%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX092_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 01:46:28 PM UTC 2026
% Result : Theorem 2.26s 0.61s
% Output : Refutation 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX092_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n013.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 15:00:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 2.26/0.61 % (1246804)Will run a generic schedule for satisfiability detection.
% 2.26/0.61 % (1246812)dis+10_1_sil=32000:sp=arity:random_seed=3812361752:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.26/0.61 % (1246810)% WARNING: option uhcvi not known.
% 2.26/0.61 % (1246811)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1812788176:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.26/0.61 % (1246809)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2235374509_2999 on theBenchmark for (2999ds/0Mi)
% 2.26/0.61 % (1246810)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2865326066:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.26/0.61 % (1246813)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1575112001:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.26/0.61 % (1246814)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2020186463:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.26/0.61 % (1246815)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=407614479:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.26/0.61 % (1246809)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246809)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246809)------------------------------
% 2.26/0.61 % (1246809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246809)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246809)Termination reason: Inappropriate
% 2.26/0.61 % (1246809)Time elapsed: 0.002 s
% 2.26/0.61 % (1246809)Peak memory usage: 11 MB
% 2.26/0.61 % (1246809)Instructions burned: 2 (million)
% 2.26/0.61 % (1246809)------------------------------
% 2.26/0.61 % (1246809)------------------------------
% 2.26/0.61 % (1246823)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3041432645:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.26/0.61 % (1246823)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246823)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246823)------------------------------
% 2.26/0.61 % (1246823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246823)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246823)Termination reason: Inappropriate
% 2.26/0.61 % (1246823)Time elapsed: 0.001 s
% 2.26/0.61 % (1246823)Peak memory usage: 10 MB
% 2.26/0.61 % (1246823)Instructions burned: 2 (million)
% 2.26/0.61 % (1246823)------------------------------
% 2.26/0.61 % (1246823)------------------------------
% 2.26/0.61 % (1246812)Instruction limit reached!
% 2.26/0.61 % (1246812)------------------------------
% 2.26/0.61 % (1246812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246812)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246812)Termination reason: Instruction limit
% 2.26/0.61 % (1246812)Termination phase: Saturation
% 2.26/0.61 % (1246812)Time elapsed: 0.035 s
% 2.26/0.61 % (1246812)Peak memory usage: 13 MB
% 2.26/0.61 % (1246812)Instructions burned: 105 (million)
% 2.26/0.61 % (1246826)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=2202137823:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.26/0.61 % (1246825)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1537146112:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.26/0.61 % (1246813)Instruction limit reached!
% 2.26/0.61 % (1246813)------------------------------
% 2.26/0.61 % (1246813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246813)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246813)Termination reason: Instruction limit
% 2.26/0.61 % (1246813)Termination phase: Saturation
% 2.26/0.61 % (1246813)Time elapsed: 0.073 s
% 2.26/0.61 % (1246813)Peak memory usage: 12 MB
% 2.26/0.61 % (1246813)Instructions burned: 117 (million)
% 2.26/0.61 % (1246814)Instruction limit reached!
% 2.26/0.61 % (1246814)------------------------------
% 2.26/0.61 % (1246814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246814)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246814)Termination reason: Instruction limit
% 2.26/0.61 % (1246814)Termination phase: Saturation
% 2.26/0.61 % (1246814)Time elapsed: 0.079 s
% 2.26/0.61 % (1246814)Peak memory usage: 13 MB
% 2.26/0.61 % (1246814)Instructions burned: 131 (million)
% 2.26/0.61 % (1246829)ott-21_1_sil=16000:fs=off:random_seed=1737991804:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.26/0.61 % (1246830)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3575711064:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.26/0.61 % (1246815)Instruction limit reached!
% 2.26/0.61 % (1246815)------------------------------
% 2.26/0.61 % (1246815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246815)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246815)Termination reason: Instruction limit
% 2.26/0.61 % (1246815)Termination phase: Saturation
% 2.26/0.61 % (1246815)Time elapsed: 0.112 s
% 2.26/0.61 % (1246815)Peak memory usage: 13 MB
% 2.26/0.61 % (1246815)Instructions burned: 159 (million)
% 2.26/0.61 % (1246825)Instruction limit reached!
% 2.26/0.61 % (1246825)------------------------------
% 2.26/0.61 % (1246825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246825)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246825)Termination reason: Instruction limit
% 2.26/0.61 % (1246825)Termination phase: Saturation
% 2.26/0.61 % (1246825)Time elapsed: 0.088 s
% 2.26/0.61 % (1246825)Peak memory usage: 13 MB
% 2.26/0.61 % (1246825)Instructions burned: 131 (million)
% 2.26/0.61 % (1246833)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2135362202:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.26/0.61 % (1246833)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246833)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246833)------------------------------
% 2.26/0.61 % (1246833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246833)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246833)Termination reason: Inappropriate
% 2.26/0.61 % (1246833)Time elapsed: 0.003 s
% 2.26/0.61 % (1246833)Peak memory usage: 10 MB
% 2.26/0.61 % (1246833)Instructions burned: 5 (million)
% 2.26/0.61 % (1246833)------------------------------
% 2.26/0.61 % (1246833)------------------------------
% 2.26/0.61 % (1246835)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3223692572:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.26/0.61 % (1246836)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=751131642:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.26/0.61 % (1246836)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246836)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246836)------------------------------
% 2.26/0.61 % (1246836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246836)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246836)Termination reason: Inappropriate
% 2.26/0.61 % (1246836)Time elapsed: 0.001 s
% 2.26/0.61 % (1246836)Peak memory usage: 10 MB
% 2.26/0.61 % (1246836)Instructions burned: 2 (million)
% 2.26/0.61 % (1246836)------------------------------
% 2.26/0.61 % (1246836)------------------------------
% 2.26/0.61 % (1246829)Instruction limit reached!
% 2.26/0.61 % (1246829)------------------------------
% 2.26/0.61 % (1246829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246829)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246829)Termination reason: Instruction limit
% 2.26/0.61 % (1246829)Termination phase: Saturation
% 2.26/0.61 % (1246829)Time elapsed: 0.081 s
% 2.26/0.61 % (1246829)Peak memory usage: 12 MB
% 2.26/0.61 % (1246829)Instructions burned: 182 (million)
% 2.26/0.61 % (1246839)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=1609713111: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)
% 2.26/0.61 % (1246840)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3142921262:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.26/0.61 % (1246826)Instruction limit reached!
% 2.26/0.61 % (1246826)------------------------------
% 2.26/0.61 % (1246826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246826)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246826)Termination reason: Instruction limit
% 2.26/0.61 % (1246826)Termination phase: Saturation
% 2.26/0.61 % (1246826)Time elapsed: 0.191 s
% 2.26/0.61 % (1246826)Peak memory usage: 16 MB
% 2.26/0.61 % (1246826)Instructions burned: 686 (million)
% 2.26/0.61 % (1246843)fmb+10_1_sil=64000:random_seed=553067939:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.26/0.61 % (1246843)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246843)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246843)------------------------------
% 2.26/0.61 % (1246843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246843)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246843)Termination reason: Inappropriate
% 2.26/0.61 % (1246843)Time elapsed: 0.001 s
% 2.26/0.61 % (1246843)Peak memory usage: 10 MB
% 2.26/0.61 % (1246843)Instructions burned: 2 (million)
% 2.26/0.61 % (1246843)------------------------------
% 2.26/0.61 % (1246843)------------------------------
% 2.26/0.61 % (1246845)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=494609672:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.26/0.61 % (1246845)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246845)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246845)------------------------------
% 2.26/0.61 % (1246845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246845)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246845)Termination reason: Inappropriate
% 2.26/0.61 % (1246845)Time elapsed: 0.001 s
% 2.26/0.61 % (1246845)Peak memory usage: 10 MB
% 2.26/0.61 % (1246845)Instructions burned: 2 (million)
% 2.26/0.61 % (1246845)------------------------------
% 2.26/0.61 % (1246845)------------------------------
% 2.26/0.61 % (1246847)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3090929740:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.26/0.61 % (1246847)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.26/0.61 % (1246847)Terminated due to inappropriate strategy.
% 2.26/0.61 % (1246847)------------------------------
% 2.26/0.61 % (1246847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246847)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246847)Termination reason: Inappropriate
% 2.26/0.61 % (1246847)Time elapsed: 0.001 s
% 2.26/0.61 % (1246847)Peak memory usage: 11 MB
% 2.26/0.61 % (1246847)Instructions burned: 2 (million)
% 2.26/0.61 % (1246847)------------------------------
% 2.26/0.61 % (1246847)------------------------------
% 2.26/0.61 % (1246849)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3632418955:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.26/0.61 % (1246849) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1246804-1246849"...
% 2.26/0.61 % (1246849)...printing done.
% 2.26/0.61 % (1246849)Refutation found. Thanks to Tanya!
% 2.26/0.61 % SZS status Theorem for theBenchmark
% 2.26/0.61 % SZS output start Proof for theBenchmark
% 2.26/0.61 tff(type_def_5, type, general: $tType).
% 2.26/0.61 tff(type_def_6, type, symbol: $tType).
% 2.26/0.61 tff(func_def_0, type, f__integer__: $int > general).
% 2.26/0.61 tff(func_def_1, type, f__symbolic__: symbol > general).
% 2.26/0.61 tff(func_def_2, type, c__infimum__: general).
% 2.26/0.61 tff(func_def_3, type, c__supremum__: general).
% 2.26/0.61 tff(func_def_4, type, n_i: $int).
% 2.26/0.61 tff(func_def_10, type, sK0: general > $int).
% 2.26/0.61 tff(func_def_11, type, sK1: general > symbol).
% 2.26/0.61 tff(func_def_12, type, sK2: $int).
% 2.26/0.61 tff(func_def_13, type, sK3: $int).
% 2.26/0.61 tff(pred_def_1, type, p__is_integer__: general > $o).
% 2.26/0.61 tff(pred_def_2, type, p__is_symbolic__: general > $o).
% 2.26/0.61 tff(pred_def_3, type, p__less_equal__: (general * general) > $o).
% 2.26/0.61 tff(pred_def_4, type, p__less__: (general * general) > $o).
% 2.26/0.61 tff(pred_def_5, type, p__greater_equal__: (general * general) > $o).
% 2.26/0.61 tff(pred_def_6, type, p__greater__: (general * general) > $o).
% 2.26/0.61 tff(pred_def_8, type, three: general > $o).
% 2.26/0.61 tff(pred_def_9, type, sqrt: general > $o).
% 2.26/0.61 tff(pred_def_10, type, three_p: general > $o).
% 2.26/0.61 tff(pred_def_11, type, more_than_three: general > $o).
% 2.26/0.61 tff(pred_def_12, type, sqrt: (general * general) > $o).
% 2.26/0.61 tff(f21,axiom,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : (sqrt(f__integer__(X0),f__integer__(X1)) <=> ($greatereq(X0,0) & $lesseq($product(X0,X0),X1) & $less(X1,$product($sum(X0,1),$sum(X0,1)))))),
% 2.26/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5_unnamed_formula)).
% 2.26/0.61 tff(f22,axiom,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : ((sqrt(f__integer__(X0),f__integer__(X1)) & $lesseq($product($sum(X0,1),$sum(X0,1)),$sum(X1,1))) => sqrt(f__integer__($sum(X0,1)),f__integer__($sum(X1,1))))),
% 2.26/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6_unnamed_formula)).
% 2.26/0.61 tff(f23,conjecture,(
% 2.26/0.61 ! [X0 : $int] : (($greatereq(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0))) => ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__($sum(X0,1))))),
% 2.26/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_7_inductive_step)).
% 2.26/0.61 tff(f24,negated_conjecture,(
% 2.26/0.61 ~ ! [X0 : $int] : (($greatereq(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0))) => ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__($sum(X0,1))))),
% 2.26/0.61 inference(negated_conjecture,[status(cth)],[f23])).
% 2.26/0.61 tff(f31,plain,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : (sqrt(f__integer__(X0),f__integer__(X1)) <=> (~$less(X0,0) & ~$less(X1,$product(X0,X0)) & $less(X1,$product($sum(X0,1),$sum(X0,1)))))),
% 2.26/0.61 inference(theory_normalization,[],[f21])).
% 2.26/0.61 tff(f32,plain,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : ((sqrt(f__integer__(X0),f__integer__(X1)) & ~$less($sum(X1,1),$product($sum(X0,1),$sum(X0,1)))) => sqrt(f__integer__($sum(X0,1)),f__integer__($sum(X1,1))))),
% 2.26/0.61 inference(theory_normalization,[],[f22])).
% 2.26/0.61 tff(f33,plain,(
% 2.26/0.61 ~ ! [X0 : $int] : ((~$less(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0))) => ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__($sum(X0,1))))),
% 2.26/0.61 inference(theory_normalization,[],[f24])).
% 2.26/0.61 tff(f34,definition,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 2.26/0.61 introduced(theory,[tha_commutativity])).
% 2.26/0.61 tff(f39,definition,(
% 2.26/0.61 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 2.26/0.61 introduced(theory,[tha_non-reflexivity])).
% 2.26/0.61 tff(f40,definition,(
% 2.26/0.61 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )),
% 2.26/0.61 introduced(theory,[tha_transitivity])).
% 2.26/0.61 tff(f43,definition,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 2.26/0.61 introduced(theory,[tha_order_plus_one_dichotomy])).
% 2.26/0.61 tff(f56,plain,(
% 2.26/0.61 ~ ! [X0 : $int] : ((~$less(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0))) => ? [X2 : $int] : sqrt(f__integer__(X2),f__integer__($sum(X0,1))))),
% 2.26/0.61 inference(rectify,[],[f33])).
% 2.26/0.61 tff(f67,plain,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : (sqrt(f__integer__($sum(X0,1)),f__integer__($sum(X1,1))) | (~sqrt(f__integer__(X0),f__integer__(X1)) | $less($sum(X1,1),$product($sum(X0,1),$sum(X0,1)))))),
% 2.26/0.61 inference(ennf_transformation,[],[f32])).
% 2.26/0.61 tff(f68,plain,(
% 2.26/0.61 ! [X0 : $int,X1 : $int] : (sqrt(f__integer__($sum(X0,1)),f__integer__($sum(X1,1))) | ~sqrt(f__integer__(X0),f__integer__(X1)) | $less($sum(X1,1),$product($sum(X0,1),$sum(X0,1))))),
% 2.26/0.61 inference(flattening,[],[f67])).
% 2.26/0.61 tff(f69,plain,(
% 2.26/0.61 ? [X0 : $int] : (! [X2 : $int] : ~sqrt(f__integer__(X2),f__integer__($sum(X0,1))) & (~$less(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0))))),
% 2.26/0.61 inference(ennf_transformation,[],[f56])).
% 2.26/0.61 tff(f70,plain,(
% 2.26/0.61 ? [X0 : $int] : (! [X2 : $int] : ~sqrt(f__integer__(X2),f__integer__($sum(X0,1))) & ~$less(X0,0) & ? [X1 : $int] : sqrt(f__integer__(X1),f__integer__(X0)))),
% 2.26/0.61 inference(flattening,[],[f69])).
% 2.26/0.61 tff(f90,plain,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : (~sqrt(f__integer__(X0),f__integer__(X1)) | ~$less(X1,$product(X0,X0))) )),
% 2.26/0.61 inference(cnf_transformation,[],[f31])).
% 2.26/0.61 tff(f91,plain,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : (~sqrt(f__integer__(X0),f__integer__(X1)) | ~$less(X0,0)) )),
% 2.26/0.61 inference(cnf_transformation,[],[f31])).
% 2.26/0.61 tff(f92,plain,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : (sqrt(f__integer__(X0),f__integer__(X1)) | $less(X1,$product(X0,X0)) | $less(X0,0) | ~$less(X1,$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(cnf_transformation,[],[f31])).
% 2.26/0.61 tff(f93,plain,(
% 2.26/0.61 ( ! [X0 : $int,X1 : $int] : (sqrt(f__integer__($sum(X0,1)),f__integer__($sum(X1,1))) | ~sqrt(f__integer__(X0),f__integer__(X1)) | $less($sum(X1,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(cnf_transformation,[],[f68])).
% 2.26/0.61 tff(f94,plain,(
% 2.26/0.61 sqrt(f__integer__(sK3),f__integer__(sK2))),
% 2.26/0.61 inference(cnf_transformation,[],[f70])).
% 2.26/0.61 tff(f96,plain,(
% 2.26/0.61 ( ! [X2 : $int] : (~sqrt(f__integer__(X2),f__integer__($sum(sK2,1)))) )),
% 2.26/0.61 inference(cnf_transformation,[],[f70])).
% 2.26/0.61 tff(f119,plain,(
% 2.26/0.61 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 2.26/0.61 inference(resolution,[],[f43,f39])).
% 2.26/0.61 tff(f122,plain,(
% 2.26/0.61 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 2.26/0.61 inference(superposition,[],[f119,f34])).
% 2.26/0.61 tff(f152,plain,(
% 2.26/0.61 ~$less(sK3,0)),
% 2.26/0.61 inference(resolution,[],[f91,f94])).
% 2.26/0.61 tff(f242,plain,(
% 2.26/0.61 ~$less(sK2,$product(sK3,sK3))),
% 2.26/0.61 inference(resolution,[],[f90,f94])).
% 2.26/0.61 tff(f357,plain,(
% 2.26/0.61 ( ! [X0 : $int] : ($less($sum(sK2,1),$product(X0,X0)) | $less(X0,0) | ~$less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(resolution,[],[f92,f96])).
% 2.26/0.61 tff(f362,plain,(
% 2.26/0.61 ( ! [X0 : $int] : ($less($sum(1,sK2),$product(X0,X0)) | $less(X0,0) | ~$less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(forward_demodulation,[],[f357,f34])).
% 2.26/0.61 tff(f363,plain,(
% 2.26/0.61 ( ! [X0 : $int] : (~$less($sum(1,sK2),$product($sum(X0,1),$sum(X0,1))) | $less($sum(1,sK2),$product(X0,X0)) | $less(X0,0)) )),
% 2.26/0.61 inference(forward_demodulation,[],[f362,f34])).
% 2.26/0.61 tff(f364,plain,(
% 2.26/0.61 ( ! [X0 : $int] : (~sqrt(f__integer__(X0),f__integer__(sK2)) | $less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(resolution,[],[f93,f96])).
% 2.26/0.61 tff(f379,plain,(
% 2.26/0.61 ( ! [X0 : $int] : (~sqrt(f__integer__(X0),f__integer__(sK2)) | $less($sum(1,sK2),$product($sum(X0,1),$sum(X0,1)))) )),
% 2.26/0.61 inference(forward_demodulation,[],[f364,f34])).
% 2.26/0.61 tff(f385,plain,(
% 2.26/0.61 $less($sum(1,sK2),$product($sum(sK3,1),$sum(sK3,1)))),
% 2.26/0.61 inference(resolution,[],[f379,f94])).
% 2.26/0.61 tff(f389,plain,(
% 2.26/0.61 $less($sum(1,sK2),$product($sum(1,sK3),$sum(1,sK3)))),
% 2.26/0.61 inference(forward_demodulation,[],[f385,f34])).
% 2.26/0.61 tff(f395,plain,(
% 2.26/0.61 ( ! [X0 : $int] : (~$less($sum(1,sK2),$product($sum(1,X0),$sum(1,X0))) | $less($sum(1,sK2),$product(X0,X0)) | $less(X0,0)) )),
% 2.26/0.61 inference(superposition,[],[f363,f34])).
% 2.26/0.61 tff(f3174,plain,(
% 2.26/0.61 ( ! [X0 : $int] : (~$less(X0,$product(sK3,sK3)) | ~$less(sK2,X0)) )),
% 2.26/0.61 inference(resolution,[],[f242,f40])).
% 2.26/0.61 tff(f3273,plain,(
% 2.26/0.61 $less($sum(1,sK2),$product(sK3,sK3)) | $less(sK3,0)),
% 2.26/0.61 inference(resolution,[],[f389,f395])).
% 2.26/0.61 tff(f3278,plain,(
% 2.26/0.61 $less($sum(1,sK2),$product(sK3,sK3))),
% 2.26/0.61 inference(forward_subsumption_resolution,[],[f3273,f152])).
% 2.26/0.61 tff(f3293,plain,(
% 2.26/0.61 ~$less(sK2,$sum(1,sK2))),
% 2.26/0.61 inference(resolution,[],[f3278,f3174])).
% 2.26/0.61 tff(f3298,plain,(
% 2.26/0.61 $false),
% 2.26/0.61 inference(forward_subsumption_resolution,[],[f3293,f122])).
% 2.26/0.61 % SZS output end Proof for theBenchmark
% 2.26/0.61 % (1246849)------------------------------
% 2.26/0.61 % (1246849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.61 % (1246849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.61 % (1246849)CaDiCaL version: 2.1.3
% 2.26/0.61 % (1246849)Termination reason: Refutation
% 2.26/0.61 % (1246849)Time elapsed: 0.049 s
% 2.26/0.61 % (1246849)Peak memory usage: 13 MB
% 2.26/0.61 % (1246849)Instructions burned: 152 (million)
% 2.26/0.61 % (1246804)Success in time 0.371 s
% 2.26/0.61 % Vampire exiting
%------------------------------------------------------------------------------