/0.44 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 0.61/0.44 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.61/0.44 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.44 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_58, type, vOR: ($o > $o > $o)).
% 0.61/0.44 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.44 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.44 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 0.61/0.44 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_63, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_64, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_65, type, sK2: ((nat > nat > $o) > nat)).
% 0.61/0.44 thf(func_def_66, type, sK3: ((nat > nat > $o) > nat)).
% 0.61/0.44 thf(func_def_67, type, sK4: ((nat > nat > $o) > nat)).
% 0.61/0.44 thf(func_def_68, type, sK5: ((nat > nat > $o) > nat)).
% 0.61/0.44 thf(func_def_69, type, sK6: ((nat > nat > $o) > nat)).
% 0.61/0.44 thf(func_def_70, type, sK7: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_71, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_72, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_73, type, sK10: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_74, type, sK11: (set @ real > real)).
% 0.61/0.44 thf(func_def_75, type, sK12: (real > set @ real > real)).
% 0.61/0.44 thf(func_def_76, type, sK13: (real > set @ real > real)).
% 0.61/0.44 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.61/0.44 thf(func_def_83, type, sK20: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_84, type, sK21: (real > poly @ real > real > real)).
% 0.61/0.44 thf(func_def_85, type, sK22: (real > poly @ real > real > real)).
% 0.61/0.44 thf(func_def_86, type, sK23: (real > poly @ real > real > real)).
% 0.61/0.44 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_89, type, sK26: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_90, type, sK27: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_91, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_92, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_93, type, sK30: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_94, type, sK31: !>[X0: $tType]:((poly @ X0 > X0))).
% 0.61/0.44 thf(func_def_95, type, sK32: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_96, type, sK33: (real > poly @ real > real)).
% 0.61/0.44 thf(func_def_97, type, sK34: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_98, type, sK35: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_99, type, sK36: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_100, type, sK37: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_101, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_102, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_103, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_104, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_105, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_106, type, sK43: ((nat > $o) > nat)).
% 0.61/0.44 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_109, type, sK46: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_110, type, sK47: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_113, type, sK50: ((nat > $o) > nat > nat)).
% 0.61/0.44 thf(func_def_114, type, sK51: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_115, type, sK52: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_116, type, sK53: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_117, type, sK54: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_120, type, sK57: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_121, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_122, type, sK59: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_123, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_124, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_125, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_128, type, sK65: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_129, type, sK66: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_130, type, sK67: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_131, type, sK68: (poly @ real > real > real > real)).
% 0.61/0.44 thf(func_def_132, type, sK69: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_133, type, sK70: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.61/0.44 thf(func_def_134, type, sK71: (nat > nat)).
% 0.61/0.44 thf(func_def_135, type, sK72: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_136, type, sK73: ((nat > $o) > nat)).
% 0.61/0.44 thf(func_def_137, type, sK74: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.44 thf(func_def_138, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_139, type, sK76: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_140, type, sK77: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_141, type, sK78: ((nat > $o) > nat)).
% 0.61/0.44 thf(func_def_142, type, sK79: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_143, type, sK80: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_144, type, sK81: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_145, type, sK82: ((nat > $o) > nat)).
% 0.61/0.44 thf(func_def_146, type, sK83: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_147, type, sK84: (real > real > poly @ real > real)).
% 0.61/0.44 thf(func_def_148, type, sK85: (real > real > poly @ real > real)).
% 0.61/0.44 thf(func_def_149, type, sK86: (real > real > poly @ real > real)).
% 0.61/0.44 thf(func_def_150, type, sK87: ((nat > nat) > nat)).
% 0.61/0.44 thf(func_def_151, type, sK88: ((nat > nat) > nat)).
% 0.61/0.44 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_153, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_154, type, sK91: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_156, type, sK93: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.61/0.44 thf(func_def_157, type, sK94: (poly @ real > real > real > real)).
% 0.61/0.44 thf(func_def_158, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_159, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_160, type, sK97: (nat > (nat > $o) > nat)).
% 0.61/0.44 thf(func_def_161, type, sK98: ((nat > $o) > nat)).
% 0.61/0.44 thf(func_def_162, type, sK99: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_163, type, sK100: (poly @ real > real > real)).
% 0.61/0.44 thf(func_def_164, type, sK101: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_165, type, sK102: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_166, type, sK103: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_167, type, sK104: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.44 thf(func_def_168, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_169, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_170, type, sK107: (nat > (nat > $o) > nat)).
% 0.61/0.44 thf(func_def_171, type, sK108: (real > real > poly @ real > real)).
% 0.61/0.44 thf(func_def_172, type, sK109: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.44 thf(func_def_173, type, sK110: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.44 thf(f1,axiom,(
% 0.61/0.44 (((poly2 @ real @ p @ x)) != zero_zero @ real)),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False)).
% 0.61/0.44 thf(f2,axiom,(
% 0.61/0.44 (sturm_1700286437_r_pos @ p @ x) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062)).
% 0.61/0.44 thf(f3,axiom,(
% 0.61/0.44 (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)) => (sturm_1700286437_r_pos @ p @ x)),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062)).
% 0.61/0.44 thf(f340,conjecture,(
% 0.61/0.44 (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.44 thf(f341,negated_conjecture,(
% 0.61/0.44 ~ (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.61/0.44 inference(negated_conjecture,[status(cth)],[f340])).
% 0.61/0.44 thf(f475,plain,(
% 0.61/0.44 ~ (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.61/0.44 inference(rectify,[],[f341])).
% 0.61/0.44 thf(f476,plain,(
% 0.61/0.44 ~(~(((((poly2 @ real @ p @ x)) = zero_zero @ real) => (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) = $true)) & ((((poly2 @ real @ p @ x)) != zero_zero @ real) => (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true))) <~> (((sturm_1700286437_r_pos @ p @ x)) = $true))),
% 0.61/0.44 inference(fool_elimination,[],[f475])).
% 0.61/0.44 thf(f635,plain,(
% 0.61/0.44 (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)) => (sturm_1700286437_r_pos @ p @ x)),
% 0.61/0.44 inference(rectify,[],[f3])).
% 0.61/0.44 thf(f636,plain,(
% 0.61/0.44 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) => (((sturm_1700286437_r_pos @ p @ x)) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f635])).
% 0.61/0.44 thf(f975,plain,(
% 0.61/0.44 (sturm_1700286437_r_pos @ p @ x) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))),
% 0.61/0.44 inference(rectify,[],[f2])).
% 0.61/0.44 thf(f976,plain,(
% 0.61/0.44 (((sturm_1700286437_r_pos @ p @ x)) = $true) => (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f975])).
% 0.61/0.44 thf(f1079,plain,(
% 0.61/0.44 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true) | (((sturm_1700286437_r_pos @ p @ x)) = $true)),
% 0.61/0.44 inference(ennf_transformation,[],[f636])).
% 0.61/0.44 thf(f1305,plain,(
% 0.61/0.44 (((sturm_1700286437_r_pos @ p @ x)) != $true) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.61/0.44 inference(ennf_transformation,[],[f976])).
% 0.61/0.44 thf(f1312,plain,(
% 0.61/0.44 (((sturm_1700286437_r_pos @ p @ x)) = $true) <=> (((((poly2 @ real @ p @ x)) = zero_zero @ real) & (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) != $true)) | ((((poly2 @ real @ p @ x)) != zero_zero @ real) & (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true)))),
% 0.61/0.44 inference(ennf_transformation,[],[f476])).
% 0.61/0.44 thf(f1481,plain,(
% 0.61/0.44 ((((sturm_1700286437_r_pos @ p @ x)) = $true) | (((((poly2 @ real @ p @ x)) != zero_zero @ real) | (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) = $true)) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)))) & ((((((poly2 @ real @ p @ x)) = zero_zero @ real) & (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) != $true)) | ((((poly2 @ real @ p @ x)) != zero_zero @ real) & (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true))) | (((sturm_1700286437_r_pos @ p @ x)) != $true))),
% 0.61/0.44 inference(nnf_transformation,[],[f1312])).
% 0.61/0.44 thf(f1482,plain,(
% 0.61/0.44 ((((sturm_1700286437_r_pos @ p @ x)) = $true) | (((((poly2 @ real @ p @ x)) != zero_zero @ real) | (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) = $true)) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)))) & (((((poly2 @ real @ p @ x)) = zero_zero @ real) & (((sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) != $true)) | ((((poly2 @ real @ p @ x)) != zero_zero @ real) & (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true)) | (((sturm_1700286437_r_pos @ p @ x)) != $true))),
% 0.61/0.44 inference(flattening,[],[f1481])).
% 0.61/0.44 thf(f1661,plain,(
% 0.61/0.44 (((poly2 @ real @ p @ x)) != zero_zero @ real)),
% 0.61/0.44 inference(cnf_transformation,[],[f1])).
% 0.61/0.44 thf(f1671,plain,(
% 0.61/0.44 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) | (((sturm_1700286437_r_pos @ p @ x)) != $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f1305])).
% 0.61/0.44 thf(f1890,plain,(
% 0.61/0.44 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true) | (((sturm_1700286437_r_pos @ p @ x)) != $true) | (((poly2 @ real @ p @ x)) = zero_zero @ real)),
% 0.61/0.44 inference(cnf_transformation,[],[f1482])).
% 0.61/0.44 thf(f1892,plain,(
% 0.61/0.44 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) | (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((poly2 @ real @ p @ x)) = zero_zero @ real)),
% 0.61/0.44 inference(cnf_transformation,[],[f1482])).
% 0.61/0.44 thf(f1907,plain,(
% 0.61/0.44 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f1079])).
% 0.61/0.44 thf(f2505,definition,(
% 0.61/0.44 spl111_11 <=> (((sturm_1700286437_r_pos @ p @ x)) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl111_11])],[avatar_definition])).
% 0.61/0.44 thf(f2509,definition,(
% 0.61/0.44 spl111_12 <=> (((poly2 @ real @ p @ x)) = zero_zero @ real)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl111_12])],[avatar_definition])).
% 0.61/0.44 thf(f2514,definition,(
% 0.61/0.44 spl111_13 <=> (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl111_13])],[avatar_definition])).
% 0.61/0.44 thf(f2517,plain,(
% 0.61/0.44 ~spl111_11 | spl111_12 | ~spl111_13),
% 0.61/0.44 inference(avatar_split_clause,[],[f1890,f2514,f2509,f2505])).
% 0.61/0.44 thf(f2616,plain,(
% 0.61/0.44 ~spl111_13 | spl111_11),
% 0.61/0.44 inference(avatar_split_clause,[],[f1907,f2505,f2514])).
% 0.61/0.44 thf(f2633,plain,(
% 0.61/0.44 spl111_11 | spl111_12 | spl111_13),
% 0.61/0.44 inference(avatar_split_clause,[],[f1892,f2514,f2509,f2505])).
% 0.61/0.44 thf(f2654,plain,(
% 0.61/0.44 spl111_13 | ~spl111_11),
% 0.61/0.44 inference(avatar_split_clause,[],[f1671,f2505,f2514])).
% 0.61/0.44 thf(f2806,plain,(
% 0.61/0.44 ~spl111_12),
% 0.61/0.44 inference(avatar_split_clause,[],[f1661,f2509])).
% 0.61/0.44 cnf(s11, plain, ~spl111_11 | spl111_12 | ~spl111_13, inference(sat_conversion,[],[f2517])).
% 0.61/0.44 cnf(s32, plain, spl111_11 | ~spl111_13, inference(sat_conversion,[],[f2616])).
% 0.61/0.44 cnf(s39, plain, spl111_11 | spl111_12 | spl111_13, inference(sat_conversion,[],[f2633])).
% 0.61/0.44 cnf(s44, plain, ~spl111_11 | spl111_13, inference(sat_conversion,[],[f2654])).
% 0.61/0.44 cnf(s78, plain, ~spl111_12, inference(sat_conversion,[],[f2806])).
% 0.61/0.44 cnf(s90, plain, spl111_11 | spl111_13, inference(rat,[],[s39,s78])).
% 0.61/0.44 cnf(s91, plain, ~spl111_11 | ~spl111_13, inference(rat,[],[s11,s78])).
% 0.61/0.44 cnf(s92, plain, spl111_11, inference(rat,[],[s32,s90])).
% 0.61/0.44 cnf(s93, plain, spl111_13, inference(rat,[],[s44,s92])).
% 0.61/0.44 cnf(s94, plain, $false, inference(rat,[],[s91,s93,s92])).
% 0.61/0.44 thf(f2857,plain,(
% 0.61/0.44 $false),
% 0.61/0.44 inference(avatar_sat_refutation,[],[s94])).
% 0.61/0.44 % SZS output end Proof for theBenchmark
% 0.61/0.44 % (583134)------------------------------
% 0.61/0.44 % (583134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (583134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (583134)CaDiCaL version: 2.1.3
% 0.61/0.44 % (583134)Termination reason: Refutation
% 0.61/0.44 % (583134)Time elapsed: 0.099 s
% 0.61/0.44 % (583134)Peak memory usage: 14 MB
% 0.61/0.44 % (583134)Instructions burned: 150 (million)
% 0.61/0.44 % (583115)Success in time 0.158 s
% 0.61/0.44 % Vampire exiting
%------------------------------------------------------------------------------