%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI673_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:35:03 AM UTC 2026
% Result : Theorem 2.43s 0.60s
% Output : Refutation 2.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI673_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n010.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
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.43/0.60 % (2324334)Will run a generic schedule for satisfiability detection.
% 2.43/0.60 % (2324342)dis+10_1_sil=32000:sp=arity:random_seed=1074188310:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.43/0.60 % (2324340)% WARNING: option uhcvi not known.
% 2.43/0.60 % (2324343)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1333592707:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.43/0.60 % (2324339)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=867464672_2999 on theBenchmark for (2999ds/0Mi)
% 2.43/0.60 % (2324341)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2483303485:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.43/0.60 % (2324340)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4106510522:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.43/0.60 % (2324339)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324339)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324339)------------------------------
% 2.43/0.60 % (2324339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324339)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324339)Termination reason: Inappropriate
% 2.43/0.60 % (2324339)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324339)Peak memory usage: 10 MB
% 2.43/0.60 % (2324339)------------------------------
% 2.43/0.60 % (2324339)------------------------------
% 2.43/0.60 % (2324345)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3858144149:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.43/0.60 % (2324344)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2907911312:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.43/0.60 % (2324352)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1943481944:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.43/0.60 % (2324352)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324352)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324352)------------------------------
% 2.43/0.60 % (2324352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324352)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324352)Termination reason: Inappropriate
% 2.43/0.60 % (2324352)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324352)Peak memory usage: 10 MB
% 2.43/0.60 % (2324352)------------------------------
% 2.43/0.60 % (2324352)------------------------------
% 2.43/0.60 % (2324342)Instruction limit reached!
% 2.43/0.60 % (2324342)------------------------------
% 2.43/0.60 % (2324342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324342)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324342)Termination reason: Instruction limit
% 2.43/0.60 % (2324342)Termination phase: Saturation
% 2.43/0.60 % (2324342)Time elapsed: 0.034 s
% 2.43/0.60 % (2324342)Peak memory usage: 13 MB
% 2.43/0.60 % (2324342)Instructions burned: 104 (million)
% 2.43/0.60 % (2324356)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=1563683708:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.43/0.60 % (2324355)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1694653174:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.43/0.60 % (2324343)Instruction limit reached!
% 2.43/0.60 % (2324343)------------------------------
% 2.43/0.60 % (2324343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324343)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324343)Termination reason: Instruction limit
% 2.43/0.60 % (2324343)Termination phase: Saturation
% 2.43/0.60 % (2324343)Time elapsed: 0.071 s
% 2.43/0.60 % (2324343)Peak memory usage: 13 MB
% 2.43/0.60 % (2324343)Instructions burned: 116 (million)
% 2.43/0.60 % (2324359)ott-21_1_sil=16000:fs=off:random_seed=565790606:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.43/0.60 % (2324345)Instruction limit reached!
% 2.43/0.60 % (2324345)------------------------------
% 2.43/0.60 % (2324345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324345)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324345)Termination reason: Instruction limit
% 2.43/0.60 % (2324345)Termination phase: Saturation
% 2.43/0.60 % (2324345)Time elapsed: 0.099 s
% 2.43/0.60 % (2324345)Peak memory usage: 13 MB
% 2.43/0.60 % (2324345)Instructions burned: 159 (million)
% 2.43/0.60 % (2324344)Instruction limit reached!
% 2.43/0.60 % (2324344)------------------------------
% 2.43/0.60 % (2324344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324344)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324344)Termination reason: Instruction limit
% 2.43/0.60 % (2324344)Termination phase: Saturation
% 2.43/0.60 % (2324344)Time elapsed: 0.095 s
% 2.43/0.60 % (2324344)Peak memory usage: 13 MB
% 2.43/0.60 % (2324344)Instructions burned: 132 (million)
% 2.43/0.60 % (2324361)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2201656743:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.43/0.60 % (2324362)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=803063185:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.43/0.60 % (2324362)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324362)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324362)------------------------------
% 2.43/0.60 % (2324362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324362)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324362)Termination reason: Inappropriate
% 2.43/0.60 % (2324362)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324362)Peak memory usage: 10 MB
% 2.43/0.60 % (2324362)------------------------------
% 2.43/0.60 % (2324362)------------------------------
% 2.43/0.60 % (2324365)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1717514125:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.43/0.60 % (2324359)Instruction limit reached!
% 2.43/0.60 % (2324359)------------------------------
% 2.43/0.60 % (2324359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324359)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324359)Termination reason: Instruction limit
% 2.43/0.60 % (2324359)Termination phase: Saturation
% 2.43/0.60 % (2324359)Time elapsed: 0.084 s
% 2.43/0.60 % (2324359)Peak memory usage: 12 MB
% 2.43/0.60 % (2324359)Instructions burned: 183 (million)
% 2.43/0.60 % (2324355)Instruction limit reached!
% 2.43/0.60 % (2324355)------------------------------
% 2.43/0.60 % (2324355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324355)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324355)Termination reason: Instruction limit
% 2.43/0.60 % (2324355)Termination phase: Saturation
% 2.43/0.60 % (2324355)Time elapsed: 0.137 s
% 2.43/0.60 % (2324355)Peak memory usage: 13 MB
% 2.43/0.60 % (2324355)Instructions burned: 131 (million)
% 2.43/0.60 % (2324367)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=67411880:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.43/0.60 % (2324367)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324367)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324367)------------------------------
% 2.43/0.60 % (2324367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324367)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324367)Termination reason: Inappropriate
% 2.43/0.60 % (2324367)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324367)Peak memory usage: 10 MB
% 2.43/0.60 % (2324367)------------------------------
% 2.43/0.60 % (2324367)------------------------------
% 2.43/0.60 % (2324370)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1795197754:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.43/0.60 % (2324368)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=3894364140: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)
% 2.43/0.60 % (2324356)Instruction limit reached!
% 2.43/0.60 % (2324356)------------------------------
% 2.43/0.60 % (2324356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324356)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324356)Termination reason: Instruction limit
% 2.43/0.60 % (2324356)Termination phase: Saturation
% 2.43/0.60 % (2324356)Time elapsed: 0.216 s
% 2.43/0.60 % (2324356)Peak memory usage: 17 MB
% 2.43/0.60 % (2324356)Instructions burned: 686 (million)
% 2.43/0.60 % (2324373)fmb+10_1_sil=64000:random_seed=1368595538:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.43/0.60 % (2324373)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324373)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324373)------------------------------
% 2.43/0.60 % (2324373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324373)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324373)Termination reason: Inappropriate
% 2.43/0.60 % (2324373)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324373)Peak memory usage: 10 MB
% 2.43/0.60 % (2324373)------------------------------
% 2.43/0.60 % (2324373)------------------------------
% 2.43/0.60 % (2324375)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1567816940:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.43/0.60 % (2324375)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324375)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324375)------------------------------
% 2.43/0.60 % (2324375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324375)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324375)Termination reason: Inappropriate
% 2.43/0.60 % (2324375)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324375)Peak memory usage: 10 MB
% 2.43/0.60 % (2324375)------------------------------
% 2.43/0.60 % (2324375)------------------------------
% 2.43/0.60 % (2324382)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1795852992:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.43/0.60 % (2324382)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.43/0.60 % (2324382)Terminated due to inappropriate strategy.
% 2.43/0.60 % (2324382)------------------------------
% 2.43/0.60 % (2324382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324382)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324382)Termination reason: Inappropriate
% 2.43/0.60 % (2324382)Time elapsed: 0.0000 s
% 2.43/0.60 % (2324382)Peak memory usage: 10 MB
% 2.43/0.60 % (2324382)------------------------------
% 2.43/0.60 % (2324382)------------------------------
% 2.43/0.60 % (2324388)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4010008569:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.43/0.60 % (2324388) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2324334-2324388"...
% 2.43/0.60 % (2324388)...printing done.
% 2.43/0.60 % (2324388)Refutation found. Thanks to Tanya!
% 2.43/0.60 % SZS status Theorem for theBenchmark
% 2.43/0.60 % SZS output start Proof for theBenchmark
% 2.43/0.60 tff(func_def_0, type, a: $int).
% 2.43/0.60 tff(f1,conjecture,(
% 2.43/0.60 $product(a,a) = 1 <=> (a = -1 | a = 1)),
% 2.43/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 2.43/0.60 tff(f2,negated_conjecture,(
% 2.43/0.60 ~($product(a,a) = 1 <=> (a = -1 | a = 1))),
% 2.43/0.60 inference(negated_conjecture,[status(cth)],[f1])).
% 2.43/0.60 tff(f3,definition,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 2.43/0.60 introduced(theory,[tha_commutativity])).
% 2.43/0.60 tff(f7,definition,(
% 2.43/0.60 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 2.43/0.60 introduced(theory,[tha_inverse_op_unit])).
% 2.43/0.60 tff(f8,definition,(
% 2.43/0.60 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 2.43/0.60 introduced(theory,[tha_non-reflexivity])).
% 2.43/0.60 tff(f10,definition,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 2.43/0.60 introduced(theory,[tha_order_totality])).
% 2.43/0.60 tff(f12,definition,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 2.43/0.60 introduced(theory,[tha_order_plus_one_dichotomy])).
% 2.43/0.60 tff(f13,definition,(
% 2.43/0.60 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 2.43/0.60 introduced(theory,[tha_minus_minus_x])).
% 2.43/0.60 tff(f14,definition,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 2.43/0.60 introduced(theory,[tha_commutativity])).
% 2.43/0.60 tff(f15,definition,(
% 2.43/0.60 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 2.43/0.60 introduced(theory,[tha_associativity])).
% 2.43/0.60 tff(f16,definition,(
% 2.43/0.60 ( ! [X0 : $int] : ($product(X0,1) = X0) )),
% 2.43/0.60 introduced(theory,[tha_right_identity])).
% 2.43/0.60 tff(f18,definition,(
% 2.43/0.60 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2))) )),
% 2.43/0.60 introduced(theory,[tha_distributivity])).
% 2.43/0.60 tff(f19,definition,(
% 2.43/0.60 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : (0 = X0 | $product(X0,X2) != X1 | $product(X0,X3) != X1 | X2 = X3) )),
% 2.43/0.60 introduced(theory,[tha_divisibility])).
% 2.43/0.60 tff(f20,definition,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 2.43/0.60 introduced(theory,[tha_extra_integer_ordering])).
% 2.43/0.60 tff(f21,plain,(
% 2.43/0.60 $product(a,a) = 1 <~> (a = -1 | a = 1)),
% 2.43/0.60 inference(ennf_transformation,[],[f2])).
% 2.43/0.60 tff(f22,plain,(
% 2.43/0.60 a != 1 | $product(a,a) != 1),
% 2.43/0.60 inference(cnf_transformation,[],[f21])).
% 2.43/0.60 tff(f23,plain,(
% 2.43/0.60 a != -1 | $product(a,a) != 1),
% 2.43/0.60 inference(cnf_transformation,[],[f21])).
% 2.43/0.60 tff(f24,plain,(
% 2.43/0.60 a = 1 | a = -1 | $product(a,a) = 1),
% 2.43/0.60 inference(cnf_transformation,[],[f21])).
% 2.43/0.60 tff(f25,plain,(
% 2.43/0.60 ( ! [X2 : $int,X3 : $int,X0 : $int] : ($product(X0,X2) != $product(X0,X3) | 0 = X0 | X2 = X3) )),
% 2.43/0.60 inference(equality_resolution,[],[f19])).
% 2.43/0.60 tff(f27,definition,(
% 2.43/0.60 spl0_1 <=> $product(a,a) = 1),
% 2.43/0.60 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 2.43/0.60 tff(f28,plain,(
% 2.43/0.60 $product(a,a) = 1 | ~spl0_1),
% 2.43/0.60 inference(avatar_component_clause,[],[f27])).
% 2.43/0.60 tff(f29,plain,(
% 2.43/0.60 $product(a,a) != 1 | spl0_1),
% 2.43/0.60 inference(avatar_component_clause,[],[f27])).
% 2.43/0.60 tff(f31,definition,(
% 2.43/0.60 spl0_2 <=> a = 1),
% 2.43/0.60 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 2.43/0.60 tff(f32,plain,(
% 2.43/0.60 a = 1 | ~spl0_2),
% 2.43/0.60 inference(avatar_component_clause,[],[f31])).
% 2.43/0.60 tff(f33,plain,(
% 2.43/0.60 a != 1 | spl0_2),
% 2.43/0.60 inference(avatar_component_clause,[],[f31])).
% 2.43/0.60 tff(f34,plain,(
% 2.43/0.60 ~spl0_1 | ~spl0_2),
% 2.43/0.60 inference(avatar_split_clause,[],[f22,f31,f27])).
% 2.43/0.60 tff(f35,plain,(
% 2.43/0.60 a = 1 | a = -1 | spl0_1),
% 2.43/0.60 inference(forward_subsumption_resolution,[],[f24,f29])).
% 2.43/0.60 tff(f37,definition,(
% 2.43/0.60 spl0_3 <=> a = -1),
% 2.43/0.60 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 2.43/0.60 tff(f38,plain,(
% 2.43/0.60 a != -1 | spl0_3),
% 2.43/0.60 inference(avatar_component_clause,[],[f37])).
% 2.43/0.60 tff(f39,plain,(
% 2.43/0.60 a = -1 | ~spl0_3),
% 2.43/0.60 inference(avatar_component_clause,[],[f37])).
% 2.43/0.60 tff(f40,plain,(
% 2.43/0.60 spl0_3 | spl0_2 | spl0_1),
% 2.43/0.60 inference(avatar_split_clause,[],[f35,f27,f31,f37])).
% 2.43/0.60 tff(f41,plain,(
% 2.43/0.60 a != -1 | ~spl0_1),
% 2.43/0.60 inference(forward_subsumption_resolution,[],[f23,f28])).
% 2.43/0.60 tff(f42,plain,(
% 2.43/0.60 ~spl0_3 | ~spl0_1),
% 2.43/0.60 inference(avatar_split_clause,[],[f41,f27,f37])).
% 2.43/0.60 tff(f43,plain,(
% 2.43/0.60 ( ! [X0 : $int] : (0 = $sum($uminus(X0),X0)) )),
% 2.43/0.60 inference(superposition,[],[f7,f13])).
% 2.43/0.60 tff(f63,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 2.43/0.60 inference(resolution,[],[f12,f8])).
% 2.43/0.60 tff(f69,plain,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 2.43/0.60 inference(superposition,[],[f20,f3])).
% 2.43/0.60 tff(f71,plain,(
% 2.43/0.60 ( ! [X0 : $int] : (~$less(X0,0) | ~$less($uminus(1),X0)) )),
% 2.43/0.60 inference(superposition,[],[f20,f43])).
% 2.43/0.60 tff(f72,plain,(
% 2.43/0.60 ( ! [X0 : $int] : (~$less(X0,0) | ~$less(-1,X0)) )),
% 2.43/0.60 inference(evaluation,[],[f71])).
% 2.43/0.60 tff(f74,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 2.43/0.60 inference(superposition,[],[f63,f3])).
% 2.43/0.60 tff(f221,plain,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) != X0 | 0 = X0 | 1 = X1) )),
% 2.43/0.60 inference(superposition,[],[f25,f16])).
% 2.43/0.60 tff(f290,definition,(
% 2.43/0.60 spl0_4 <=> a = 0),
% 2.43/0.60 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 2.43/0.60 tff(f291,plain,(
% 2.43/0.60 a != 0 | spl0_4),
% 2.43/0.60 inference(avatar_component_clause,[],[f290])).
% 2.43/0.60 tff(f292,plain,(
% 2.43/0.60 a = 0 | ~spl0_4),
% 2.43/0.60 inference(avatar_component_clause,[],[f290])).
% 2.43/0.60 tff(f299,plain,(
% 2.43/0.60 1 != $product(1,1) | (spl0_1 | ~spl0_2)),
% 2.43/0.60 inference(forward_demodulation,[],[f29,f32])).
% 2.43/0.60 tff(f300,plain,(
% 2.43/0.60 $false | (spl0_1 | ~spl0_2)),
% 2.43/0.60 inference(evaluation,[],[f299])).
% 2.43/0.60 tff(f301,plain,(
% 2.43/0.60 spl0_1 | ~spl0_2),
% 2.43/0.60 inference(avatar_contradiction_clause,[],[f300])).
% 2.43/0.60 tff(f303,plain,(
% 2.43/0.60 1 != $product(-1,-1) | (spl0_1 | ~spl0_3)),
% 2.43/0.60 inference(forward_demodulation,[],[f29,f39])).
% 2.43/0.60 tff(f304,plain,(
% 2.43/0.60 $false | (spl0_1 | ~spl0_3)),
% 2.43/0.60 inference(evaluation,[],[f303])).
% 2.43/0.60 tff(f305,plain,(
% 2.43/0.60 spl0_1 | ~spl0_3),
% 2.43/0.60 inference(avatar_contradiction_clause,[],[f304])).
% 2.43/0.60 tff(f306,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($product(1,X0) = $product(a,$product(a,X0))) ) | ~spl0_1),
% 2.43/0.60 inference(superposition,[],[f15,f28])).
% 2.43/0.60 tff(f307,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($product(a,$sum(a,X0)) = $sum(1,$product(a,X0))) ) | ~spl0_1),
% 2.43/0.60 inference(superposition,[],[f18,f28])).
% 2.43/0.60 tff(f311,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($product(a,$product(a,X0)) = X0) ) | ~spl0_1),
% 2.43/0.60 inference(evaluation,[],[f306])).
% 2.43/0.60 tff(f312,plain,(
% 2.43/0.60 1 = $product(0,0) | (~spl0_1 | ~spl0_4)),
% 2.43/0.60 inference(superposition,[],[f28,f292])).
% 2.43/0.60 tff(f315,plain,(
% 2.43/0.60 $false | (~spl0_1 | ~spl0_4)),
% 2.43/0.60 inference(evaluation,[],[f312])).
% 2.43/0.60 tff(f316,plain,(
% 2.43/0.60 ~spl0_1 | ~spl0_4),
% 2.43/0.60 inference(avatar_contradiction_clause,[],[f315])).
% 2.43/0.60 tff(f320,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($product(a,$product(X0,a)) = X0) ) | ~spl0_1),
% 2.43/0.60 inference(superposition,[],[f311,f14])).
% 2.43/0.60 tff(f345,plain,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($product(a,X1) != X0 | a = 0 | $product(X0,a) = X1) ) | ~spl0_1),
% 2.43/0.60 inference(superposition,[],[f25,f320])).
% 2.43/0.60 tff(f346,plain,(
% 2.43/0.60 ( ! [X0 : $int,X1 : $int] : ($product(a,X1) != X0 | $product(X0,a) = X1) ) | (~spl0_1 | spl0_4)),
% 2.43/0.60 inference(forward_subsumption_resolution,[],[f345,f291])).
% 2.43/0.60 tff(f352,plain,(
% 2.43/0.60 $product(a,$sum(a,1)) = $sum(1,a) | ~spl0_1),
% 2.43/0.60 inference(superposition,[],[f307,f16])).
% 2.43/0.60 tff(f362,plain,(
% 2.43/0.60 $sum(1,a) = $product(a,$sum(1,a)) | ~spl0_1),
% 2.43/0.60 inference(forward_demodulation,[],[f352,f3])).
% 2.43/0.60 tff(f1784,plain,(
% 2.43/0.60 ( ! [X0 : $int] : ($product($product(a,X0),a) = X0) ) | (~spl0_1 | spl0_4)),
% 2.43/0.60 inference(equality_resolution,[],[f346])).
% 2.43/0.60 tff(f1869,plain,(
% 2.43/0.60 $sum(1,a) = $product($sum(1,a),a) | (~spl0_1 | spl0_4)),
% 2.43/0.60 inference(superposition,[],[f1784,f362])).
% 2.43/0.60 tff(f2077,plain,(
% 2.43/0.60 $sum(1,a) != $sum(1,a) | 0 = $sum(1,a) | a = 1 | (~spl0_1 | spl0_4)),
% 2.43/0.60 inference(superposition,[],[f221,f1869])).
% 2.43/0.60 tff(f2079,plain,(
% 2.43/0.60 0 = $sum(1,a) | a = 1 | (~spl0_1 | spl0_4)),
% 2.43/0.60 inference(trivial_inequality_removal,[],[f2077])).
% 2.43/0.60 tff(f2080,plain,(
% 2.43/0.60 0 = $sum(1,a) | (~spl0_1 | spl0_2 | spl0_4)),
% 2.43/0.60 inference(forward_subsumption_resolution,[],[f2079,f33])).
% 2.43/0.60 tff(f2094,plain,(
% 2.43/0.60 ( ! [X0 : $int] : (~$less(X0,0) | ~$less(a,X0)) ) | (~spl0_1 | spl0_2 | spl0_4)),
% 2.43/0.60 inference(superposition,[],[f69,f2080])).
% 2.43/0.60 tff(f2096,plain,(
% 2.43/0.60 $less(a,0) | (~spl0_1 | spl0_2 | spl0_4)),
% 2.43/0.60 inference(superposition,[],[f74,f2080])).
% 2.43/0.60 tff(f2121,plain,(
% 2.43/0.60 ~$less(-1,a) | (~spl0_1 | spl0_2 | spl0_4)),
% 2.43/0.60 inference(resolution,[],[f2096,f72])).
% 2.43/0.60 tff(f2163,plain,(
% 2.43/0.60 $less(a,-1) | a = -1 | (~spl0_1 | spl0_2 | spl0_4)),
% 2.43/0.60 inference(resolution,[],[f2121,f10])).
% 2.43/0.60 tff(f2165,plain,(
% 2.43/0.60 $less(a,-1) | (~spl0_1 | spl0_2 | spl0_3 | spl0_4)),
% 2.43/0.60 inference(forward_subsumption_resolution,[],[f2163,f38])).
% 2.43/0.60 tff(f2452,plain,(
% 2.43/0.60 ~$less(-1,0) | (~spl0_1 | spl0_2 | spl0_3 | spl0_4)),
% 2.43/0.60 inference(resolution,[],[f2094,f2165])).
% 2.43/0.60 tff(f2455,plain,(
% 2.43/0.60 $false | (~spl0_1 | spl0_2 | spl0_3 | spl0_4)),
% 2.43/0.60 inference(evaluation,[],[f2452])).
% 2.43/0.60 tff(f2456,plain,(
% 2.43/0.60 ~spl0_1 | spl0_2 | spl0_3 | spl0_4),
% 2.43/0.60 inference(avatar_contradiction_clause,[],[f2455])).
% 2.43/0.60 cnf(s1, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f34])).
% 2.43/0.60 cnf(s2, plain, spl0_1 | spl0_2 | spl0_3, inference(sat_conversion,[],[f40])).
% 2.43/0.60 cnf(s3, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f42])).
% 2.43/0.60 cnf(s5, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f301])).
% 2.43/0.60 cnf(s6, plain, spl0_1 | ~spl0_3, inference(sat_conversion,[],[f305])).
% 2.43/0.60 cnf(s7, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f316])).
% 2.43/0.60 cnf(s9, plain, ~spl0_1 | spl0_2 | spl0_3 | spl0_4, inference(sat_conversion,[],[f2456])).
% 2.43/0.60 cnf(s10, plain, spl0_1, inference(rat,[],[s2,s5,s6])).
% 2.43/0.60 cnf(s11, plain, ~spl0_4, inference(rat,[],[s7,s10])).
% 2.43/0.60 cnf(s12, plain, ~spl0_3, inference(rat,[],[s3,s10])).
% 2.43/0.60 cnf(s13, plain, ~spl0_2, inference(rat,[],[s1,s10])).
% 2.43/0.60 cnf(s15, plain, $false, inference(rat,[],[s9,s11,s10,s12,s13])).
% 2.43/0.60 tff(f2457,plain,(
% 2.43/0.60 $false),
% 2.43/0.60 inference(avatar_sat_refutation,[],[s15])).
% 2.43/0.60 % SZS output end Proof for theBenchmark
% 2.43/0.60 % (2324388)------------------------------
% 2.43/0.60 % (2324388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.60 % (2324388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.60 % (2324388)CaDiCaL version: 2.1.3
% 2.43/0.60 % (2324388)Termination reason: Refutation
% 2.43/0.60 % (2324388)Time elapsed: 0.033 s
% 2.43/0.60 % (2324388)Peak memory usage: 14 MB
% 2.43/0.60 % (2324388)Instructions burned: 103 (million)
% 2.43/0.60 % (2324334)Success in time 0.374 s
% 2.43/0.60 % Vampire exiting
%------------------------------------------------------------------------------