%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI583_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 : n015.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 09:34:55 AM UTC 2026
% Result : Theorem 3.71s 0.82s
% Output : Refutation 3.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI583_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:56:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 3.71/0.82 % (3006190)Will run a generic schedule for satisfiability detection.
% 3.71/0.82 % (3006201)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=14508903:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.71/0.82 % (3006196)% WARNING: option uhcvi not known.
% 3.71/0.82 % (3006197)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1592933566:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.71/0.82 % (3006195)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1246218745_2999 on theBenchmark for (2999ds/0Mi)
% 3.71/0.82 % (3006198)dis+10_1_sil=32000:sp=arity:random_seed=2904685571:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.71/0.82 % (3006196)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=343996394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.71/0.82 % (3006199)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2295724056:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.71/0.82 % (3006195)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006195)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006195)------------------------------
% 3.71/0.82 % (3006195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006200)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1244370981:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.71/0.82 % (3006195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006195)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006195)Termination reason: Inappropriate
% 3.71/0.82 % (3006195)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006195)Peak memory usage: 10 MB
% 3.71/0.82 % (3006195)------------------------------
% 3.71/0.82 % (3006195)------------------------------
% 3.71/0.82 % (3006209)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1635378654:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.71/0.82 % (3006209)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006209)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006209)------------------------------
% 3.71/0.82 % (3006209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006209)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006209)Termination reason: Inappropriate
% 3.71/0.82 % (3006209)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006209)Peak memory usage: 10 MB
% 3.71/0.82 % (3006209)------------------------------
% 3.71/0.82 % (3006209)------------------------------
% 3.71/0.82 % (3006211)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=162464393:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.71/0.82 % (3006201)Instruction limit reached!
% 3.71/0.82 % (3006201)------------------------------
% 3.71/0.82 % (3006201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006201)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006201)Termination reason: Instruction limit
% 3.71/0.82 % (3006201)Termination phase: Saturation
% 3.71/0.82 % (3006201)Time elapsed: 0.062 s
% 3.71/0.82 % (3006201)Peak memory usage: 13 MB
% 3.71/0.82 % (3006201)Instructions burned: 159 (million)
% 3.71/0.82 % (3006213)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=1645267934:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.71/0.82 % (3006198)Instruction limit reached!
% 3.71/0.82 % (3006198)------------------------------
% 3.71/0.82 % (3006198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006198)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006198)Termination reason: Instruction limit
% 3.71/0.82 % (3006198)Termination phase: Saturation
% 3.71/0.82 % (3006198)Time elapsed: 0.066 s
% 3.71/0.82 % (3006198)Peak memory usage: 12 MB
% 3.71/0.82 % (3006198)Instructions burned: 104 (million)
% 3.71/0.82 % (3006199)Instruction limit reached!
% 3.71/0.82 % (3006199)------------------------------
% 3.71/0.82 % (3006199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006199)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006199)Termination reason: Instruction limit
% 3.71/0.82 % (3006199)Termination phase: Saturation
% 3.71/0.82 % (3006199)Time elapsed: 0.070 s
% 3.71/0.82 % (3006199)Peak memory usage: 12 MB
% 3.71/0.82 % (3006199)Instructions burned: 116 (million)
% 3.71/0.82 % (3006215)ott-21_1_sil=16000:fs=off:random_seed=1966278407:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.71/0.82 % (3006200)Instruction limit reached!
% 3.71/0.82 % (3006200)------------------------------
% 3.71/0.82 % (3006200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006200)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006200)Termination reason: Instruction limit
% 3.71/0.82 % (3006200)Termination phase: Saturation
% 3.71/0.82 % (3006200)Time elapsed: 0.084 s
% 3.71/0.82 % (3006200)Peak memory usage: 13 MB
% 3.71/0.82 % (3006200)Instructions burned: 132 (million)
% 3.71/0.82 % (3006216)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1693346860:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.71/0.82 % (3006218)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=859783904:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.71/0.82 % (3006218)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006218)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006218)------------------------------
% 3.71/0.82 % (3006218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006218)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006218)Termination reason: Inappropriate
% 3.71/0.82 % (3006218)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006218)Peak memory usage: 10 MB
% 3.71/0.82 % (3006218)------------------------------
% 3.71/0.82 % (3006218)------------------------------
% 3.71/0.82 % (3006221)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2548589161:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.71/0.82 % (3006211)Instruction limit reached!
% 3.71/0.82 % (3006211)------------------------------
% 3.71/0.82 % (3006211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006211)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006211)Termination reason: Instruction limit
% 3.71/0.82 % (3006211)Termination phase: Saturation
% 3.71/0.82 % (3006211)Time elapsed: 0.088 s
% 3.71/0.82 % (3006211)Peak memory usage: 12 MB
% 3.71/0.82 % (3006211)Instructions burned: 132 (million)
% 3.71/0.82 % (3006223)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3841866062:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.71/0.82 % (3006223)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006223)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006223)------------------------------
% 3.71/0.82 % (3006223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006223)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006223)Termination reason: Inappropriate
% 3.71/0.82 % (3006223)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006223)Peak memory usage: 10 MB
% 3.71/0.82 % (3006223)------------------------------
% 3.71/0.82 % (3006223)------------------------------
% 3.71/0.82 % (3006215)Instruction limit reached!
% 3.71/0.82 % (3006215)------------------------------
% 3.71/0.82 % (3006215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006215)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006215)Termination reason: Instruction limit
% 3.71/0.82 % (3006215)Termination phase: Saturation
% 3.71/0.82 % (3006215)Time elapsed: 0.079 s
% 3.71/0.82 % (3006215)Peak memory usage: 12 MB
% 3.71/0.82 % (3006215)Instructions burned: 183 (million)
% 3.71/0.82 % (3006225)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=1639641201:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.71/0.82 % (3006226)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1483155156:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.71/0.82 % (3006213)Instruction limit reached!
% 3.71/0.82 % (3006213)------------------------------
% 3.71/0.82 % (3006213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006213)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006213)Termination reason: Instruction limit
% 3.71/0.82 % (3006213)Termination phase: Saturation
% 3.71/0.82 % (3006213)Time elapsed: 0.167 s
% 3.71/0.82 % (3006213)Peak memory usage: 15 MB
% 3.71/0.82 % (3006213)Instructions burned: 685 (million)
% 3.71/0.82 % (3006229)fmb+10_1_sil=64000:random_seed=226531307:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.71/0.82 % (3006229)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006229)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006229)------------------------------
% 3.71/0.82 % (3006229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006229)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006229)Termination reason: Inappropriate
% 3.71/0.82 % (3006229)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006229)Peak memory usage: 10 MB
% 3.71/0.82 % (3006229)------------------------------
% 3.71/0.82 % (3006229)------------------------------
% 3.71/0.82 % (3006231)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3976496919:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.71/0.82 % (3006231)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006231)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006231)------------------------------
% 3.71/0.82 % (3006231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006231)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006231)Termination reason: Inappropriate
% 3.71/0.82 % (3006231)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006231)Peak memory usage: 10 MB
% 3.71/0.82 % (3006231)------------------------------
% 3.71/0.82 % (3006231)------------------------------
% 3.71/0.82 % (3006233)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2818018513:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.71/0.82 % (3006233)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 3.71/0.82 % (3006233)Terminated due to inappropriate strategy.
% 3.71/0.82 % (3006233)------------------------------
% 3.71/0.82 % (3006233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006233)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006233)Termination reason: Inappropriate
% 3.71/0.82 % (3006233)Time elapsed: 0.0000 s
% 3.71/0.82 % (3006233)Peak memory usage: 10 MB
% 3.71/0.82 % (3006233)------------------------------
% 3.71/0.82 % (3006233)------------------------------
% 3.71/0.82 % (3006235)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3653779611:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.71/0.82 % (3006216)Instruction limit reached!
% 3.71/0.82 % (3006216)------------------------------
% 3.71/0.82 % (3006216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006216)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006216)Termination reason: Instruction limit
% 3.71/0.82 % (3006216)Termination phase: Saturation
% 3.71/0.82 % (3006216)Time elapsed: 0.320 s
% 3.71/0.82 % (3006216)Peak memory usage: 14 MB
% 3.71/0.82 % (3006216)Instructions burned: 478 (million)
% 3.71/0.82 % (3006237)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3835106833:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.71/0.82 % (3006221) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3006190-3006221"...
% 3.71/0.82 % (3006221)...printing done.
% 3.71/0.82 % (3006221)Refutation found. Thanks to Tanya!
% 3.71/0.82 % SZS status Theorem for theBenchmark
% 3.71/0.82 % SZS output start Proof for theBenchmark
% 3.71/0.82 tff(func_def_6, type, sK0: $int).
% 3.71/0.82 tff(func_def_7, type, sK1: $int).
% 3.71/0.82 tff(func_def_8, type, sK2: $int).
% 3.71/0.82 tff(func_def_9, type, sF3: $int > $int).
% 3.71/0.82 tff(func_def_10, type, sF4: $int).
% 3.71/0.82 tff(func_def_11, type, sF5: $int > $int).
% 3.71/0.82 tff(f1,conjecture,(
% 3.71/0.82 ! [X0 : $int,X1 : $int,X2 : $int] : (($less(0,X0) & $lesseq(0,X1) & $lesseq(0,X2) & ($less(X0,X1) | $less(X0,X2))) => ? [X3 : $int] : ($less($sum(X0,X3),4) & $less(3,$sum($sum(X1,X2),X3))))),
% 3.71/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mix_quant_ineq_sys_solvable_4)).
% 3.71/0.82 tff(f2,negated_conjecture,(
% 3.71/0.82 ~ ! [X0 : $int,X1 : $int,X2 : $int] : (($less(0,X0) & $lesseq(0,X1) & $lesseq(0,X2) & ($less(X0,X1) | $less(X0,X2))) => ? [X3 : $int] : ($less($sum(X0,X3),4) & $less(3,$sum($sum(X1,X2),X3))))),
% 3.71/0.82 inference(negated_conjecture,[status(cth)],[f1])).
% 3.71/0.82 tff(f3,plain,(
% 3.71/0.82 ~ ! [X0 : $int,X1 : $int,X2 : $int] : (($less(0,X0) & ~$less(X1,0) & ~$less(X2,0) & ($less(X0,X1) | $less(X0,X2))) => ? [X3 : $int] : ($less($sum(X0,X3),4) & $less(3,$sum($sum(X1,X2),X3))))),
% 3.71/0.82 inference(theory_normalization,[],[f2])).
% 3.71/0.82 tff(f4,definition,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 3.71/0.82 introduced(theory,[tha_commutativity])).
% 3.71/0.82 tff(f5,definition,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 3.71/0.82 introduced(theory,[tha_associativity])).
% 3.71/0.82 tff(f8,definition,(
% 3.71/0.82 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 3.71/0.82 introduced(theory,[tha_inverse_op_unit])).
% 3.71/0.82 tff(f10,definition,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 3.71/0.82 introduced(theory,[tha_transitivity])).
% 3.71/0.82 tff(f11,definition,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 3.71/0.82 introduced(theory,[tha_order_totality])).
% 3.71/0.82 tff(f12,definition,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 3.71/0.82 introduced(theory,[tha_order_monotonicity])).
% 3.71/0.82 tff(f13,definition,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
% 3.71/0.82 introduced(theory,[tha_order_plus_one_dichotomy])).
% 3.71/0.82 tff(f15,definition,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 3.71/0.82 introduced(theory,[tha_extra_integer_ordering])).
% 3.71/0.82 tff(f16,plain,(
% 3.71/0.82 ? [X0 : $int,X1 : $int,X2 : $int] : (! [X3 : $int] : (~$less($sum(X0,X3),4) | ~$less(3,$sum($sum(X1,X2),X3))) & ($less(0,X0) & ~$less(X1,0) & ~$less(X2,0) & ($less(X0,X1) | $less(X0,X2))))),
% 3.71/0.82 inference(ennf_transformation,[],[f3])).
% 3.71/0.82 tff(f17,plain,(
% 3.71/0.82 ? [X0 : $int,X1 : $int,X2 : $int] : (! [X3 : $int] : (~$less($sum(X0,X3),4) | ~$less(3,$sum($sum(X1,X2),X3))) & $less(0,X0) & ~$less(X1,0) & ~$less(X2,0) & ($less(X0,X1) | $less(X0,X2)))),
% 3.71/0.82 inference(flattening,[],[f16])).
% 3.71/0.82 tff(f18,plain,(
% 3.71/0.82 ! [X3 : $int] : (~$less($sum(sK0,X3),4) | ~$less(3,$sum($sum(sK1,sK2),X3))) & $less(0,sK0) & ~$less(sK1,0) & ~$less(sK2,0) & ($less(sK0,sK1) | $less(sK0,sK2))),
% 3.71/0.82 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17])).
% 3.71/0.82 tff(f19,plain,(
% 3.71/0.82 $less(sK0,sK1) | $less(sK0,sK2)),
% 3.71/0.82 inference(cnf_transformation,[],[f18])).
% 3.71/0.82 tff(f20,plain,(
% 3.71/0.82 ~$less(sK2,0)),
% 3.71/0.82 inference(cnf_transformation,[],[f18])).
% 3.71/0.82 tff(f21,plain,(
% 3.71/0.82 ~$less(sK1,0)),
% 3.71/0.82 inference(cnf_transformation,[],[f18])).
% 3.71/0.82 tff(f23,plain,(
% 3.71/0.82 ( ! [X3 : $int] : (~$less($sum(sK0,X3),4) | ~$less(3,$sum($sum(sK1,sK2),X3))) )),
% 3.71/0.82 inference(cnf_transformation,[],[f18])).
% 3.71/0.82 tff(f24,definition,(
% 3.71/0.82 ( ! [X3 : $int] : (sF3(X3) = $sum(sK0,X3)) )),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 3.71/0.82 tff(f25,plain,(
% 3.71/0.82 ( ! [X3 : $int] : ($sum(sK0,X3) = sF3(X3)) )),
% 3.71/0.82 inference(reorient_equations,[],[f24])).
% 3.71/0.82 tff(f26,definition,(
% 3.71/0.82 sF4 = $sum(sK1,sK2)),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 3.71/0.82 tff(f27,plain,(
% 3.71/0.82 $sum(sK1,sK2) = sF4),
% 3.71/0.82 inference(reorient_equations,[],[f26])).
% 3.71/0.82 tff(f28,definition,(
% 3.71/0.82 ( ! [X3 : $int] : (sF5(X3) = $sum(sF4,X3)) )),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 3.71/0.82 tff(f29,plain,(
% 3.71/0.82 ( ! [X3 : $int] : ($sum(sF4,X3) = sF5(X3)) )),
% 3.71/0.82 inference(reorient_equations,[],[f28])).
% 3.71/0.82 tff(f30,plain,(
% 3.71/0.82 ( ! [X3 : $int] : (~$less(sF3(X3),4) | ~$less(3,sF5(X3))) )),
% 3.71/0.82 inference(definition_folding,[],[f23,f29,f27,f25])).
% 3.71/0.82 tff(f32,definition,(
% 3.71/0.82 spl6_1 <=> $less(sK0,sK2)),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 3.71/0.82 tff(f34,plain,(
% 3.71/0.82 $less(sK0,sK2) | ~spl6_1),
% 3.71/0.82 inference(avatar_component_clause,[],[f32])).
% 3.71/0.82 tff(f36,definition,(
% 3.71/0.82 spl6_2 <=> $less(sK0,sK1)),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 3.71/0.82 tff(f38,plain,(
% 3.71/0.82 $less(sK0,sK1) | ~spl6_2),
% 3.71/0.82 inference(avatar_component_clause,[],[f36])).
% 3.71/0.82 tff(f39,plain,(
% 3.71/0.82 spl6_1 | spl6_2),
% 3.71/0.82 inference(avatar_split_clause,[],[f19,f36,f32])).
% 3.71/0.82 tff(f42,plain,(
% 3.71/0.82 ( ! [X0 : $int] : (~$less($sum(sK0,X0),4) | ~$less(3,sF5(X0))) )),
% 3.71/0.82 inference(superposition,[],[f30,f25])).
% 3.71/0.82 tff(f43,plain,(
% 3.71/0.82 ( ! [X0 : $int] : (~$less(3,$sum(sF4,X0)) | ~$less($sum(sK0,X0),4)) )),
% 3.71/0.82 inference(forward_demodulation,[],[f42,f29])).
% 3.71/0.82 tff(f68,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 3.71/0.82 inference(superposition,[],[f13,f4])).
% 3.71/0.82 tff(f78,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 3.71/0.82 inference(superposition,[],[f15,f4])).
% 3.71/0.82 tff(f92,plain,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,X0) | X0 = X1 | $less(X1,X0) | $less(X2,X1)) )),
% 3.71/0.82 inference(resolution,[],[f11,f10])).
% 3.71/0.82 tff(f166,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(0,$sum(X1,$uminus(X0)))) )),
% 3.71/0.82 inference(superposition,[],[f12,f8])).
% 3.71/0.82 tff(f173,plain,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X2,X0),$sum(X0,X1)) | ~$less(X2,X1)) )),
% 3.71/0.82 inference(superposition,[],[f12,f4])).
% 3.71/0.82 tff(f174,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less($sum(X0,sK2),sF4) | ~$less(X0,sK1)) )),
% 3.71/0.82 inference(superposition,[],[f12,f27])).
% 3.71/0.82 tff(f187,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 3.71/0.82 inference(superposition,[],[f5,f8])).
% 3.71/0.82 tff(f205,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 3.71/0.82 inference(evaluation,[],[f187])).
% 3.71/0.82 tff(f284,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less(X0,0) | $less($uminus(1),X0)) )),
% 3.71/0.82 inference(superposition,[],[f68,f8])).
% 3.71/0.82 tff(f287,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less(X0,0) | $less(-1,X0)) )),
% 3.71/0.82 inference(evaluation,[],[f284])).
% 3.71/0.82 tff(f323,plain,(
% 3.71/0.82 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X1,$sum($uminus(X2),X0)),X0) | ~$less(X1,X2)) )),
% 3.71/0.82 inference(superposition,[],[f12,f205])).
% 3.71/0.82 tff(f327,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : (~$less(X1,X0) | ~$less($sum($uminus(1),X0),X1)) )),
% 3.71/0.82 inference(superposition,[],[f78,f205])).
% 3.71/0.82 tff(f331,plain,(
% 3.71/0.82 ( ! [X0 : $int] : (~$less($sum(sK0,$sum($uminus(sF4),X0)),4) | ~$less(3,X0)) )),
% 3.71/0.82 inference(superposition,[],[f43,f205])).
% 3.71/0.82 tff(f333,plain,(
% 3.71/0.82 ( ! [X0 : $int,X1 : $int] : (~$less($sum(-1,X0),X1) | ~$less(X1,X0)) )),
% 3.71/0.82 inference(evaluation,[],[f327])).
% 3.71/0.82 tff(f492,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less($sum(X0,sK1),sF4) | ~$less(X0,sK2)) )),
% 3.71/0.82 inference(superposition,[],[f173,f27])).
% 3.71/0.82 tff(f2545,plain,(
% 3.71/0.82 $less(-1,sK1)),
% 3.71/0.82 inference(resolution,[],[f287,f21])).
% 3.71/0.82 tff(f2546,plain,(
% 3.71/0.82 $less(-1,sK2)),
% 3.71/0.82 inference(resolution,[],[f287,f20])).
% 3.71/0.82 tff(f2987,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less(sK0,X0) | $less(X0,sK2) | sK2 = X0) ) | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f34,f92])).
% 3.71/0.82 tff(f2990,plain,(
% 3.71/0.82 $less(0,$sum(sK2,$uminus(sK0))) | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f34,f166])).
% 3.71/0.82 tff(f2991,plain,(
% 3.71/0.82 ( ! [X0 : $int] : (~$less(X0,sK0) | $less(X0,sK2)) ) | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f34,f10])).
% 3.71/0.82 tff(f3309,plain,(
% 3.71/0.82 ( ! [X0 : $int] : ($less(sK0,X0) | $less(X0,sK2) | sK0 = X0) ) | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f2991,f11])).
% 3.71/0.82 tff(f8929,plain,(
% 3.71/0.82 ~$less(sF4,sK2) | ~$less(-1,sK1)),
% 3.71/0.82 inference(resolution,[],[f333,f174])).
% 3.71/0.82 tff(f8997,plain,(
% 3.71/0.82 ~$less(sF4,sK2)),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f8929,f2545])).
% 3.71/0.82 tff(f9424,plain,(
% 3.71/0.82 ~$less(-1,sK2) | ~$less(sF4,sK1)),
% 3.71/0.82 inference(resolution,[],[f492,f333])).
% 3.71/0.82 tff(f9436,plain,(
% 3.71/0.82 ~$less(sF4,sK1)),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f9424,f2546])).
% 3.71/0.82 tff(f12082,plain,(
% 3.71/0.82 ~$less(sK0,sF4) | ~$less(3,4)),
% 3.71/0.82 inference(resolution,[],[f323,f331])).
% 3.71/0.82 tff(f12121,plain,(
% 3.71/0.82 ~$less(sK0,sF4)),
% 3.71/0.82 inference(evaluation,[],[f12082])).
% 3.71/0.82 tff(f12157,plain,(
% 3.71/0.82 $less(sF4,sK2) | sK2 = sF4 | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f12121,f2987])).
% 3.71/0.82 tff(f12159,plain,(
% 3.71/0.82 $less(sF4,sK2) | sK0 = sF4 | ~spl6_1),
% 3.71/0.82 inference(resolution,[],[f12121,f3309])).
% 3.71/0.82 tff(f12164,plain,(
% 3.71/0.82 $less(sF4,sK0) | sK0 = sF4),
% 3.71/0.82 inference(resolution,[],[f12121,f11])).
% 3.71/0.82 tff(f12168,definition,(
% 3.71/0.82 spl6_60 <=> sK0 = sF4),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[spl6_60])],[avatar_definition])).
% 3.71/0.82 tff(f12170,plain,(
% 3.71/0.82 sK0 = sF4 | ~spl6_60),
% 3.71/0.82 inference(avatar_component_clause,[],[f12168])).
% 3.71/0.82 tff(f12172,definition,(
% 3.71/0.82 spl6_61 <=> $less(sF4,sK0)),
% 3.71/0.82 introduced(definition,[new_symbols(definition,[spl6_61])],[avatar_definition])).
% 3.71/0.82 tff(f12174,plain,(
% 3.71/0.82 $less(sF4,sK0) | ~spl6_61),
% 3.71/0.82 inference(avatar_component_clause,[],[f12172])).
% 3.71/0.82 tff(f12175,plain,(
% 3.71/0.82 spl6_60 | spl6_61),
% 3.71/0.82 inference(avatar_split_clause,[],[f12164,f12172,f12168])).
% 3.71/0.82 tff(f12178,plain,(
% 3.71/0.82 sK0 = sF4 | ~spl6_1),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f12159,f8997])).
% 3.71/0.82 tff(f12179,plain,(
% 3.71/0.82 sK2 = sF4 | ~spl6_1),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f12157,f8997])).
% 3.71/0.82 tff(f12180,plain,(
% 3.71/0.82 spl6_60 | ~spl6_1),
% 3.71/0.82 inference(avatar_split_clause,[],[f12178,f32,f12168])).
% 3.71/0.82 tff(f12984,plain,(
% 3.71/0.82 $less(0,$sum(sK2,$uminus(sF4))) | (~spl6_1 | ~spl6_60)),
% 3.71/0.82 inference(superposition,[],[f2990,f12170])).
% 3.71/0.82 tff(f13016,plain,(
% 3.71/0.82 $less(0,$sum(sF4,$uminus(sF4))) | (~spl6_1 | ~spl6_60)),
% 3.71/0.82 inference(forward_demodulation,[],[f12984,f12179])).
% 3.71/0.82 tff(f13027,plain,(
% 3.71/0.82 $less(0,0) | (~spl6_1 | ~spl6_60)),
% 3.71/0.82 inference(forward_demodulation,[],[f13016,f8])).
% 3.71/0.82 tff(f13028,plain,(
% 3.71/0.82 $false | (~spl6_1 | ~spl6_60)),
% 3.71/0.82 inference(evaluation,[],[f13027])).
% 3.71/0.82 tff(f13029,plain,(
% 3.71/0.82 ~spl6_1 | ~spl6_60),
% 3.71/0.82 inference(avatar_contradiction_clause,[],[f13028])).
% 3.71/0.82 tff(f13033,plain,(
% 3.71/0.82 $less(sF4,sK1) | (~spl6_2 | ~spl6_60)),
% 3.71/0.82 inference(forward_demodulation,[],[f38,f12170])).
% 3.71/0.82 tff(f13059,plain,(
% 3.71/0.82 $false | (~spl6_2 | ~spl6_60)),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f13033,f9436])).
% 3.71/0.82 tff(f13060,plain,(
% 3.71/0.82 ~spl6_2 | ~spl6_60),
% 3.71/0.82 inference(avatar_contradiction_clause,[],[f13059])).
% 3.71/0.82 tff(f13081,plain,(
% 3.71/0.82 ( ! [X0 : $int] : (~$less(X0,sK0) | $less(X0,sK1)) ) | ~spl6_2),
% 3.71/0.82 inference(resolution,[],[f38,f10])).
% 3.71/0.82 tff(f13196,plain,(
% 3.71/0.82 $less(sF4,sK1) | (~spl6_2 | ~spl6_61)),
% 3.71/0.82 inference(resolution,[],[f12174,f13081])).
% 3.71/0.82 tff(f13212,plain,(
% 3.71/0.82 $false | (~spl6_2 | ~spl6_61)),
% 3.71/0.82 inference(forward_subsumption_resolution,[],[f13196,f9436])).
% 3.71/0.82 tff(f13213,plain,(
% 3.71/0.82 ~spl6_2 | ~spl6_61),
% 3.71/0.82 inference(avatar_contradiction_clause,[],[f13212])).
% 3.71/0.82 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f39])).
% 3.71/0.82 cnf(s69, plain, spl6_60 | spl6_61, inference(sat_conversion,[],[f12175])).
% 3.71/0.82 cnf(s71, plain, ~spl6_1 | spl6_60, inference(sat_conversion,[],[f12180])).
% 3.71/0.82 cnf(s75, plain, ~spl6_1 | ~spl6_60, inference(sat_conversion,[],[f13029])).
% 3.71/0.82 cnf(s78, plain, ~spl6_2 | ~spl6_60, inference(sat_conversion,[],[f13060])).
% 3.71/0.82 cnf(s79, plain, ~spl6_2 | ~spl6_61, inference(sat_conversion,[],[f13213])).
% 3.71/0.82 cnf(s81, plain, ~spl6_2, inference(rat,[],[s69,s78,s79])).
% 3.71/0.82 cnf(s82, plain, spl6_1, inference(rat,[],[s1,s81])).
% 3.71/0.82 cnf(s83, plain, ~spl6_60, inference(rat,[],[s75,s82])).
% 3.71/0.82 cnf(s84, plain, $false, inference(rat,[],[s71,s83,s82])).
% 3.71/0.82 tff(f13214,plain,(
% 3.71/0.82 $false),
% 3.71/0.82 inference(avatar_sat_refutation,[],[s84])).
% 3.71/0.82 % SZS output end Proof for theBenchmark
% 3.71/0.82 % (3006221)------------------------------
% 3.71/0.82 % (3006221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.71/0.82 % (3006221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/0.82 % (3006221)CaDiCaL version: 2.1.3
% 3.71/0.82 % (3006221)Termination reason: Refutation
% 3.71/0.82 % (3006221)Time elapsed: 0.431 s
% 3.71/0.82 % (3006221)Peak memory usage: 16 MB
% 3.71/0.82 % (3006221)Instructions burned: 700 (million)
% 3.71/0.82 % (3006190)Success in time 0.598 s
% 3.71/0.82 % Vampire exiting
%------------------------------------------------------------------------------