%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI652_1 : TPTP v9.3.1. Released v6.3.0.
% 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 09:35:02 AM UTC 2026
% Result : Theorem 1.64s 0.52s
% Output : Refutation 1.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI652_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:58:17 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 1.64/0.52 % (3011234)Will run a generic schedule for satisfiability detection.
% 1.64/0.52 % (3011241)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2914447041:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.64/0.52 % (3011240)% WARNING: option uhcvi not known.
% 1.64/0.52 % (3011240)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=124952649:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.64/0.52 % (3011239)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3018957457_2999 on theBenchmark for (2999ds/0Mi)
% 1.64/0.52 % (3011242)dis+10_1_sil=32000:sp=arity:random_seed=4204791875:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.64/0.52 % (3011243)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2351694563:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.64/0.52 % (3011239)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.64/0.52 % (3011239)Terminated due to inappropriate strategy.
% 1.64/0.52 % (3011239)------------------------------
% 1.64/0.52 % (3011239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011239)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011239)Termination reason: Inappropriate
% 1.64/0.52 % (3011239)Time elapsed: 0.0000 s
% 1.64/0.52 % (3011239)Peak memory usage: 10 MB
% 1.64/0.52 % (3011244)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=500823127:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.64/0.52 % (3011245)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=586233081:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.64/0.52 % (3011239)------------------------------
% 1.64/0.52 % (3011239)------------------------------
% 1.64/0.52 % (3011253)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=378358669:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.64/0.52 % (3011253)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.64/0.52 % (3011253)Terminated due to inappropriate strategy.
% 1.64/0.52 % (3011253)------------------------------
% 1.64/0.52 % (3011253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011253)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011253)Termination reason: Inappropriate
% 1.64/0.52 % (3011253)Time elapsed: 0.0000 s
% 1.64/0.52 % (3011253)Peak memory usage: 10 MB
% 1.64/0.52 % (3011253)------------------------------
% 1.64/0.52 % (3011253)------------------------------
% 1.64/0.52 % (3011255)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2322096873:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.64/0.52 % (3011242)Instruction limit reached!
% 1.64/0.52 % (3011242)------------------------------
% 1.64/0.52 % (3011242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011242)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011242)Termination reason: Instruction limit
% 1.64/0.52 % (3011242)Termination phase: Saturation
% 1.64/0.52 % (3011242)Time elapsed: 0.061 s
% 1.64/0.52 % (3011242)Peak memory usage: 12 MB
% 1.64/0.52 % (3011242)Instructions burned: 103 (million)
% 1.64/0.52 % (3011243)Instruction limit reached!
% 1.64/0.52 % (3011243)------------------------------
% 1.64/0.52 % (3011243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011243)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011243)Termination reason: Instruction limit
% 1.64/0.52 % (3011243)Termination phase: Saturation
% 1.64/0.52 % (3011243)Time elapsed: 0.070 s
% 1.64/0.52 % (3011243)Peak memory usage: 12 MB
% 1.64/0.52 % (3011243)Instructions burned: 116 (million)
% 1.64/0.52 % (3011257)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=2875295701:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.64/0.52 % (3011244)Instruction limit reached!
% 1.64/0.52 % (3011244)------------------------------
% 1.64/0.52 % (3011244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011244)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011244)Termination reason: Instruction limit
% 1.64/0.52 % (3011244)Termination phase: Saturation
% 1.64/0.52 % (3011244)Time elapsed: 0.082 s
% 1.64/0.52 % (3011244)Peak memory usage: 13 MB
% 1.64/0.52 % (3011244)Instructions burned: 132 (million)
% 1.64/0.52 % (3011258)ott-21_1_sil=16000:fs=off:random_seed=3404908247:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.64/0.52 % (3011245)Instruction limit reached!
% 1.64/0.52 % (3011245)------------------------------
% 1.64/0.52 % (3011245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011245)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011245)Termination reason: Instruction limit
% 1.64/0.52 % (3011245)Termination phase: Saturation
% 1.64/0.52 % (3011245)Time elapsed: 0.098 s
% 1.64/0.52 % (3011245)Peak memory usage: 13 MB
% 1.64/0.52 % (3011245)Instructions burned: 160 (million)
% 1.64/0.52 % (3011260)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1126377140:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.64/0.52 % (3011262)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1468299996:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.64/0.52 % (3011262)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.64/0.52 % (3011262)Terminated due to inappropriate strategy.
% 1.64/0.52 % (3011262)------------------------------
% 1.64/0.52 % (3011262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011262)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011262)Termination reason: Inappropriate
% 1.64/0.52 % (3011262)Time elapsed: 0.0000 s
% 1.64/0.52 % (3011262)Peak memory usage: 10 MB
% 1.64/0.52 % (3011262)------------------------------
% 1.64/0.52 % (3011262)------------------------------
% 1.64/0.52 % (3011255)Instruction limit reached!
% 1.64/0.52 % (3011255)------------------------------
% 1.64/0.52 % (3011255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011255)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011255)Termination reason: Instruction limit
% 1.64/0.52 % (3011255)Termination phase: Saturation
% 1.64/0.52 % (3011255)Time elapsed: 0.087 s
% 1.64/0.52 % (3011255)Peak memory usage: 13 MB
% 1.64/0.52 % (3011255)Instructions burned: 132 (million)
% 1.64/0.52 % (3011265)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2034563645:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.64/0.52 % (3011266)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1279517473:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.64/0.52 % (3011266)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.64/0.52 % (3011266)Terminated due to inappropriate strategy.
% 1.64/0.52 % (3011266)------------------------------
% 1.64/0.52 % (3011266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011266)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011266)Termination reason: Inappropriate
% 1.64/0.52 % (3011266)Time elapsed: 0.0000 s
% 1.64/0.52 % (3011266)Peak memory usage: 10 MB
% 1.64/0.52 % (3011266)------------------------------
% 1.64/0.52 % (3011266)------------------------------
% 1.64/0.52 % (3011269)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=2646422340: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)
% 1.64/0.52 % (3011258)Instruction limit reached!
% 1.64/0.52 % (3011258)------------------------------
% 1.64/0.52 % (3011258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011258)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011258)Termination reason: Instruction limit
% 1.64/0.52 % (3011258)Termination phase: Saturation
% 1.64/0.52 % (3011258)Time elapsed: 0.080 s
% 1.64/0.52 % (3011258)Peak memory usage: 12 MB
% 1.64/0.52 % (3011258)Instructions burned: 180 (million)
% 1.64/0.52 % (3011271)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3306302575:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.64/0.52 % (3011240) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3011234-3011240"...
% 1.64/0.52 % (3011240)...printing done.
% 1.64/0.52 % (3011240)Refutation found. Thanks to Tanya!
% 1.64/0.52 % SZS status Theorem for theBenchmark
% 1.64/0.52 % SZS output start Proof for theBenchmark
% 1.64/0.52 tff(func_def_0, type, a: $int).
% 1.64/0.52 tff(f1,axiom,(
% 1.64/0.52 $less(2,$sum(a,4))),
% 1.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 1.64/0.52 tff(f2,axiom,(
% 1.64/0.52 $lesseq(-2,$difference(-3,a))),
% 1.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001)).
% 1.64/0.52 tff(f3,conjecture,(
% 1.64/0.52 $product(a,a) = 1),
% 1.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002)).
% 1.64/0.52 tff(f4,negated_conjecture,(
% 1.64/0.52 ~ $product(a,a) = 1),
% 1.64/0.52 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/0.52 tff(f5,plain,(
% 1.64/0.52 ~$less($sum(-3,$uminus(a)),-2)),
% 1.64/0.52 inference(theory_normalization,[],[f2])).
% 1.64/0.52 tff(f6,definition,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 1.64/0.52 introduced(theory,[tha_commutativity])).
% 1.64/0.52 tff(f7,definition,(
% 1.64/0.52 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 1.64/0.52 introduced(theory,[tha_associativity])).
% 1.64/0.52 tff(f9,definition,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0))) )),
% 1.64/0.52 introduced(theory,[tha_inverse_op_op_inverses])).
% 1.64/0.52 tff(f10,definition,(
% 1.64/0.52 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 1.64/0.52 introduced(theory,[tha_inverse_op_unit])).
% 1.64/0.52 tff(f13,definition,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 1.64/0.52 introduced(theory,[tha_order_totality])).
% 1.64/0.52 tff(f14,definition,(
% 1.64/0.52 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 1.64/0.52 introduced(theory,[tha_order_monotonicity])).
% 1.64/0.52 tff(f15,definition,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 1.64/0.52 introduced(theory,[tha_order_plus_one_dichotomy])).
% 1.64/0.52 tff(f16,definition,(
% 1.64/0.52 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 1.64/0.52 introduced(theory,[tha_minus_minus_x])).
% 1.64/0.52 tff(f23,definition,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 1.64/0.52 introduced(theory,[tha_extra_integer_ordering])).
% 1.64/0.52 tff(f24,plain,(
% 1.64/0.52 $product(a,a) != 1),
% 1.64/0.52 inference(flattening,[],[f4])).
% 1.64/0.52 tff(f25,plain,(
% 1.64/0.52 $less(2,$sum(a,4))),
% 1.64/0.52 inference(cnf_transformation,[],[f1])).
% 1.64/0.52 tff(f26,plain,(
% 1.64/0.52 ~$less($sum(-3,$uminus(a)),-2)),
% 1.64/0.52 inference(cnf_transformation,[],[f5])).
% 1.64/0.52 tff(f27,plain,(
% 1.64/0.52 $product(a,a) != 1),
% 1.64/0.52 inference(cnf_transformation,[],[f24])).
% 1.64/0.52 tff(f29,plain,(
% 1.64/0.52 ( ! [X0 : $int] : (0 = $sum($uminus(X0),X0)) )),
% 1.64/0.52 inference(superposition,[],[f10,f16])).
% 1.64/0.52 tff(f38,plain,(
% 1.64/0.52 $less(2,$sum(4,a))),
% 1.64/0.52 inference(superposition,[],[f25,f6])).
% 1.64/0.52 tff(f52,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 1.64/0.52 inference(superposition,[],[f15,f6])).
% 1.64/0.52 tff(f57,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 1.64/0.52 inference(superposition,[],[f23,f6])).
% 1.64/0.52 tff(f59,plain,(
% 1.64/0.52 ( ! [X0 : $int] : (~$less(X0,0) | ~$less($uminus(1),X0)) )),
% 1.64/0.52 inference(superposition,[],[f23,f29])).
% 1.64/0.52 tff(f60,plain,(
% 1.64/0.52 ( ! [X0 : $int] : (~$less(X0,0) | ~$less(-1,X0)) )),
% 1.64/0.52 inference(evaluation,[],[f59])).
% 1.64/0.52 tff(f67,plain,(
% 1.64/0.52 $less(-2,$sum(-3,$uminus(a))) | -2 = $sum(-3,$uminus(a))),
% 1.64/0.52 inference(resolution,[],[f13,f26])).
% 1.64/0.52 tff(f73,definition,(
% 1.64/0.52 spl0_1 <=> -2 = $sum(-3,$uminus(a))),
% 1.64/0.52 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 1.64/0.52 tff(f75,plain,(
% 1.64/0.52 -2 = $sum(-3,$uminus(a)) | ~spl0_1),
% 1.64/0.52 inference(avatar_component_clause,[],[f73])).
% 1.64/0.52 tff(f77,definition,(
% 1.64/0.52 spl0_2 <=> $less(-2,$sum(-3,$uminus(a)))),
% 1.64/0.52 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 1.64/0.52 tff(f79,plain,(
% 1.64/0.52 $less(-2,$sum(-3,$uminus(a))) | ~spl0_2),
% 1.64/0.52 inference(avatar_component_clause,[],[f77])).
% 1.64/0.52 tff(f81,plain,(
% 1.64/0.52 spl0_1 | spl0_2),
% 1.64/0.52 inference(avatar_split_clause,[],[f67,f77,f73])).
% 1.64/0.52 tff(f86,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($uminus($sum(X0,X1)) = $sum($uminus(X0),$uminus(X1))) )),
% 1.64/0.52 inference(superposition,[],[f9,f6])).
% 1.64/0.52 tff(f108,plain,(
% 1.64/0.52 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | $less($sum(X0,X1),$sum(X2,X0))) )),
% 1.64/0.52 inference(superposition,[],[f14,f6])).
% 1.64/0.52 tff(f116,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : (~$less(X0,$uminus(X1)) | $less($sum(X0,X1),0)) )),
% 1.64/0.52 inference(superposition,[],[f14,f29])).
% 1.64/0.52 tff(f127,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 1.64/0.52 inference(superposition,[],[f7,f10])).
% 1.64/0.52 tff(f147,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 1.64/0.52 inference(evaluation,[],[f127])).
% 1.64/0.52 tff(f235,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(X1,$sum(X0,$uminus(X1))) = X0) )),
% 1.64/0.52 inference(superposition,[],[f147,f6])).
% 1.64/0.52 tff(f245,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : (~$less(X1,X0) | ~$less($sum($uminus(1),X0),X1)) )),
% 1.64/0.52 inference(superposition,[],[f57,f147])).
% 1.64/0.52 tff(f250,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : (~$less(X1,X0) | ~$less($sum(-1,X0),X1)) )),
% 1.64/0.52 inference(evaluation,[],[f245])).
% 1.64/0.52 tff(f362,plain,(
% 1.64/0.52 ( ! [X0 : $int,X1 : $int] : ($uminus(X1) = $sum(X0,$uminus($sum(X0,X1)))) )),
% 1.64/0.52 inference(superposition,[],[f147,f86])).
% 1.64/0.52 tff(f404,plain,(
% 1.64/0.52 ( ! [X0 : $int] : ($less($sum(X0,2),$sum($sum(4,a),X0))) )),
% 1.64/0.52 inference(resolution,[],[f108,f38])).
% 1.64/0.52 tff(f406,plain,(
% 1.64/0.52 ( ! [X0 : $int] : ($less($sum(X0,-2),$sum($sum(-3,$uminus(a)),X0))) ) | ~spl0_2),
% 1.64/0.52 inference(resolution,[],[f108,f79])).
% 1.64/0.52 tff(f416,plain,(
% 1.64/0.52 ( ! [X0 : $int] : ($less($sum(X0,-2),$sum(-3,$sum($uminus(a),X0)))) ) | ~spl0_2),
% 1.64/0.52 inference(forward_demodulation,[],[f406,f7])).
% 1.64/0.52 tff(f418,plain,(
% 1.64/0.52 ( ! [X0 : $int] : ($less($sum(X0,2),$sum(4,$sum(a,X0)))) )),
% 1.64/0.52 inference(forward_demodulation,[],[f404,f7])).
% 1.64/0.52 tff(f3561,plain,(
% 1.64/0.52 $less($sum($uminus(4),2),a)),
% 1.64/0.52 inference(superposition,[],[f418,f235])).
% 1.64/0.52 tff(f3563,plain,(
% 1.64/0.52 $less(-2,a)),
% 1.64/0.52 inference(evaluation,[],[f3561])).
% 1.64/0.52 tff(f4947,plain,(
% 1.64/0.52 $less($sum($uminus(-3),-2),$uminus(a)) | ~spl0_2),
% 1.64/0.52 inference(superposition,[],[f416,f235])).
% 1.64/0.52 tff(f4949,plain,(
% 1.64/0.52 $less(1,$uminus(a)) | ~spl0_2),
% 1.64/0.52 inference(evaluation,[],[f4947])).
% 1.64/0.52 tff(f5152,plain,(
% 1.64/0.52 $less($sum(1,a),0) | ~spl0_2),
% 1.64/0.52 inference(resolution,[],[f4949,f116])).
% 1.64/0.52 tff(f9623,plain,(
% 1.64/0.52 ~$less(-1,$sum(1,a)) | ~spl0_2),
% 1.64/0.52 inference(resolution,[],[f5152,f60])).
% 1.64/0.52 tff(f10167,plain,(
% 1.64/0.52 $less(a,-1) | ~spl0_2),
% 1.64/0.52 inference(resolution,[],[f9623,f52])).
% 1.64/0.52 tff(f10178,plain,(
% 1.64/0.52 ~$less($sum(-1,-1),a) | ~spl0_2),
% 1.64/0.52 inference(resolution,[],[f10167,f250])).
% 1.64/0.52 tff(f10186,plain,(
% 1.64/0.52 ~$less(-2,a) | ~spl0_2),
% 1.64/0.52 inference(evaluation,[],[f10178])).
% 1.64/0.52 tff(f10190,plain,(
% 1.64/0.52 $false | ~spl0_2),
% 1.64/0.52 inference(forward_subsumption_resolution,[],[f10186,f3563])).
% 1.64/0.52 tff(f10191,plain,(
% 1.64/0.52 ~spl0_2),
% 1.64/0.52 inference(avatar_contradiction_clause,[],[f10190])).
% 1.64/0.52 tff(f10216,plain,(
% 1.64/0.52 $uminus($uminus(a)) = $sum(-3,$uminus(-2)) | ~spl0_1),
% 1.64/0.52 inference(superposition,[],[f362,f75])).
% 1.64/0.52 tff(f10233,plain,(
% 1.64/0.52 a = -1 | ~spl0_1),
% 1.64/0.52 inference(evaluation,[],[f10216])).
% 1.64/0.52 tff(f10429,plain,(
% 1.64/0.52 1 != $product(-1,-1) | ~spl0_1),
% 1.64/0.52 inference(superposition,[],[f27,f10233])).
% 1.64/0.52 tff(f10472,plain,(
% 1.64/0.52 $false | ~spl0_1),
% 1.64/0.52 inference(evaluation,[],[f10429])).
% 1.64/0.52 tff(f10473,plain,(
% 1.64/0.52 ~spl0_1),
% 1.64/0.52 inference(avatar_contradiction_clause,[],[f10472])).
% 1.64/0.52 cnf(s2, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f81])).
% 1.64/0.52 cnf(s13, plain, ~spl0_2, inference(sat_conversion,[],[f10191])).
% 1.64/0.52 cnf(s20, plain, ~spl0_1, inference(sat_conversion,[],[f10473])).
% 1.64/0.52 cnf(s23, plain, $false, inference(rat,[],[s2,s13,s20])).
% 1.64/0.52 tff(f10478,plain,(
% 1.64/0.52 $false),
% 1.64/0.52 inference(avatar_sat_refutation,[],[s23])).
% 1.64/0.52 % SZS output end Proof for theBenchmark
% 1.64/0.52 % (3011240)------------------------------
% 1.64/0.52 % (3011240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.52 % (3011240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.52 % (3011240)CaDiCaL version: 2.1.3
% 1.64/0.52 % (3011240)Termination reason: Refutation
% 1.64/0.52 % (3011240)Time elapsed: 0.247 s
% 1.64/0.52 % (3011240)Peak memory usage: 16 MB
% 1.64/0.52 % (3011240)Instructions burned: 437 (million)
% 1.64/0.52 % (3011234)Success in time 0.281 s
% 1.64/0.52 % Vampire exiting
%------------------------------------------------------------------------------