%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI594_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:34:56 AM UTC 2026
% Result : Theorem 4.25s 1.21s
% Output : Refutation 4.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI594_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.28 % Computer : n014.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Mon Sep 28 20:53:00 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.33 Running first-order model finding
% 0.26/0.33 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
% 5.81/1.15 % (2174127)Will run a generic schedule for satisfiability detection.
% 5.81/1.15 % (2174138)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4078660385:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 5.81/1.15 % (2174133)% WARNING: option uhcvi not known.
% 5.81/1.15 % (2174136)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=90548155:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 5.81/1.15 % (2174135)dis+10_1_sil=32000:sp=arity:random_seed=1862616218:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 5.81/1.15 % (2174132)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2996278075_3000 on theBenchmark for (3000ds/0Mi)
% 5.81/1.15 % (2174133)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=423898238:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 5.81/1.15 % (2174134)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1233918423:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 5.81/1.15 % (2174137)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2717294918:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 5.81/1.15 % (2174132)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 5.81/1.15 % (2174132)Terminated due to inappropriate strategy.
% 5.81/1.15 % (2174132)------------------------------
% 5.81/1.15 % (2174132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.81/1.15 % (2174132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/1.15 % (2174132)CaDiCaL version: 2.1.3
% 5.81/1.15 % (2174132)Termination reason: Inappropriate
% 5.81/1.15 % (2174132)Time elapsed: 0.001 s
% 5.81/1.15 % (2174132)Peak memory usage: 10 MB
% 5.81/1.15 % (2174132)------------------------------
% 5.81/1.15 % (2174132)------------------------------
% 5.81/1.15 % (2174146)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2092009691:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.81/1.15 % (2174146)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 5.81/1.15 % (2174146)Terminated due to inappropriate strategy.
% 5.81/1.15 % (2174146)------------------------------
% 5.81/1.15 % (2174146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.81/1.15 % (2174146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/1.15 % (2174146)CaDiCaL version: 2.1.3
% 5.81/1.15 % (2174146)Termination reason: Inappropriate
% 5.81/1.15 % (2174146)Time elapsed: 0.001 s
% 5.81/1.15 % (2174146)Peak memory usage: 10 MB
% 5.81/1.15 % (2174146)------------------------------
% 5.81/1.15 % (2174146)------------------------------
% 5.81/1.15 % (2174148)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=719959116:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.81/1.15 % (2174138)Instruction limit reached!
% 5.81/1.15 % (2174138)------------------------------
% 5.81/1.15 % (2174138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.81/1.15 % (2174138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/1.15 % (2174138)CaDiCaL version: 2.1.3
% 5.81/1.15 % (2174138)Termination reason: Instruction limit
% 5.81/1.15 % (2174138)Termination phase: Saturation
% 5.81/1.15 % (2174138)Time elapsed: 0.080 s
% 5.81/1.15 % (2174138)Peak memory usage: 13 MB
% 5.81/1.15 % (2174138)Instructions burned: 159 (million)
% 5.81/1.15 % (2174150)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=3327556003:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.81/1.15 % (2174135)Instruction limit reached!
% 5.81/1.15 % (2174135)------------------------------
% 5.81/1.15 % (2174135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.81/1.15 % (2174135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/1.15 % (2174135)CaDiCaL version: 2.1.3
% 5.81/1.15 % (2174135)Termination reason: Instruction limit
% 5.81/1.15 % (2174135)Termination phase: Saturation
% 5.81/1.15 % (2174135)Time elapsed: 0.101 s
% 5.81/1.15 % (2174135)Peak memory usage: 12 MB
% 5.81/1.15 % (2174135)Instructions burned: 103 (million)
% 5.81/1.15 % (2174136)Instruction limit reached!
% 5.81/1.15 % (2174136)------------------------------
% 5.81/1.15 % (2174136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.81/1.15 % (2174136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174136)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174136)Termination reason: Instruction limit
% 4.25/1.20 % (2174136)Termination phase: Saturation
% 4.25/1.20 % (2174136)Time elapsed: 0.112 s
% 4.25/1.20 % (2174136)Peak memory usage: 12 MB
% 4.25/1.20 % (2174136)Instructions burned: 116 (million)
% 4.25/1.20 % (2174153)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2823060125:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.25/1.20 % (2174152)ott-21_1_sil=16000:fs=off:random_seed=2438519766:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.25/1.20 % (2174137)Instruction limit reached!
% 4.25/1.20 % (2174137)------------------------------
% 4.25/1.20 % (2174137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.20 % (2174137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174137)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174137)Termination reason: Instruction limit
% 4.25/1.20 % (2174137)Termination phase: Saturation
% 4.25/1.20 % (2174137)Time elapsed: 0.135 s
% 4.25/1.20 % (2174137)Peak memory usage: 12 MB
% 4.25/1.20 % (2174137)Instructions burned: 131 (million)
% 4.25/1.20 % (2174156)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3551377824:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.25/1.20 % (2174156)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.20 % (2174156)Terminated due to inappropriate strategy.
% 4.25/1.20 % (2174156)------------------------------
% 4.25/1.20 % (2174156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.20 % (2174156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174156)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174156)Termination reason: Inappropriate
% 4.25/1.20 % (2174156)Time elapsed: 0.0000 s
% 4.25/1.20 % (2174156)Peak memory usage: 10 MB
% 4.25/1.20 % (2174156)------------------------------
% 4.25/1.20 % (2174156)------------------------------
% 4.25/1.20 % (2174158)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2004124601:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.25/1.20 % (2174148)Instruction limit reached!
% 4.25/1.20 % (2174148)------------------------------
% 4.25/1.20 % (2174148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.20 % (2174148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174148)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174148)Termination reason: Instruction limit
% 4.25/1.20 % (2174148)Termination phase: Saturation
% 4.25/1.20 % (2174148)Time elapsed: 0.145 s
% 4.25/1.20 % (2174148)Peak memory usage: 13 MB
% 4.25/1.20 % (2174148)Instructions burned: 131 (million)
% 4.25/1.20 % (2174160)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3710706300:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 4.25/1.20 % (2174160)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.20 % (2174160)Terminated due to inappropriate strategy.
% 4.25/1.20 % (2174160)------------------------------
% 4.25/1.20 % (2174160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.20 % (2174160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174160)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174160)Termination reason: Inappropriate
% 4.25/1.20 % (2174160)Time elapsed: 0.001 s
% 4.25/1.20 % (2174160)Peak memory usage: 10 MB
% 4.25/1.20 % (2174160)------------------------------
% 4.25/1.20 % (2174160)------------------------------
% 4.25/1.20 % (2174162)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=3946181027: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)
% 4.25/1.20 % (2174152)Instruction limit reached!
% 4.25/1.20 % (2174152)------------------------------
% 4.25/1.20 % (2174152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.20 % (2174152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.20 % (2174152)CaDiCaL version: 2.1.3
% 4.25/1.20 % (2174152)Termination reason: Instruction limit
% 4.25/1.20 % (2174152)Termination phase: Saturation
% 4.25/1.20 % (2174152)Time elapsed: 0.140 s
% 4.25/1.20 % (2174152)Peak memory usage: 12 MB
% 4.25/1.20 % (2174152)Instructions burned: 181 (million)
% 4.25/1.20 % (2174164)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1128417795:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 4.25/1.21 % (2174150)Instruction limit reached!
% 4.25/1.21 % (2174150)------------------------------
% 4.25/1.21 % (2174150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174150)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174150)Termination reason: Instruction limit
% 4.25/1.21 % (2174150)Termination phase: Saturation
% 4.25/1.21 % (2174150)Time elapsed: 0.310 s
% 4.25/1.21 % (2174150)Peak memory usage: 15 MB
% 4.25/1.21 % (2174150)Instructions burned: 686 (million)
% 4.25/1.21 % (2174170)fmb+10_1_sil=64000:random_seed=608292802:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 4.25/1.21 % (2174170)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.21 % (2174170)Terminated due to inappropriate strategy.
% 4.25/1.21 % (2174170)------------------------------
% 4.25/1.21 % (2174170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174170)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174170)Termination reason: Inappropriate
% 4.25/1.21 % (2174170)Time elapsed: 0.001 s
% 4.25/1.21 % (2174170)Peak memory usage: 10 MB
% 4.25/1.21 % (2174170)------------------------------
% 4.25/1.21 % (2174170)------------------------------
% 4.25/1.21 % (2174174)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2722854887:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 4.25/1.21 % (2174174)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.21 % (2174174)Terminated due to inappropriate strategy.
% 4.25/1.21 % (2174174)------------------------------
% 4.25/1.21 % (2174174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174174)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174174)Termination reason: Inappropriate
% 4.25/1.21 % (2174174)Time elapsed: 0.001 s
% 4.25/1.21 % (2174174)Peak memory usage: 10 MB
% 4.25/1.21 % (2174174)------------------------------
% 4.25/1.21 % (2174174)------------------------------
% 4.25/1.21 % (2174176)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1109907015:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 4.25/1.21 % (2174176)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.21 % (2174176)Terminated due to inappropriate strategy.
% 4.25/1.21 % (2174176)------------------------------
% 4.25/1.21 % (2174176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174176)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174176)Termination reason: Inappropriate
% 4.25/1.21 % (2174176)Time elapsed: 0.001 s
% 4.25/1.21 % (2174176)Peak memory usage: 10 MB
% 4.25/1.21 % (2174176)------------------------------
% 4.25/1.21 % (2174176)------------------------------
% 4.25/1.21 % (2174180)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2914721858:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 4.25/1.21 % (2174153)Instruction limit reached!
% 4.25/1.21 % (2174153)------------------------------
% 4.25/1.21 % (2174153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174153)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174153)Termination reason: Instruction limit
% 4.25/1.21 % (2174153)Termination phase: Saturation
% 4.25/1.21 % (2174153)Time elapsed: 0.477 s
% 4.25/1.21 % (2174153)Peak memory usage: 14 MB
% 4.25/1.21 % (2174153)Instructions burned: 477 (million)
% 4.25/1.21 % (2174182)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2853886424:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 4.25/1.21 % (2174164)Instruction limit reached!
% 4.25/1.21 % (2174164)------------------------------
% 4.25/1.21 % (2174164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174164)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174164)Termination reason: Instruction limit
% 4.25/1.21 % (2174164)Termination phase: Saturation
% 4.25/1.21 % (2174164)Time elapsed: 0.477 s
% 4.25/1.21 % (2174164)Peak memory usage: 19 MB
% 4.25/1.21 % (2174164)Instructions burned: 882 (million)
% 4.25/1.21 % (2174184)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1252852536:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 4.25/1.21 % (2174184)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 4.25/1.21 % (2174184)Terminated due to inappropriate strategy.
% 4.25/1.21 % (2174184)------------------------------
% 4.25/1.21 % (2174184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174184)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174184)Termination reason: Inappropriate
% 4.25/1.21 % (2174184)Time elapsed: 0.001 s
% 4.25/1.21 % (2174184)Peak memory usage: 10 MB
% 4.25/1.21 % (2174184)------------------------------
% 4.25/1.21 % (2174184)------------------------------
% 4.25/1.21 % (2174162) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2174127-2174162"...
% 4.25/1.21 % (2174162)...printing done.
% 4.25/1.21 % (2174162)Refutation found. Thanks to Tanya!
% 4.25/1.21 % SZS status Theorem for theBenchmark
% 4.25/1.21 % SZS output start Proof for theBenchmark
% 4.25/1.21 tff(pred_def_1, type, p: $int > $o).
% 4.25/1.21 tff(f1,conjecture,(
% 4.25/1.21 ! [X0 : $int] : (($lesseq(5,X0) & $lesseq(X0,7)) => p(X0)) => ? [X1 : $int] : p($product(3,X1))),
% 4.25/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_X_in_5_to_7_div_3)).
% 4.25/1.21 tff(f2,negated_conjecture,(
% 4.25/1.21 ~(! [X0 : $int] : (($lesseq(5,X0) & $lesseq(X0,7)) => p(X0)) => ? [X1 : $int] : p($product(3,X1)))),
% 4.25/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 4.25/1.21 tff(f3,plain,(
% 4.25/1.21 ~(! [X0 : $int] : ((~$less(X0,5) & ~$less(7,X0)) => p(X0)) => ? [X1 : $int] : p($product(3,X1)))),
% 4.25/1.21 inference(theory_normalization,[],[f2])).
% 4.25/1.21 tff(f15,definition,(
% 4.25/1.21 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 4.25/1.21 introduced(theory,[tha_commutativity])).
% 4.25/1.21 tff(f17,definition,(
% 4.25/1.21 ( ! [X0 : $int] : ($product(X0,1) = X0) )),
% 4.25/1.21 introduced(theory,[tha_right_identity])).
% 4.25/1.21 tff(f19,definition,(
% 4.25/1.21 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2))) )),
% 4.25/1.21 introduced(theory,[tha_distributivity])).
% 4.25/1.21 tff(f22,plain,(
% 4.25/1.21 ! [X1 : $int] : ~p($product(3,X1)) & ! [X0 : $int] : (p(X0) | ($less(X0,5) | $less(7,X0)))),
% 4.25/1.21 inference(ennf_transformation,[],[f3])).
% 4.25/1.21 tff(f23,plain,(
% 4.25/1.21 ! [X1 : $int] : ~p($product(3,X1)) & ! [X0 : $int] : (p(X0) | $less(X0,5) | $less(7,X0))),
% 4.25/1.21 inference(flattening,[],[f22])).
% 4.25/1.21 tff(f24,plain,(
% 4.25/1.21 ( ! [X0 : $int] : ($less(7,X0) | $less(X0,5) | p(X0)) )),
% 4.25/1.21 inference(cnf_transformation,[],[f23])).
% 4.25/1.21 tff(f25,plain,(
% 4.25/1.21 ( ! [X1 : $int] : (~p($product(3,X1))) )),
% 4.25/1.21 inference(cnf_transformation,[],[f23])).
% 4.25/1.21 tff(f27,plain,(
% 4.25/1.21 ( ! [X1 : $int] : (p($product(3,X1))) )),
% 4.25/1.21 inference(consistent_polarity_flipping,[],[f25])).
% 4.25/1.21 tff(f28,plain,(
% 4.25/1.21 ( ! [X0 : $int] : (~p(X0) | $less(X0,5) | $less(7,X0)) )),
% 4.25/1.21 inference(consistent_polarity_flipping,[],[f24])).
% 4.25/1.21 tff(f1070,plain,(
% 4.25/1.21 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X1,$sum(X0,X2)) = $sum($product(X0,X1),$product(X1,X2))) )),
% 4.25/1.21 inference(superposition,[],[f19,f15])).
% 4.25/1.21 tff(f1075,plain,(
% 4.25/1.21 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X1,$sum(X2,X0)) = $sum($product(X1,X2),$product(X0,X1))) )),
% 4.25/1.21 inference(superposition,[],[f19,f15])).
% 4.25/1.21 tff(f3821,plain,(
% 4.25/1.21 ( ! [X0 : $int,X1 : $int] : ($product(X0,$sum(X1,X1)) = $product(X1,$sum(X0,X0))) )),
% 4.25/1.21 inference(superposition,[],[f1070,f1075])).
% 4.25/1.21 tff(f16487,plain,(
% 4.25/1.21 ( ! [X0 : $int] : (p($product(X0,$sum(3,3)))) )),
% 4.25/1.21 inference(superposition,[],[f27,f3821])).
% 4.25/1.21 tff(f16528,plain,(
% 4.25/1.21 ( ! [X0 : $int] : (p($product(X0,6))) )),
% 4.25/1.21 inference(evaluation,[],[f16487])).
% 4.25/1.21 tff(f16575,plain,(
% 4.25/1.21 ( ! [X0 : $int] : (p($product(6,X0))) )),
% 4.25/1.21 inference(superposition,[],[f16528,f15])).
% 4.25/1.21 tff(f16589,plain,(
% 4.25/1.21 p(6)),
% 4.25/1.21 inference(superposition,[],[f16575,f17])).
% 4.25/1.21 tff(f16594,plain,(
% 4.25/1.21 $less(6,5) | $less(7,6)),
% 4.25/1.21 inference(resolution,[],[f16589,f28])).
% 4.25/1.21 tff(f16595,plain,(
% 4.25/1.21 $false),
% 4.25/1.21 inference(evaluation,[],[f16594])).
% 4.25/1.21 % SZS output end Proof for theBenchmark
% 4.25/1.21 % (2174162)------------------------------
% 4.25/1.21 % (2174162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/1.21 % (2174162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.21 % (2174162)CaDiCaL version: 2.1.3
% 4.25/1.21 % (2174162)Termination reason: Refutation
% 4.25/1.21 % (2174162)Time elapsed: 0.562 s
% 4.25/1.21 % (2174162)Peak memory usage: 17 MB
% 4.25/1.21 % (2174162)Instructions burned: 552 (million)
% 4.25/1.21 % (2174127)Success in time 0.86 s
% 4.25/1.21 % Vampire exiting
%------------------------------------------------------------------------------