%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI632_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 : Tue Sep 29 09:35:00 AM UTC 2026
% Result : Theorem 2.30s 0.58s
% Output : Refutation 2.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI632_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 20:54:18 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.30/0.58 % (268781)Will run a generic schedule for satisfiability detection.
% 2.30/0.58 % (268787)% WARNING: option uhcvi not known.
% 2.30/0.58 % (268786)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1458979134_2999 on theBenchmark for (2999ds/0Mi)
% 2.30/0.58 % (268787)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2629180358:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.30/0.58 % (268789)dis+10_1_sil=32000:sp=arity:random_seed=2445660452:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.30/0.58 % (268788)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2065983387:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.30/0.58 % (268790)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=249538647:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.30/0.58 % (268786)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268786)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268786)------------------------------
% 2.30/0.58 % (268786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268786)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268786)Termination reason: Inappropriate
% 2.30/0.58 % (268786)Time elapsed: 0.001 s
% 2.30/0.58 % (268786)Peak memory usage: 10 MB
% 2.30/0.58 % (268786)------------------------------
% 2.30/0.58 % (268786)------------------------------
% 2.30/0.58 % (268791)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3658741541:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.30/0.58 % (268792)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3891170249:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.30/0.58 % (268800)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2860973018:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.30/0.58 % (268800)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268800)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268800)------------------------------
% 2.30/0.58 % (268800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268800)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268800)Termination reason: Inappropriate
% 2.30/0.58 % (268800)Time elapsed: 0.0000 s
% 2.30/0.58 % (268800)Peak memory usage: 10 MB
% 2.30/0.58 % (268800)------------------------------
% 2.30/0.58 % (268800)------------------------------
% 2.30/0.58 % (268802)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2662931761:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.30/0.58 % (268789)Instruction limit reached!
% 2.30/0.58 % (268789)------------------------------
% 2.30/0.58 % (268789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268789)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268789)Termination reason: Instruction limit
% 2.30/0.58 % (268789)Termination phase: Saturation
% 2.30/0.58 % (268789)Time elapsed: 0.067 s
% 2.30/0.58 % (268789)Peak memory usage: 12 MB
% 2.30/0.58 % (268789)Instructions burned: 103 (million)
% 2.30/0.58 % (268790)Instruction limit reached!
% 2.30/0.58 % (268790)------------------------------
% 2.30/0.58 % (268790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268790)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268790)Termination reason: Instruction limit
% 2.30/0.58 % (268790)Termination phase: Saturation
% 2.30/0.58 % (268790)Time elapsed: 0.075 s
% 2.30/0.58 % (268790)Peak memory usage: 12 MB
% 2.30/0.58 % (268790)Instructions burned: 116 (million)
% 2.30/0.58 % (268802)Instruction limit reached!
% 2.30/0.58 % (268802)------------------------------
% 2.30/0.58 % (268802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268802)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268802)Termination reason: Instruction limit
% 2.30/0.58 % (268802)Termination phase: Saturation
% 2.30/0.58 % (268802)Time elapsed: 0.048 s
% 2.30/0.58 % (268802)Peak memory usage: 13 MB
% 2.30/0.58 % (268802)Instructions burned: 131 (million)
% 2.30/0.58 % (268791)Instruction limit reached!
% 2.30/0.58 % (268791)------------------------------
% 2.30/0.58 % (268791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268791)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268791)Termination reason: Instruction limit
% 2.30/0.58 % (268791)Termination phase: Saturation
% 2.30/0.58 % (268791)Time elapsed: 0.085 s
% 2.30/0.58 % (268791)Peak memory usage: 13 MB
% 2.30/0.58 % (268791)Instructions burned: 132 (million)
% 2.30/0.58 % (268806)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3779331729:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.30/0.58 % (268804)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=584674556:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.30/0.58 % (268805)ott-21_1_sil=16000:fs=off:random_seed=2252170731:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.30/0.58 % (268809)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1887227934:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.30/0.58 % (268809)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268809)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268809)------------------------------
% 2.30/0.58 % (268809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268809)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268809)Termination reason: Inappropriate
% 2.30/0.58 % (268809)Time elapsed: 0.001 s
% 2.30/0.58 % (268809)Peak memory usage: 10 MB
% 2.30/0.58 % (268809)------------------------------
% 2.30/0.58 % (268809)------------------------------
% 2.30/0.58 % (268812)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=601225978:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.30/0.58 % (268792)Instruction limit reached!
% 2.30/0.58 % (268792)------------------------------
% 2.30/0.58 % (268792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268792)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268792)Termination reason: Instruction limit
% 2.30/0.58 % (268792)Termination phase: Saturation
% 2.30/0.58 % (268792)Time elapsed: 0.147 s
% 2.30/0.58 % (268792)Peak memory usage: 13 MB
% 2.30/0.58 % (268792)Instructions burned: 160 (million)
% 2.30/0.58 % (268814)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3864368769:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.30/0.58 % (268814)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268814)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268814)------------------------------
% 2.30/0.58 % (268814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268814)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268814)Termination reason: Inappropriate
% 2.30/0.58 % (268814)Time elapsed: 0.0000 s
% 2.30/0.58 % (268814)Peak memory usage: 10 MB
% 2.30/0.58 % (268814)------------------------------
% 2.30/0.58 % (268814)------------------------------
% 2.30/0.58 % (268805)Instruction limit reached!
% 2.30/0.58 % (268805)------------------------------
% 2.30/0.58 % (268805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268805)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268805)Termination reason: Instruction limit
% 2.30/0.58 % (268805)Termination phase: Saturation
% 2.30/0.58 % (268805)Time elapsed: 0.082 s
% 2.30/0.58 % (268805)Peak memory usage: 12 MB
% 2.30/0.58 % (268805)Instructions burned: 182 (million)
% 2.30/0.58 % (268816)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3298579442:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.30/0.58 % (268817)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4279115217:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.30/0.58 % (268806)Instruction limit reached!
% 2.30/0.58 % (268806)------------------------------
% 2.30/0.58 % (268806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268806)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268806)Termination reason: Instruction limit
% 2.30/0.58 % (268806)Termination phase: Saturation
% 2.30/0.58 % (268806)Time elapsed: 0.155 s
% 2.30/0.58 % (268806)Peak memory usage: 14 MB
% 2.30/0.58 % (268806)Instructions burned: 481 (million)
% 2.30/0.58 % (268837)fmb+10_1_sil=64000:random_seed=284979488:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.30/0.58 % (268837)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268837)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268837)------------------------------
% 2.30/0.58 % (268837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268837)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268837)Termination reason: Inappropriate
% 2.30/0.58 % (268837)Time elapsed: 0.0000 s
% 2.30/0.58 % (268837)Peak memory usage: 10 MB
% 2.30/0.58 % (268837)------------------------------
% 2.30/0.58 % (268837)------------------------------
% 2.30/0.58 % (268842)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2474411499:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.30/0.58 % (268842)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268842)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268842)------------------------------
% 2.30/0.58 % (268842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268842)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268842)Termination reason: Inappropriate
% 2.30/0.58 % (268842)Time elapsed: 0.0000 s
% 2.30/0.58 % (268842)Peak memory usage: 10 MB
% 2.30/0.58 % (268842)------------------------------
% 2.30/0.58 % (268842)------------------------------
% 2.30/0.58 % (268851)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3840308188:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.30/0.58 % (268851)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.30/0.58 % (268851)Terminated due to inappropriate strategy.
% 2.30/0.58 % (268851)------------------------------
% 2.30/0.58 % (268851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268851)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268851)Termination reason: Inappropriate
% 2.30/0.58 % (268851)Time elapsed: 0.0000 s
% 2.30/0.58 % (268851)Peak memory usage: 10 MB
% 2.30/0.58 % (268851)------------------------------
% 2.30/0.58 % (268851)------------------------------
% 2.30/0.58 % (268858)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1310056023:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.30/0.58 % (268858) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-268781-268858"...
% 2.30/0.58 % (268858)...printing done.
% 2.30/0.58 % (268858)Refutation found. Thanks to Tanya!
% 2.30/0.58 % SZS status Theorem for theBenchmark
% 2.30/0.58 % SZS output start Proof for theBenchmark
% 2.30/0.58 tff(func_def_0, type, x: $real).
% 2.30/0.58 tff(func_def_1, type, y: $real).
% 2.30/0.58 tff(func_def_2, type, u: $real).
% 2.30/0.58 tff(func_def_3, type, v: $real).
% 2.30/0.58 tff(func_def_4, type, f: $real > $real).
% 2.30/0.58 tff(f1,axiom,(
% 2.30/0.58 ! [X0 : $real,X1 : $real] : ($greatereq(X0,X1) => $greatereq(f(X0),f(X1)))),
% 2.30/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_non_decreasing)).
% 2.30/0.58 tff(f2,axiom,(
% 2.30/0.58 $less(u,v)),
% 2.30/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis)).
% 2.30/0.58 tff(f3,axiom,(
% 2.30/0.58 $lesseq(x,y)),
% 2.30/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01)).
% 2.30/0.58 tff(f4,conjecture,(
% 2.30/0.58 $less($sum(u,f(x)),$sum(v,f(y)))),
% 2.30/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion)).
% 2.30/0.58 tff(f5,negated_conjecture,(
% 2.30/0.58 ~ $less($sum(u,f(x)),$sum(v,f(y)))),
% 2.30/0.58 inference(negated_conjecture,[status(cth)],[f4])).
% 2.30/0.58 tff(f6,plain,(
% 2.30/0.58 ! [X0 : $real,X1 : $real] : (~$less(X0,X1) => ~$less(f(X0),f(X1)))),
% 2.30/0.58 inference(theory_normalization,[],[f1])).
% 2.30/0.58 tff(f7,plain,(
% 2.30/0.58 ~$less(y,x)),
% 2.30/0.58 inference(theory_normalization,[],[f3])).
% 2.30/0.58 tff(f8,definition,(
% 2.30/0.58 ( ! [X0 : $real,X1 : $real] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 2.30/0.58 introduced(theory,[tha_commutativity])).
% 2.30/0.58 tff(f9,definition,(
% 2.30/0.58 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 2.30/0.58 introduced(theory,[tha_associativity])).
% 2.30/0.58 tff(f12,definition,(
% 2.30/0.58 ( ! [X0 : $real] : (0/1 = $sum(X0,$uminus(X0))) )),
% 2.30/0.58 introduced(theory,[tha_inverse_op_unit])).
% 2.30/0.58 tff(f13,definition,(
% 2.30/0.58 ( ! [X0 : $real] : (~$less(X0,X0)) )),
% 2.30/0.58 introduced(theory,[tha_non-reflexivity])).
% 2.30/0.58 tff(f14,definition,(
% 2.30/0.58 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )),
% 2.30/0.58 introduced(theory,[tha_transitivity])).
% 2.30/0.58 tff(f15,definition,(
% 2.30/0.58 ( ! [X0 : $real,X1 : $real] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 2.30/0.58 introduced(theory,[tha_order_totality])).
% 2.30/0.58 tff(f16,definition,(
% 2.30/0.58 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 2.30/0.58 introduced(theory,[tha_order_monotonicity])).
% 2.30/0.58 tff(f19,plain,(
% 2.30/0.58 ~$less($sum(u,f(x)),$sum(v,f(y)))),
% 2.30/0.58 inference(flattening,[],[f5])).
% 2.30/0.58 tff(f20,plain,(
% 2.30/0.58 ! [X0 : $real,X1 : $real] : (~$less(f(X0),f(X1)) | $less(X0,X1))),
% 2.30/0.58 inference(ennf_transformation,[],[f6])).
% 2.30/0.58 tff(f21,plain,(
% 2.30/0.58 ( ! [X0 : $real,X1 : $real] : (~$less(f(X0),f(X1)) | $less(X0,X1)) )),
% 2.30/0.58 inference(cnf_transformation,[],[f20])).
% 2.30/0.58 tff(f22,plain,(
% 2.30/0.58 $less(u,v)),
% 2.30/0.58 inference(cnf_transformation,[],[f2])).
% 2.30/0.58 tff(f23,plain,(
% 2.30/0.58 ~$less(y,x)),
% 2.30/0.58 inference(cnf_transformation,[],[f7])).
% 2.30/0.58 tff(f24,plain,(
% 2.30/0.58 ~$less($sum(u,f(x)),$sum(v,f(y)))),
% 2.30/0.58 inference(cnf_transformation,[],[f19])).
% 2.30/0.58 tff(f49,plain,(
% 2.30/0.58 ( ! [X0 : $real,X1 : $real] : (~$less(X0,X1) | ~$less(X1,X0)) )),
% 2.30/0.58 inference(resolution,[],[f14,f13])).
% 2.30/0.58 tff(f52,plain,(
% 2.30/0.58 ( ! [X0 : $real] : (~$less(X0,$sum(v,f(y))) | ~$less($sum(u,f(x)),X0)) )),
% 2.30/0.58 inference(resolution,[],[f14,f24])).
% 2.30/0.58 tff(f59,plain,(
% 2.30/0.58 ( ! [X0 : $real,X1 : $real] : ($less(f(X0),f(X1)) | f(X0) = f(X1) | $less(X1,X0)) )),
% 2.30/0.58 inference(resolution,[],[f15,f21])).
% 2.30/0.58 tff(f60,plain,(
% 2.30/0.58 $less($sum(v,f(y)),$sum(u,f(x))) | $sum(u,f(x)) = $sum(v,f(y))),
% 2.30/0.58 inference(resolution,[],[f15,f24])).
% 2.30/0.58 tff(f98,plain,(
% 2.30/0.58 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($less($sum(X0,X1),$sum(X2,X0)) | ~$less(X1,X2)) )),
% 2.30/0.58 inference(superposition,[],[f16,f8])).
% 2.30/0.58 tff(f140,definition,(
% 2.30/0.58 spl0_3 <=> $sum(u,f(x)) = $sum(v,f(y))),
% 2.30/0.58 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 2.30/0.58 tff(f142,plain,(
% 2.30/0.58 $sum(u,f(x)) = $sum(v,f(y)) | ~spl0_3),
% 2.30/0.58 inference(avatar_component_clause,[],[f140])).
% 2.30/0.58 tff(f144,definition,(
% 2.30/0.58 spl0_4 <=> $less($sum(v,f(y)),$sum(u,f(x)))),
% 2.30/0.58 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 2.30/0.58 tff(f146,plain,(
% 2.30/0.58 $less($sum(v,f(y)),$sum(u,f(x))) | ~spl0_4),
% 2.30/0.58 inference(avatar_component_clause,[],[f144])).
% 2.30/0.58 tff(f147,plain,(
% 2.30/0.58 spl0_3 | spl0_4),
% 2.30/0.58 inference(avatar_split_clause,[],[f60,f144,f140])).
% 2.30/0.58 tff(f153,plain,(
% 2.30/0.58 ( ! [X0 : $real] : ($sum(v,$sum(f(y),X0)) = $sum($sum(u,f(x)),X0)) ) | ~spl0_3),
% 2.30/0.58 inference(superposition,[],[f9,f142])).
% 2.30/0.58 tff(f156,plain,(
% 2.30/0.58 ( ! [X0 : $real] : ($sum(v,$sum(f(y),X0)) = $sum(u,$sum(f(x),X0))) ) | ~spl0_3),
% 2.30/0.58 inference(forward_demodulation,[],[f153,f9])).
% 2.30/0.58 tff(f392,plain,(
% 2.30/0.58 ( ! [X0 : $real] : (~$less($sum(u,f(x)),$sum(f(y),X0)) | ~$less(X0,v)) )),
% 2.30/0.58 inference(resolution,[],[f98,f52])).
% 2.30/0.58 tff(f1336,plain,(
% 2.30/0.58 ~$less(u,v) | ~$less(f(x),f(y))),
% 2.30/0.58 inference(resolution,[],[f392,f98])).
% 2.30/0.58 tff(f1351,plain,(
% 2.30/0.58 ~$less(f(x),f(y))),
% 2.30/0.58 inference(forward_subsumption_resolution,[],[f1336,f22])).
% 2.30/0.58 tff(f1352,plain,(
% 2.30/0.58 f(x) = f(y) | $less(y,x)),
% 2.30/0.58 inference(resolution,[],[f1351,f59])).
% 2.30/0.58 tff(f1356,plain,(
% 2.30/0.58 f(x) = f(y)),
% 2.30/0.58 inference(forward_subsumption_resolution,[],[f1352,f23])).
% 2.30/0.58 tff(f1513,plain,(
% 2.30/0.58 ( ! [X0 : $real] : ($sum(u,$sum(f(x),X0)) = $sum(v,$sum(f(x),X0))) ) | ~spl0_3),
% 2.30/0.58 inference(forward_demodulation,[],[f156,f1356])).
% 2.30/0.58 tff(f1542,plain,(
% 2.30/0.58 $sum(u,0/1) = $sum(v,0/1) | ~spl0_3),
% 2.30/0.58 inference(superposition,[],[f1513,f12])).
% 2.30/0.58 tff(f1569,plain,(
% 2.30/0.58 u = v | ~spl0_3),
% 2.30/0.58 inference(evaluation,[],[f1542])).
% 2.30/0.58 tff(f1581,plain,(
% 2.30/0.58 $less(u,u) | ~spl0_3),
% 2.30/0.58 inference(superposition,[],[f22,f1569])).
% 2.30/0.58 tff(f1605,plain,(
% 2.30/0.58 $false | ~spl0_3),
% 2.30/0.58 inference(forward_subsumption_resolution,[],[f1581,f13])).
% 2.30/0.58 tff(f1606,plain,(
% 2.30/0.58 ~spl0_3),
% 2.30/0.58 inference(avatar_contradiction_clause,[],[f1605])).
% 2.30/0.58 tff(f1608,plain,(
% 2.30/0.58 $less($sum(v,f(x)),$sum(u,f(x))) | ~spl0_4),
% 2.30/0.58 inference(forward_demodulation,[],[f146,f1356])).
% 2.30/0.58 tff(f1618,plain,(
% 2.30/0.58 ~$less($sum(u,f(x)),$sum(v,f(x))) | ~spl0_4),
% 2.30/0.58 inference(resolution,[],[f1608,f49])).
% 2.30/0.58 tff(f1620,plain,(
% 2.30/0.58 ~$less(u,v) | ~spl0_4),
% 2.30/0.58 inference(resolution,[],[f1618,f16])).
% 2.30/0.58 tff(f1624,plain,(
% 2.30/0.58 $false | ~spl0_4),
% 2.30/0.58 inference(forward_subsumption_resolution,[],[f1620,f22])).
% 2.30/0.58 tff(f1625,plain,(
% 2.30/0.58 ~spl0_4),
% 2.30/0.58 inference(avatar_contradiction_clause,[],[f1624])).
% 2.30/0.58 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f147])).
% 2.30/0.58 cnf(s15, plain, ~spl0_3, inference(sat_conversion,[],[f1606])).
% 2.30/0.58 cnf(s16, plain, ~spl0_4, inference(sat_conversion,[],[f1625])).
% 2.30/0.58 cnf(s18, plain, $false, inference(rat,[],[s2,s16,s15])).
% 2.30/0.58 tff(f1626,plain,(
% 2.30/0.58 $false),
% 2.30/0.58 inference(avatar_sat_refutation,[],[s18])).
% 2.30/0.58 % SZS output end Proof for theBenchmark
% 2.30/0.58 % (268858)------------------------------
% 2.30/0.58 % (268858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.58 % (268858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.58 % (268858)CaDiCaL version: 2.1.3
% 2.30/0.58 % (268858)Termination reason: Refutation
% 2.30/0.58 % (268858)Time elapsed: 0.025 s
% 2.30/0.58 % (268858)Peak memory usage: 13 MB
% 2.30/0.58 % (268858)Instructions burned: 71 (million)
% 2.30/0.58 % (268781)Success in time 0.364 s
% 2.30/0.58 % Vampire exiting
%------------------------------------------------------------------------------