%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW642_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:40:35 PM UTC 2026
% Result : Theorem 0.96s 0.45s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW642_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 % Computer : n016.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Mon Sep 28 14:28:33 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 Running first-order model finding
% 0.11/0.27 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
% 0.96/0.45 % (3659655)Will run a generic schedule for satisfiability detection.
% 0.96/0.45 % (3659661)% WARNING: option uhcvi not known.
% 0.96/0.45 % (3659661)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4150960180:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.96/0.45 % (3659660)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1901988993_2999 on theBenchmark for (2999ds/0Mi)
% 0.96/0.45 % (3659664)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2422308993:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.96/0.45 % (3659662)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1090327182:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.96/0.45 % (3659663)dis+10_1_sil=32000:sp=arity:random_seed=1800809601:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.96/0.45 % (3659665)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1709929320:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.45 % (3659666)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3249182356:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.96/0.45 % (3659660)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.96/0.45 % (3659660)Terminated due to inappropriate strategy.
% 0.96/0.45 % (3659660)------------------------------
% 0.96/0.45 % (3659660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.45 % (3659660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.45 % (3659660)CaDiCaL version: 2.1.3
% 0.96/0.45 % (3659660)Termination reason: Inappropriate
% 0.96/0.45 % (3659660)Time elapsed: 0.003 s
% 0.96/0.45 % (3659660)Peak memory usage: 10 MB
% 0.96/0.45 % (3659660)Instructions burned: 2 (million)
% 0.96/0.45 % (3659660)------------------------------
% 0.96/0.45 % (3659660)------------------------------
% 0.96/0.45 % (3659674)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1234629785:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.96/0.45 % (3659674)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.96/0.45 % (3659674)Terminated due to inappropriate strategy.
% 0.96/0.45 % (3659674)------------------------------
% 0.96/0.45 % (3659674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.45 % (3659674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.45 % (3659674)CaDiCaL version: 2.1.3
% 0.96/0.45 % (3659674)Termination reason: Inappropriate
% 0.96/0.45 % (3659674)Time elapsed: 0.002 s
% 0.96/0.45 % (3659674)Peak memory usage: 10 MB
% 0.96/0.45 % (3659674)Instructions burned: 2 (million)
% 0.96/0.45 % (3659674)------------------------------
% 0.96/0.45 % (3659674)------------------------------
% 0.96/0.45 % (3659663)Instruction limit reached!
% 0.96/0.45 % (3659663)------------------------------
% 0.96/0.45 % (3659663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.45 % (3659663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.45 % (3659663)CaDiCaL version: 2.1.3
% 0.96/0.45 % (3659663)Termination reason: Instruction limit
% 0.96/0.45 % (3659663)Termination phase: Saturation
% 0.96/0.45 % (3659663)Time elapsed: 0.108 s
% 0.96/0.45 % (3659663)Peak memory usage: 13 MB
% 0.96/0.45 % (3659663)Instructions burned: 105 (million)
% 0.96/0.45 % (3659676)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1924809273:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.45 % (3659664)Instruction limit reached!
% 0.96/0.45 % (3659664)------------------------------
% 0.96/0.45 % (3659664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.45 % (3659664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.45 % (3659664)CaDiCaL version: 2.1.3
% 0.96/0.45 % (3659664)Termination reason: Instruction limit
% 0.96/0.45 % (3659664)Termination phase: Saturation
% 0.96/0.45 % (3659664)Time elapsed: 0.117 s
% 0.96/0.45 % (3659664)Peak memory usage: 13 MB
% 0.96/0.45 % (3659664)Instructions burned: 117 (million)
% 0.96/0.45 % (3659661) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3659655-3659661"...
% 0.96/0.45 % (3659661)...printing done.
% 0.96/0.45 % (3659661)Refutation found. Thanks to Tanya!
% 0.96/0.45 % SZS status Theorem for theBenchmark
% 0.96/0.45 % SZS output start Proof for theBenchmark
% 0.96/0.45 tff(type_def_5, type, uni: $tType).
% 0.96/0.45 tff(type_def_6, type, ty: $tType).
% 0.96/0.45 tff(type_def_7, type, bool1: $tType).
% 0.96/0.45 tff(type_def_8, type, tuple02: $tType).
% 0.96/0.45 tff(func_def_0, type, witness1: ty > uni).
% 0.96/0.45 tff(func_def_1, type, int: ty).
% 0.96/0.45 tff(func_def_2, type, real: ty).
% 0.96/0.45 tff(func_def_3, type, bool: ty).
% 0.96/0.45 tff(func_def_4, type, true1: bool1).
% 0.96/0.45 tff(func_def_5, type, false1: bool1).
% 0.96/0.45 tff(func_def_6, type, match_bool1: (ty * bool1 * uni * uni) > uni).
% 0.96/0.45 tff(func_def_7, type, tuple0: ty).
% 0.96/0.45 tff(func_def_8, type, tuple03: tuple02).
% 0.96/0.45 tff(func_def_9, type, qtmark: ty).
% 0.96/0.45 tff(func_def_12, type, ref: ty > ty).
% 0.96/0.45 tff(func_def_13, type, mk_ref: (ty * uni) > uni).
% 0.96/0.45 tff(func_def_14, type, contents: (ty * uni) > uni).
% 0.96/0.45 tff(func_def_18, type, fact1: $int > $int).
% 0.96/0.45 tff(func_def_21, type, sK0: $int > $int).
% 0.96/0.45 tff(func_def_22, type, sK1: $int).
% 0.96/0.45 tff(func_def_23, type, sK2: $int).
% 0.96/0.45 tff(func_def_24, type, sK3: $int).
% 0.96/0.45 tff(func_def_25, type, sK4: $int).
% 0.96/0.45 tff(func_def_26, type, sK5: $int).
% 0.96/0.45 tff(func_def_27, type, sK6: $int).
% 0.96/0.45 tff(func_def_28, type, sK7: $int).
% 0.96/0.45 tff(pred_def_1, type, sort1: (ty * uni) > $o).
% 0.96/0.45 tff(pred_def_3, type, even1: $int > $o).
% 0.96/0.45 tff(f17,axiom,(
% 0.96/0.45 fact1(0) = 1),
% 0.96/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0)).
% 0.96/0.45 tff(f18,axiom,(
% 0.96/0.45 ! [X0 : $int] : ($less(0,X0) => fact1(X0) = $product(X0,fact1($difference(X0,1))))),
% 0.96/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n)).
% 0.96/0.45 tff(f19,conjecture,(
% 0.96/0.45 ! [X0 : $int] : ($lesseq(0,X0) => ! [X1 : $int] : (X1 = 1 => ! [X2 : $int] : (X2 = X0 => ($lesseq(0,X2) & $product(X1,fact1(X2)) = fact1(X0) & ! [X3 : $int,X4 : $int] : (($lesseq(0,X3) & $product(X4,fact1(X3)) = fact1(X0)) => ((X3 != 0 => ! [X5 : $int] : (X5 = $product(X4,X3) => ! [X6 : $int] : (X6 = $difference(X3,1) => ($lesseq(0,X6) & $product(X5,fact1(X6)) = fact1(X0) & $lesseq(0,X3) & $less(X6,X3))))) & (X3 = 0 => X4 = fact1(X0))))))))),
% 0.96/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_factorial)).
% 0.96/0.45 tff(f20,negated_conjecture,(
% 0.96/0.45 ~ ! [X0 : $int] : ($lesseq(0,X0) => ! [X1 : $int] : (X1 = 1 => ! [X2 : $int] : (X2 = X0 => ($lesseq(0,X2) & $product(X1,fact1(X2)) = fact1(X0) & ! [X3 : $int,X4 : $int] : (($lesseq(0,X3) & $product(X4,fact1(X3)) = fact1(X0)) => ((X3 != 0 => ! [X5 : $int] : (X5 = $product(X4,X3) => ! [X6 : $int] : (X6 = $difference(X3,1) => ($lesseq(0,X6) & $product(X5,fact1(X6)) = fact1(X0) & $lesseq(0,X3) & $less(X6,X3))))) & (X3 = 0 => X4 = fact1(X0))))))))),
% 0.96/0.45 inference(negated_conjecture,[status(cth)],[f19])).
% 0.96/0.45 tff(f22,plain,(
% 0.96/0.45 ! [X0 : $int] : ($less(0,X0) => fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1)))))),
% 0.96/0.45 inference(theory_normalization,[],[f18])).
% 0.96/0.45 tff(f23,plain,(
% 0.96/0.45 ~ ! [X0 : $int] : (~$less(X0,0) => ! [X1 : $int] : (X1 = 1 => ! [X2 : $int] : (X2 = X0 => (~$less(X2,0) & $product(X1,fact1(X2)) = fact1(X0) & ! [X3 : $int,X4 : $int] : ((~$less(X3,0) & $product(X4,fact1(X3)) = fact1(X0)) => ((X3 != 0 => ! [X5 : $int] : (X5 = $product(X4,X3) => ! [X6 : $int] : ($sum(X3,$uminus(1)) = X6 => (~$less(X6,0) & $product(X5,fact1(X6)) = fact1(X0) & ~$less(X3,0) & $less(X6,X3))))) & (X3 = 0 => X4 = fact1(X0))))))))),
% 0.96/0.45 inference(theory_normalization,[],[f20])).
% 0.96/0.45 tff(f25,definition,(
% 0.96/0.45 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.96/0.45 introduced(theory,[tha_associativity])).
% 0.96/0.45 tff(f28,definition,(
% 0.96/0.45 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.96/0.45 introduced(theory,[tha_inverse_op_unit])).
% 0.96/0.45 tff(f29,definition,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.96/0.45 introduced(theory,[tha_non-reflexivity])).
% 0.96/0.45 tff(f31,definition,(
% 0.96/0.45 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.96/0.45 introduced(theory,[tha_order_totality])).
% 0.96/0.45 tff(f33,definition,(
% 0.96/0.45 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.96/0.45 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.96/0.45 tff(f36,definition,(
% 0.96/0.45 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 0.96/0.45 introduced(theory,[tha_associativity])).
% 0.96/0.45 tff(f41,definition,(
% 0.96/0.45 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.96/0.45 introduced(theory,[tha_extra_integer_ordering])).
% 0.96/0.45 tff(f53,plain,(
% 0.96/0.45 ! [X0 : $int] : (fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1)))) | ~$less(0,X0))),
% 0.96/0.45 inference(ennf_transformation,[],[f22])).
% 0.96/0.45 tff(f54,plain,(
% 0.96/0.45 ? [X0 : $int] : (? [X1 : $int] : (? [X2 : $int] : (($less(X2,0) | fact1(X0) != $product(X1,fact1(X2)) | ? [X3 : $int,X4 : $int] : (((? [X5 : $int] : (? [X6 : $int] : (($less(X6,0) | fact1(X0) != $product(X5,fact1(X6)) | $less(X3,0) | ~$less(X6,X3)) & $sum(X3,$uminus(1)) = X6) & X5 = $product(X4,X3)) & X3 != 0) | (fact1(X0) != X4 & X3 = 0)) & (~$less(X3,0) & $product(X4,fact1(X3)) = fact1(X0)))) & X2 = X0) & X1 = 1) & ~$less(X0,0))),
% 0.96/0.45 inference(ennf_transformation,[],[f23])).
% 0.96/0.45 tff(f55,plain,(
% 0.96/0.45 ? [X0 : $int] : (? [X1 : $int] : (? [X2 : $int] : (($less(X2,0) | fact1(X0) != $product(X1,fact1(X2)) | ? [X3 : $int,X4 : $int] : (((? [X5 : $int] : (? [X6 : $int] : (($less(X6,0) | fact1(X0) != $product(X5,fact1(X6)) | $less(X3,0) | ~$less(X6,X3)) & $sum(X3,$uminus(1)) = X6) & X5 = $product(X4,X3)) & X3 != 0) | (fact1(X0) != X4 & X3 = 0)) & ~$less(X3,0) & $product(X4,fact1(X3)) = fact1(X0))) & X2 = X0) & X1 = 1) & ~$less(X0,0))),
% 0.96/0.45 inference(flattening,[],[f54])).
% 0.96/0.45 tff(f73,plain,(
% 0.96/0.45 1 = fact1(0)),
% 0.96/0.45 inference(cnf_transformation,[],[f17])).
% 0.96/0.45 tff(f74,plain,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(0,X0) | fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1))))) )),
% 0.96/0.45 inference(cnf_transformation,[],[f53])).
% 0.96/0.45 tff(f75,plain,(
% 0.96/0.45 0 = sK4 | ~$less(sK7,sK4) | $less(sK4,0) | fact1(sK1) != $product(sK6,fact1(sK7)) | $less(sK7,0) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f77,plain,(
% 0.96/0.45 sK5 != fact1(sK1) | sK7 = $sum(sK4,$uminus(1)) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f78,plain,(
% 0.96/0.45 0 = sK4 | sK7 = $sum(sK4,$uminus(1)) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f79,plain,(
% 0.96/0.45 0 = sK4 | sK6 = $product(sK5,sK4) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f81,plain,(
% 0.96/0.45 sK5 != fact1(sK1) | 0 != sK4 | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f82,plain,(
% 0.96/0.45 fact1(sK1) = $product(sK5,fact1(sK4)) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f83,plain,(
% 0.96/0.45 ~$less(sK4,0) | fact1(sK1) != $product(sK2,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f84,plain,(
% 0.96/0.45 sK1 = sK3),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f85,plain,(
% 0.96/0.45 1 = sK2),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f86,plain,(
% 0.96/0.45 ~$less(sK1,0)),
% 0.96/0.45 inference(cnf_transformation,[],[f55])).
% 0.96/0.45 tff(f87,plain,(
% 0.96/0.45 ~$less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f86,f84])).
% 0.96/0.45 tff(f88,plain,(
% 0.96/0.45 ~$less(sK4,0) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f83,f84,f85])).
% 0.96/0.45 tff(f89,plain,(
% 0.96/0.45 fact1(sK3) = $product(sK5,fact1(sK4)) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f82,f84,f84,f85])).
% 0.96/0.45 tff(f90,plain,(
% 0.96/0.45 sK5 != fact1(sK3) | 0 != sK4 | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f81,f84,f84,f85])).
% 0.96/0.45 tff(f92,plain,(
% 0.96/0.45 0 = sK4 | sK6 = $product(sK5,sK4) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f79,f84,f85])).
% 0.96/0.45 tff(f93,plain,(
% 0.96/0.45 0 = sK4 | sK7 = $sum(sK4,$uminus(1)) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f78,f84,f85])).
% 0.96/0.45 tff(f94,plain,(
% 0.96/0.45 sK5 != fact1(sK3) | sK7 = $sum(sK4,$uminus(1)) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f77,f84,f84,f85])).
% 0.96/0.45 tff(f96,plain,(
% 0.96/0.45 0 = sK4 | ~$less(sK7,sK4) | $less(sK4,0) | $product(sK6,fact1(sK7)) != fact1(sK3) | $less(sK7,0) | fact1(sK3) != $product(1,fact1(sK3)) | $less(sK3,0)),
% 0.96/0.45 inference(definition_unfolding,[],[f75,f84,f84,f85])).
% 0.96/0.45 tff(f111,plain,(
% 0.96/0.45 0 = sK4 | ~$less(sK7,sK4) | $less(sK4,0) | $product(sK6,fact1(sK7)) != fact1(sK3) | $less(sK7,0) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f96])).
% 0.96/0.45 tff(f113,plain,(
% 0.96/0.45 sK5 != fact1(sK3) | sK7 = $sum(sK4,-1) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f94])).
% 0.96/0.45 tff(f114,plain,(
% 0.96/0.45 0 = sK4 | sK7 = $sum(sK4,-1) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f93])).
% 0.96/0.45 tff(f115,plain,(
% 0.96/0.45 0 = sK4 | sK6 = $product(sK5,sK4) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f92])).
% 0.96/0.45 tff(f117,plain,(
% 0.96/0.45 sK5 != fact1(sK3) | 0 != sK4 | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f90])).
% 0.96/0.45 tff(f118,plain,(
% 0.96/0.45 fact1(sK3) = $product(sK5,fact1(sK4)) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f89])).
% 0.96/0.45 tff(f119,plain,(
% 0.96/0.45 ~$less(sK4,0) | $less(sK3,0)),
% 0.96/0.45 inference(evaluation,[],[f88])).
% 0.96/0.45 tff(f120,plain,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(0,X0) | fact1(X0) = $product(X0,fact1($sum(X0,-1)))) )),
% 0.96/0.45 inference(evaluation,[],[f74])).
% 0.96/0.45 tff(f122,definition,(
% 0.96/0.45 spl8_1 <=> $less(sK3,0)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.96/0.45 tff(f126,definition,(
% 0.96/0.45 spl8_2 <=> $less(sK7,0)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.96/0.45 tff(f130,definition,(
% 0.96/0.45 spl8_3 <=> $product(sK6,fact1(sK7)) = fact1(sK3)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.96/0.45 tff(f132,plain,(
% 0.96/0.45 $product(sK6,fact1(sK7)) != fact1(sK3) | spl8_3),
% 0.96/0.45 inference(avatar_component_clause,[],[f130])).
% 0.96/0.45 tff(f134,definition,(
% 0.96/0.45 spl8_4 <=> $less(sK4,0)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.96/0.45 tff(f135,plain,(
% 0.96/0.45 ~$less(sK4,0) | spl8_4),
% 0.96/0.45 inference(avatar_component_clause,[],[f134])).
% 0.96/0.45 tff(f138,definition,(
% 0.96/0.45 spl8_5 <=> $less(sK7,sK4)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.96/0.45 tff(f142,definition,(
% 0.96/0.45 spl8_6 <=> 0 = sK4),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.96/0.45 tff(f143,plain,(
% 0.96/0.45 0 != sK4 | spl8_6),
% 0.96/0.45 inference(avatar_component_clause,[],[f142])).
% 0.96/0.45 tff(f144,plain,(
% 0.96/0.45 0 = sK4 | ~spl8_6),
% 0.96/0.45 inference(avatar_component_clause,[],[f142])).
% 0.96/0.45 tff(f145,plain,(
% 0.96/0.45 spl8_1 | spl8_2 | ~spl8_3 | spl8_4 | ~spl8_5 | spl8_6),
% 0.96/0.45 inference(avatar_split_clause,[],[f111,f142,f138,f134,f130,f126,f122])).
% 0.96/0.45 tff(f147,definition,(
% 0.96/0.45 spl8_7 <=> sK5 = fact1(sK3)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 0.96/0.45 tff(f149,plain,(
% 0.96/0.45 sK5 != fact1(sK3) | spl8_7),
% 0.96/0.45 inference(avatar_component_clause,[],[f147])).
% 0.96/0.45 tff(f152,definition,(
% 0.96/0.45 spl8_8 <=> sK7 = $sum(sK4,-1)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.96/0.45 tff(f154,plain,(
% 0.96/0.45 sK7 = $sum(sK4,-1) | ~spl8_8),
% 0.96/0.45 inference(avatar_component_clause,[],[f152])).
% 0.96/0.45 tff(f155,plain,(
% 0.96/0.45 spl8_1 | spl8_8 | ~spl8_7),
% 0.96/0.45 inference(avatar_split_clause,[],[f113,f147,f152,f122])).
% 0.96/0.45 tff(f156,plain,(
% 0.96/0.45 spl8_1 | spl8_8 | spl8_6),
% 0.96/0.45 inference(avatar_split_clause,[],[f114,f142,f152,f122])).
% 0.96/0.45 tff(f158,definition,(
% 0.96/0.45 spl8_9 <=> sK6 = $product(sK5,sK4)),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.96/0.45 tff(f160,plain,(
% 0.96/0.45 sK6 = $product(sK5,sK4) | ~spl8_9),
% 0.96/0.45 inference(avatar_component_clause,[],[f158])).
% 0.96/0.45 tff(f161,plain,(
% 0.96/0.45 spl8_1 | spl8_9 | spl8_6),
% 0.96/0.45 inference(avatar_split_clause,[],[f115,f142,f158,f122])).
% 0.96/0.45 tff(f163,plain,(
% 0.96/0.45 spl8_1 | ~spl8_6 | ~spl8_7),
% 0.96/0.45 inference(avatar_split_clause,[],[f117,f147,f142,f122])).
% 0.96/0.45 tff(f165,definition,(
% 0.96/0.45 spl8_10 <=> fact1(sK3) = $product(sK5,fact1(sK4))),
% 0.96/0.45 introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition])).
% 0.96/0.45 tff(f167,plain,(
% 0.96/0.45 fact1(sK3) = $product(sK5,fact1(sK4)) | ~spl8_10),
% 0.96/0.45 inference(avatar_component_clause,[],[f165])).
% 0.96/0.45 tff(f168,plain,(
% 0.96/0.45 spl8_1 | spl8_10),
% 0.96/0.45 inference(avatar_split_clause,[],[f118,f165,f122])).
% 0.96/0.45 tff(f169,plain,(
% 0.96/0.45 spl8_1 | ~spl8_4),
% 0.96/0.45 inference(avatar_split_clause,[],[f119,f134,f122])).
% 0.96/0.45 tff(f170,plain,(
% 0.96/0.45 ~spl8_1),
% 0.96/0.45 inference(avatar_split_clause,[],[f87,f122])).
% 0.96/0.45 tff(f172,plain,(
% 0.96/0.45 fact1(sK3) = $product(sK5,fact1(0)) | (~spl8_6 | ~spl8_10)),
% 0.96/0.45 inference(forward_demodulation,[],[f167,f144])).
% 0.96/0.45 tff(f176,plain,(
% 0.96/0.45 fact1(sK3) = $product(sK5,1) | (~spl8_6 | ~spl8_10)),
% 0.96/0.45 inference(superposition,[],[f172,f73])).
% 0.96/0.45 tff(f177,plain,(
% 0.96/0.45 sK5 = fact1(sK3) | (~spl8_6 | ~spl8_10)),
% 0.96/0.45 inference(evaluation,[],[f176])).
% 0.96/0.45 tff(f178,plain,(
% 0.96/0.45 $false | (~spl8_6 | spl8_7 | ~spl8_10)),
% 0.96/0.45 inference(forward_subsumption_resolution,[],[f177,f149])).
% 0.96/0.45 tff(f179,plain,(
% 0.96/0.45 ~spl8_6 | spl8_7 | ~spl8_10),
% 0.96/0.45 inference(avatar_contradiction_clause,[],[f178])).
% 0.96/0.45 tff(f208,plain,(
% 0.96/0.45 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.96/0.45 inference(resolution,[],[f33,f29])).
% 0.96/0.45 tff(f221,plain,(
% 0.96/0.45 $less(0,sK4) | 0 = sK4 | spl8_4),
% 0.96/0.45 inference(resolution,[],[f31,f135])).
% 0.96/0.45 tff(f224,plain,(
% 0.96/0.45 $less(0,sK4) | (spl8_4 | spl8_6)),
% 0.96/0.45 inference(forward_subsumption_resolution,[],[f221,f143])).
% 0.96/0.45 tff(f275,plain,(
% 0.96/0.45 ( ! [X0 : $int] : ($sum(sK4,$sum(-1,X0)) = $sum(sK7,X0)) ) | ~spl8_8),
% 0.96/0.45 inference(superposition,[],[f25,f154])).
% 0.96/0.45 tff(f285,plain,(
% 0.96/0.45 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,$sum(X0,$sum(X1,1))) | ~$less($sum(X0,X1),X2)) )),
% 0.96/0.45 inference(superposition,[],[f41,f25])).
% 0.96/0.45 tff(f292,plain,(
% 0.96/0.45 ( ! [X0 : $int] : ($product(sK5,$product(sK4,X0)) = $product(sK6,X0)) ) | ~spl8_9),
% 0.96/0.45 inference(superposition,[],[f36,f160])).
% 0.96/0.45 tff(f317,plain,(
% 0.96/0.45 fact1(sK4) = $product(sK4,fact1($sum(sK4,-1))) | (spl8_4 | spl8_6)),
% 0.96/0.45 inference(resolution,[],[f120,f224])).
% 0.96/0.45 tff(f324,plain,(
% 0.96/0.45 fact1(sK4) = $product(sK4,fact1(sK7)) | (spl8_4 | spl8_6 | ~spl8_8)),
% 0.96/0.45 inference(forward_demodulation,[],[f317,f154])).
% 0.96/0.45 tff(f487,plain,(
% 0.96/0.45 $sum(sK7,$uminus(-1)) = $sum(sK4,0) | ~spl8_8),
% 0.96/0.45 inference(superposition,[],[f275,f28])).
% 0.96/0.45 tff(f491,plain,(
% 0.96/0.45 sK4 = $sum(sK7,1) | ~spl8_8),
% 0.96/0.45 inference(evaluation,[],[f487])).
% 0.96/0.45 tff(f1057,plain,(
% 0.96/0.45 $less(sK7,sK4) | ~spl8_8),
% 0.96/0.45 inference(superposition,[],[f208,f491])).
% 0.96/0.45 tff(f1073,plain,(
% 0.96/0.45 spl8_5 | ~spl8_8),
% 0.96/0.45 inference(avatar_split_clause,[],[f1057,f152,f138])).
% 0.96/0.45 tff(f2051,plain,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(X0,$sum(sK7,1)) | ~$less($sum(sK4,-1),X0)) ) | ~spl8_8),
% 0.96/0.45 inference(superposition,[],[f285,f275])).
% 0.96/0.45 tff(f2054,plain,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(X0,sK4) | ~$less($sum(sK4,-1),X0)) ) | ~spl8_8),
% 0.96/0.45 inference(forward_demodulation,[],[f2051,f491])).
% 0.96/0.45 tff(f2064,plain,(
% 0.96/0.45 ( ! [X0 : $int] : (~$less(X0,sK4) | ~$less(sK7,X0)) ) | ~spl8_8),
% 0.96/0.45 inference(forward_demodulation,[],[f2054,f154])).
% 0.96/0.45 tff(f3776,plain,(
% 0.96/0.45 ~$less(sK7,0) | (spl8_4 | spl8_6 | ~spl8_8)),
% 0.96/0.45 inference(resolution,[],[f2064,f224])).
% 0.96/0.45 tff(f3786,plain,(
% 0.96/0.45 ~spl8_2 | spl8_4 | spl8_6 | ~spl8_8),
% 0.96/0.45 inference(avatar_split_clause,[],[f3776,f152,f142,f134,f126])).
% 0.96/0.45 tff(f6663,plain,(
% 0.96/0.45 $product(sK6,fact1(sK7)) = $product(sK5,fact1(sK4)) | (spl8_4 | spl8_6 | ~spl8_8 | ~spl8_9)),
% 0.96/0.45 inference(superposition,[],[f292,f324])).
% 0.96/0.45 tff(f6754,plain,(
% 0.96/0.45 $product(sK6,fact1(sK7)) = fact1(sK3) | (spl8_4 | spl8_6 | ~spl8_8 | ~spl8_9 | ~spl8_10)),
% 0.96/0.45 inference(forward_demodulation,[],[f6663,f167])).
% 0.96/0.45 tff(f6793,plain,(
% 0.96/0.45 $false | (spl8_3 | spl8_4 | spl8_6 | ~spl8_8 | ~spl8_9 | ~spl8_10)),
% 0.96/0.45 inference(forward_subsumption_resolution,[],[f6754,f132])).
% 0.96/0.45 tff(f6794,plain,(
% 0.96/0.45 spl8_3 | spl8_4 | spl8_6 | ~spl8_8 | ~spl8_9 | ~spl8_10),
% 0.96/0.45 inference(avatar_contradiction_clause,[],[f6793])).
% 0.96/0.45 cnf(s1, plain, spl8_1 | spl8_2 | ~spl8_3 | spl8_4 | ~spl8_5 | spl8_6, inference(sat_conversion,[],[f145])).
% 0.96/0.45 cnf(s3, plain, spl8_1 | ~spl8_7 | spl8_8, inference(sat_conversion,[],[f155])).
% 0.96/0.45 cnf(s4, plain, spl8_1 | spl8_6 | spl8_8, inference(sat_conversion,[],[f156])).
% 0.96/0.45 cnf(s5, plain, spl8_1 | spl8_6 | spl8_9, inference(sat_conversion,[],[f161])).
% 0.96/0.45 cnf(s7, plain, spl8_1 | ~spl8_6 | ~spl8_7, inference(sat_conversion,[],[f163])).
% 0.96/0.45 cnf(s8, plain, spl8_1 | spl8_10, inference(sat_conversion,[],[f168])).
% 0.96/0.45 cnf(s9, plain, spl8_1 | ~spl8_4, inference(sat_conversion,[],[f169])).
% 0.96/0.45 cnf(s10, plain, ~spl8_1, inference(sat_conversion,[],[f170])).
% 0.96/0.45 cnf(s11, plain, ~spl8_6 | spl8_7 | ~spl8_10, inference(sat_conversion,[],[f179])).
% 0.96/0.45 cnf(s51, plain, spl8_5 | ~spl8_8, inference(sat_conversion,[],[f1073])).
% 0.96/0.45 cnf(s60, plain, ~spl8_2 | spl8_4 | spl8_6 | ~spl8_8, inference(sat_conversion,[],[f3786])).
% 0.96/0.45 cnf(s316, plain, spl8_3 | spl8_4 | spl8_6 | ~spl8_8 | ~spl8_9 | ~spl8_10, inference(sat_conversion,[],[f6794])).
% 0.96/0.45 cnf(s319, plain, ~spl8_4, inference(rat,[],[s9,s10])).
% 0.96/0.45 cnf(s320, plain, spl8_10, inference(rat,[],[s8,s10])).
% 0.96/0.45 cnf(s321, plain, ~spl8_6 | ~spl8_7, inference(rat,[],[s7,s10])).
% 0.96/0.45 cnf(s323, plain, spl8_6 | spl8_9, inference(rat,[],[s5,s10])).
% 0.96/0.45 cnf(s324, plain, spl8_6 | spl8_8, inference(rat,[],[s4,s10])).
% 0.96/0.45 cnf(s325, plain, ~spl8_7 | spl8_8, inference(rat,[],[s3,s10])).
% 0.96/0.45 cnf(s327, plain, spl8_2 | ~spl8_3 | ~spl8_5 | spl8_6, inference(rat,[],[s1,s319,s10])).
% 0.96/0.45 cnf(s328, plain, spl8_8, inference(rat,[],[s11,s325,s324,s320])).
% 0.96/0.45 cnf(s329, plain, spl8_5, inference(rat,[],[s51,s328])).
% 0.96/0.45 cnf(s330, plain, ~spl8_6, inference(rat,[],[s321,s11,s320])).
% 0.96/0.45 cnf(s331, plain, spl8_9, inference(rat,[],[s323,s330])).
% 0.96/0.45 cnf(s332, plain, spl8_3, inference(rat,[],[s316,s320,s330,s328,s319,s331])).
% 0.96/0.45 cnf(s333, plain, ~spl8_2, inference(rat,[],[s60,s328,s319,s330])).
% 0.96/0.45 cnf(s334, plain, $false, inference(rat,[],[s327,s329,s333,s330,s332])).
% 0.96/0.45 tff(f6795,plain,(
% 0.96/0.45 $false),
% 0.96/0.45 inference(avatar_sat_refutation,[],[s334])).
% 0.96/0.45 % SZS output end Proof for theBenchmark
% 0.96/0.45 % (3659661)------------------------------
% 0.96/0.45 % (3659661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.45 % (3659661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.45 % (3659661)CaDiCaL version: 2.1.3
% 0.96/0.45 % (3659661)Termination reason: Refutation
% 0.96/0.45 % (3659661)Time elapsed: 0.142 s
% 0.96/0.45 % (3659661)Peak memory usage: 15 MB
% 0.96/0.45 % (3659661)Instructions burned: 273 (million)
% 0.96/0.45 % (3659655)Success in time 0.166 s
% 0.96/0.45 % Vampire exiting
%------------------------------------------------------------------------------