%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX100_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 01:46:29 PM UTC 2026
% Result : Theorem 3.31s 1.00s
% Output : Refutation 3.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX100_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n002.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 15:03:52 UTC 2026
% 0.26/0.27 % CPUTime :
% 0.26/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.31/1.00 % (420944)Will run a generic schedule for satisfiability detection.
% 3.31/1.00 % (420953)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2618627502:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.31/1.00 % (420950)% WARNING: option uhcvi not known.
% 3.31/1.00 % (420949)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2727247591_2999 on theBenchmark for (2999ds/0Mi)
% 3.31/1.00 % (420951)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4220983770:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.31/1.00 % (420952)dis+10_1_sil=32000:sp=arity:random_seed=3994056138:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.31/1.00 % (420950)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3839959286:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.31/1.00 % (420949)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420949)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420949)------------------------------
% 3.31/1.00 % (420949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420949)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420949)Termination reason: Inappropriate
% 3.31/1.00 % (420949)Time elapsed: 0.003 s
% 3.31/1.00 % (420949)Peak memory usage: 11 MB
% 3.31/1.00 % (420949)Instructions burned: 2 (million)
% 3.31/1.00 % (420954)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2858886615:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.31/1.00 % (420955)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1110150806:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.31/1.00 % (420949)------------------------------
% 3.31/1.00 % (420949)------------------------------
% 3.31/1.00 % (420963)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=796895911:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.31/1.00 % (420963)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420963)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420963)------------------------------
% 3.31/1.00 % (420963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420963)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420963)Termination reason: Inappropriate
% 3.31/1.00 % (420963)Time elapsed: 0.003 s
% 3.31/1.00 % (420963)Peak memory usage: 10 MB
% 3.31/1.00 % (420963)Instructions burned: 2 (million)
% 3.31/1.00 % (420963)------------------------------
% 3.31/1.00 % (420963)------------------------------
% 3.31/1.00 % (420953)Instruction limit reached!
% 3.31/1.00 % (420953)------------------------------
% 3.31/1.00 % (420953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420953)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420953)Termination reason: Instruction limit
% 3.31/1.00 % (420953)Termination phase: Saturation
% 3.31/1.00 % (420953)Time elapsed: 0.057 s
% 3.31/1.00 % (420953)Peak memory usage: 12 MB
% 3.31/1.00 % (420953)Instructions burned: 116 (million)
% 3.31/1.00 % (420966)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=2046565324:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.31/1.00 % (420965)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=818976934:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.31/1.00 % (420952)Instruction limit reached!
% 3.31/1.00 % (420952)------------------------------
% 3.31/1.00 % (420952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420952)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420952)Termination reason: Instruction limit
% 3.31/1.00 % (420952)Termination phase: Saturation
% 3.31/1.00 % (420952)Time elapsed: 0.107 s
% 3.31/1.00 % (420952)Peak memory usage: 13 MB
% 3.31/1.00 % (420952)Instructions burned: 103 (million)
% 3.31/1.00 % (420954)Instruction limit reached!
% 3.31/1.00 % (420954)------------------------------
% 3.31/1.00 % (420954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420954)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420954)Termination reason: Instruction limit
% 3.31/1.00 % (420954)Termination phase: Saturation
% 3.31/1.00 % (420954)Time elapsed: 0.135 s
% 3.31/1.00 % (420954)Peak memory usage: 13 MB
% 3.31/1.00 % (420954)Instructions burned: 131 (million)
% 3.31/1.00 % (420969)ott-21_1_sil=16000:fs=off:random_seed=4018090730:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.31/1.00 % (420970)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3022663914:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.31/1.00 % (420955)Instruction limit reached!
% 3.31/1.00 % (420955)------------------------------
% 3.31/1.00 % (420955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420955)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420955)Termination reason: Instruction limit
% 3.31/1.00 % (420955)Termination phase: Saturation
% 3.31/1.00 % (420955)Time elapsed: 0.176 s
% 3.31/1.00 % (420955)Peak memory usage: 13 MB
% 3.31/1.00 % (420955)Instructions burned: 161 (million)
% 3.31/1.00 % (420965)Instruction limit reached!
% 3.31/1.00 % (420965)------------------------------
% 3.31/1.00 % (420965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420973)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1940314033:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.31/1.00 % (420965)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420965)Termination reason: Instruction limit
% 3.31/1.00 % (420965)Termination phase: Saturation
% 3.31/1.00 % (420965)Time elapsed: 0.149 s
% 3.31/1.00 % (420965)Peak memory usage: 13 MB
% 3.31/1.00 % (420965)Instructions burned: 131 (million)
% 3.31/1.00 % (420973)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420973)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420973)------------------------------
% 3.31/1.00 % (420973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420973)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420973)Termination reason: Inappropriate
% 3.31/1.00 % (420973)Time elapsed: 0.004 s
% 3.31/1.00 % (420973)Peak memory usage: 10 MB
% 3.31/1.00 % (420973)Instructions burned: 3 (million)
% 3.31/1.00 % (420973)------------------------------
% 3.31/1.00 % (420973)------------------------------
% 3.31/1.00 % (420975)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3672963243:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 3.31/1.00 % (420976)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3638692650:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.31/1.00 % (420976)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420976)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420976)------------------------------
% 3.31/1.00 % (420976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420976)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420976)Termination reason: Inappropriate
% 3.31/1.00 % (420976)Time elapsed: 0.003 s
% 3.31/1.00 % (420976)Peak memory usage: 10 MB
% 3.31/1.00 % (420976)Instructions burned: 1 (million)
% 3.31/1.00 % (420976)------------------------------
% 3.31/1.00 % (420976)------------------------------
% 3.31/1.00 % (420969)Instruction limit reached!
% 3.31/1.00 % (420969)------------------------------
% 3.31/1.00 % (420969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420969)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420969)Termination reason: Instruction limit
% 3.31/1.00 % (420969)Termination phase: Saturation
% 3.31/1.00 % (420969)Time elapsed: 0.149 s
% 3.31/1.00 % (420969)Peak memory usage: 12 MB
% 3.31/1.00 % (420969)Instructions burned: 180 (million)
% 3.31/1.00 % (420979)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=3115838491: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)
% 3.31/1.00 % (420981)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3626845729:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 3.31/1.00 % (420966)Instruction limit reached!
% 3.31/1.00 % (420966)------------------------------
% 3.31/1.00 % (420966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420966)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420966)Termination reason: Instruction limit
% 3.31/1.00 % (420966)Termination phase: Saturation
% 3.31/1.00 % (420966)Time elapsed: 0.302 s
% 3.31/1.00 % (420966)Peak memory usage: 15 MB
% 3.31/1.00 % (420966)Instructions burned: 685 (million)
% 3.31/1.00 % (420983)fmb+10_1_sil=64000:random_seed=2525584489:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.31/1.00 % (420983)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420983)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420983)------------------------------
% 3.31/1.00 % (420983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420983)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420983)Termination reason: Inappropriate
% 3.31/1.00 % (420983)Time elapsed: 0.001 s
% 3.31/1.00 % (420983)Peak memory usage: 10 MB
% 3.31/1.00 % (420983)Instructions burned: 2 (million)
% 3.31/1.00 % (420983)------------------------------
% 3.31/1.00 % (420983)------------------------------
% 3.31/1.00 % (420985)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3502082099:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.31/1.00 % (420985)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420985)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420985)------------------------------
% 3.31/1.00 % (420985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420985)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420985)Termination reason: Inappropriate
% 3.31/1.00 % (420985)Time elapsed: 0.001 s
% 3.31/1.00 % (420985)Peak memory usage: 10 MB
% 3.31/1.00 % (420985)Instructions burned: 2 (million)
% 3.31/1.00 % (420985)------------------------------
% 3.31/1.00 % (420985)------------------------------
% 3.31/1.00 % (420987)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2791336512:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.31/1.00 % (420987)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.31/1.00 % (420987)Terminated due to inappropriate strategy.
% 3.31/1.00 % (420987)------------------------------
% 3.31/1.00 % (420987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420987)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420987)Termination reason: Inappropriate
% 3.31/1.00 % (420987)Time elapsed: 0.003 s
% 3.31/1.00 % (420987)Peak memory usage: 11 MB
% 3.31/1.00 % (420987)Instructions burned: 2 (million)
% 3.31/1.00 % (420987)------------------------------
% 3.31/1.00 % (420987)------------------------------
% 3.31/1.00 % (420989)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=955811037:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.31/1.00 % (420989) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-420944-420989"...
% 3.31/1.00 % (420989)...printing done.
% 3.31/1.00 % (420989)Refutation found. Thanks to Tanya!
% 3.31/1.00 % SZS status Theorem for theBenchmark
% 3.31/1.00 % SZS output start Proof for theBenchmark
% 3.31/1.00 tff(type_def_5, type, general: $tType).
% 3.31/1.00 tff(type_def_6, type, symbol: $tType).
% 3.31/1.00 tff(func_def_0, type, f__integer__: $int > general).
% 3.31/1.00 tff(func_def_1, type, f__symbolic__: symbol > general).
% 3.31/1.00 tff(func_def_2, type, c__infimum__: general).
% 3.31/1.00 tff(func_def_3, type, c__supremum__: general).
% 3.31/1.00 tff(func_def_4, type, a_i: $int).
% 3.31/1.00 tff(func_def_5, type, b_i: $int).
% 3.31/1.00 tff(func_def_12, type, sK0: general > $int).
% 3.31/1.00 tff(func_def_13, type, sK1: general > symbol).
% 3.31/1.00 tff(func_def_14, type, sK2: $int).
% 3.31/1.00 tff(func_def_15, type, sK3: $int).
% 3.31/1.00 tff(pred_def_1, type, p__is_integer__: general > $o).
% 3.31/1.00 tff(pred_def_2, type, p__is_symbolic__: general > $o).
% 3.31/1.00 tff(pred_def_3, type, p__less_equal__: (general * general) > $o).
% 3.31/1.00 tff(pred_def_4, type, p__less__: (general * general) > $o).
% 3.31/1.00 tff(pred_def_5, type, p__greater_equal__: (general * general) > $o).
% 3.31/1.00 tff(pred_def_6, type, p__greater__: (general * general) > $o).
% 3.31/1.00 tff(pred_def_8, type, composite: general > $o).
% 3.31/1.00 tff(pred_def_9, type, sqrtb: general > $o).
% 3.31/1.00 tff(pred_def_10, type, composite_p: general > $o).
% 3.31/1.00 tff(pred_def_11, type, prime: general > $o).
% 3.31/1.00 tff(pred_def_12, type, sqrt: (general * general) > $o).
% 3.31/1.00 tff(f21,axiom,(
% 3.31/1.00 ! [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)))))),
% 3.31/1.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_5_unnamed_formula)).
% 3.31/1.00 tff(f22,axiom,(
% 3.31/1.00 ! [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))))),
% 3.31/1.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_6_unnamed_formula)).
% 3.31/1.00 tff(f23,conjecture,(
% 3.31/1.00 ! [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))))),
% 3.31/1.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_7_inductive_step)).
% 3.31/1.00 tff(f24,negated_conjecture,(
% 3.31/1.00 ~ ! [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))))),
% 3.31/1.00 inference(negated_conjecture,[status(cth)],[f23])).
% 3.31/1.00 tff(f31,plain,(
% 3.31/1.00 ! [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)))))),
% 3.31/1.00 inference(theory_normalization,[],[f21])).
% 3.31/1.00 tff(f32,plain,(
% 3.31/1.00 ! [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))))),
% 3.31/1.00 inference(theory_normalization,[],[f22])).
% 3.31/1.00 tff(f33,plain,(
% 3.31/1.00 ~ ! [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))))),
% 3.31/1.00 inference(theory_normalization,[],[f24])).
% 3.31/1.00 tff(f34,definition,(
% 3.31/1.00 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 3.31/1.00 introduced(theory,[tha_commutativity])).
% 3.31/1.00 tff(f39,definition,(
% 3.31/1.00 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 3.31/1.00 introduced(theory,[tha_non-reflexivity])).
% 3.31/1.00 tff(f40,definition,(
% 3.31/1.00 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )),
% 3.31/1.00 introduced(theory,[tha_transitivity])).
% 3.31/1.00 tff(f43,definition,(
% 3.31/1.00 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 3.31/1.00 introduced(theory,[tha_order_plus_one_dichotomy])).
% 3.31/1.00 tff(f56,plain,(
% 3.31/1.00 ~ ! [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))))),
% 3.31/1.00 inference(rectify,[],[f33])).
% 3.31/1.00 tff(f67,plain,(
% 3.31/1.00 ! [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)))))),
% 3.31/1.00 inference(ennf_transformation,[],[f32])).
% 3.31/1.00 tff(f68,plain,(
% 3.31/1.00 ! [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))))),
% 3.31/1.00 inference(flattening,[],[f67])).
% 3.31/1.00 tff(f69,plain,(
% 3.31/1.00 ? [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))))),
% 3.31/1.00 inference(ennf_transformation,[],[f56])).
% 3.31/1.00 tff(f70,plain,(
% 3.31/1.00 ? [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)))),
% 3.31/1.00 inference(flattening,[],[f69])).
% 3.31/1.00 tff(f90,plain,(
% 3.31/1.00 ( ! [X0 : $int,X1 : $int] : (~sqrt(f__integer__(X0),f__integer__(X1)) | ~$less(X1,$product(X0,X0))) )),
% 3.31/1.00 inference(cnf_transformation,[],[f31])).
% 3.31/1.00 tff(f91,plain,(
% 3.31/1.00 ( ! [X0 : $int,X1 : $int] : (~sqrt(f__integer__(X0),f__integer__(X1)) | ~$less(X0,0)) )),
% 3.31/1.00 inference(cnf_transformation,[],[f31])).
% 3.31/1.00 tff(f92,plain,(
% 3.31/1.00 ( ! [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)))) )),
% 3.31/1.00 inference(cnf_transformation,[],[f31])).
% 3.31/1.00 tff(f93,plain,(
% 3.31/1.00 ( ! [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)))) )),
% 3.31/1.00 inference(cnf_transformation,[],[f68])).
% 3.31/1.00 tff(f94,plain,(
% 3.31/1.00 sqrt(f__integer__(sK3),f__integer__(sK2))),
% 3.31/1.00 inference(cnf_transformation,[],[f70])).
% 3.31/1.00 tff(f96,plain,(
% 3.31/1.00 ( ! [X2 : $int] : (~sqrt(f__integer__(X2),f__integer__($sum(sK2,1)))) )),
% 3.31/1.00 inference(cnf_transformation,[],[f70])).
% 3.31/1.00 tff(f119,plain,(
% 3.31/1.00 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 3.31/1.00 inference(resolution,[],[f43,f39])).
% 3.31/1.00 tff(f122,plain,(
% 3.31/1.00 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 3.31/1.00 inference(superposition,[],[f119,f34])).
% 3.31/1.00 tff(f152,plain,(
% 3.31/1.00 ~$less(sK3,0)),
% 3.31/1.00 inference(resolution,[],[f91,f94])).
% 3.31/1.00 tff(f240,plain,(
% 3.31/1.00 ~$less(sK2,$product(sK3,sK3))),
% 3.31/1.00 inference(resolution,[],[f90,f94])).
% 3.31/1.00 tff(f355,plain,(
% 3.31/1.00 ( ! [X0 : $int] : ($less($sum(sK2,1),$product(X0,X0)) | $less(X0,0) | ~$less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 3.31/1.00 inference(resolution,[],[f92,f96])).
% 3.31/1.00 tff(f360,plain,(
% 3.31/1.00 ( ! [X0 : $int] : ($less($sum(1,sK2),$product(X0,X0)) | $less(X0,0) | ~$less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 3.31/1.00 inference(forward_demodulation,[],[f355,f34])).
% 3.31/1.00 tff(f361,plain,(
% 3.31/1.00 ( ! [X0 : $int] : (~$less($sum(1,sK2),$product($sum(X0,1),$sum(X0,1))) | $less($sum(1,sK2),$product(X0,X0)) | $less(X0,0)) )),
% 3.31/1.00 inference(forward_demodulation,[],[f360,f34])).
% 3.31/1.00 tff(f362,plain,(
% 3.31/1.00 ( ! [X0 : $int] : (~sqrt(f__integer__(X0),f__integer__(sK2)) | $less($sum(sK2,1),$product($sum(X0,1),$sum(X0,1)))) )),
% 3.31/1.00 inference(resolution,[],[f93,f96])).
% 3.31/1.00 tff(f377,plain,(
% 3.31/1.00 ( ! [X0 : $int] : (~sqrt(f__integer__(X0),f__integer__(sK2)) | $less($sum(1,sK2),$product($sum(X0,1),$sum(X0,1)))) )),
% 3.31/1.00 inference(forward_demodulation,[],[f362,f34])).
% 3.31/1.00 tff(f383,plain,(
% 3.31/1.00 $less($sum(1,sK2),$product($sum(sK3,1),$sum(sK3,1)))),
% 3.31/1.00 inference(resolution,[],[f377,f94])).
% 3.31/1.00 tff(f387,plain,(
% 3.31/1.00 $less($sum(1,sK2),$product($sum(1,sK3),$sum(1,sK3)))),
% 3.31/1.00 inference(forward_demodulation,[],[f383,f34])).
% 3.31/1.00 tff(f393,plain,(
% 3.31/1.00 ( ! [X0 : $int] : (~$less($sum(1,sK2),$product($sum(1,X0),$sum(1,X0))) | $less($sum(1,sK2),$product(X0,X0)) | $less(X0,0)) )),
% 3.31/1.00 inference(superposition,[],[f361,f34])).
% 3.31/1.00 tff(f3059,plain,(
% 3.31/1.00 ( ! [X0 : $int] : (~$less(X0,$product(sK3,sK3)) | ~$less(sK2,X0)) )),
% 3.31/1.00 inference(resolution,[],[f240,f40])).
% 3.31/1.00 tff(f3125,plain,(
% 3.31/1.00 $less($sum(1,sK2),$product(sK3,sK3)) | $less(sK3,0)),
% 3.31/1.00 inference(resolution,[],[f387,f393])).
% 3.31/1.00 tff(f3130,plain,(
% 3.31/1.00 $less($sum(1,sK2),$product(sK3,sK3))),
% 3.31/1.00 inference(forward_subsumption_resolution,[],[f3125,f152])).
% 3.31/1.00 tff(f3145,plain,(
% 3.31/1.00 ~$less(sK2,$sum(1,sK2))),
% 3.31/1.00 inference(resolution,[],[f3130,f3059])).
% 3.31/1.00 tff(f3153,plain,(
% 3.31/1.00 $false),
% 3.31/1.00 inference(forward_subsumption_resolution,[],[f3145,f122])).
% 3.31/1.00 % SZS output end Proof for theBenchmark
% 3.31/1.00 % (420989)------------------------------
% 3.31/1.00 % (420989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/1.00 % (420989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.00 % (420989)CaDiCaL version: 2.1.3
% 3.31/1.00 % (420989)Termination reason: Refutation
% 3.31/1.00 % (420989)Time elapsed: 0.142 s
% 3.31/1.00 % (420989)Peak memory usage: 13 MB
% 3.31/1.00 % (420989)Instructions burned: 141 (million)
% 3.31/1.00 % (420944)Success in time 0.67 s
% 3.31/1.00 % Vampire exiting
%------------------------------------------------------------------------------