%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI622_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 09:34:59 AM UTC 2026
% Result : Theorem 0.09s 0.18s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ARI622_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 20:53:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 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
% 0.09/0.18 % (3751401)Will run a generic schedule for satisfiability detection.
% 0.09/0.18 % (3751407)% WARNING: option uhcvi not known.
% 0.09/0.18 % (3751408)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1975470568:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.18 % (3751406)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4085113436_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.18 % (3751407)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=875922853:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.18 % (3751409)dis+10_1_sil=32000:sp=arity:random_seed=3850707532:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.18 % (3751410)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1823489876:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.18 % (3751411)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=25631271:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.18 % (3751412)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2711455677:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.18 % (3751406)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.18 % (3751406)Terminated due to inappropriate strategy.
% 0.09/0.18 % (3751406)------------------------------
% 0.09/0.18 % (3751406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3751406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3751406)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3751406)Termination reason: Inappropriate
% 0.09/0.18 % (3751406)Time elapsed: 0.0000 s
% 0.09/0.18 % (3751406)Peak memory usage: 10 MB
% 0.09/0.18 % (3751406)------------------------------
% 0.09/0.18 % (3751406)------------------------------
% 0.09/0.18 % (3751420)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3150311982:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.18 % (3751420)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.18 % (3751420)Terminated due to inappropriate strategy.
% 0.09/0.18 % (3751420)------------------------------
% 0.09/0.18 % (3751420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3751420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3751420)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3751420)Termination reason: Inappropriate
% 0.09/0.18 % (3751420)Time elapsed: 0.0000 s
% 0.09/0.18 % (3751420)Peak memory usage: 10 MB
% 0.09/0.18 % (3751420)------------------------------
% 0.09/0.18 % (3751420)------------------------------
% 0.09/0.18 % (3751422)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1180899294:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.18 % (3751407) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3751401-3751407"...
% 0.09/0.18 % (3751407)...printing done.
% 0.09/0.18 % (3751407)Refutation found. Thanks to Tanya!
% 0.09/0.18 % SZS status Theorem for theBenchmark
% 0.09/0.18 % SZS output start Proof for theBenchmark
% 0.09/0.18 tff(func_def_7, type, sK0: $int > $int).
% 0.09/0.18 tff(pred_def_1, type, pow2: $int > $o).
% 0.09/0.18 tff(f1,conjecture,(
% 0.09/0.18 ! [X0 : $int] : (pow2(X0) <=> (X0 = 1 | ($lesseq(2,X0) & ? [X1 : $int] : ($product(2,X1) = X0 & pow2(X1))))) => ? [X0 : $int,X1 : $int] : (pow2(X0) & pow2(X1) & $sum(X0,X1) = 10)),
% 0.09/0.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_of_pows_of_2_eq_10)).
% 0.09/0.18 tff(f2,negated_conjecture,(
% 0.09/0.18 ~(! [X0 : $int] : (pow2(X0) <=> (X0 = 1 | ($lesseq(2,X0) & ? [X1 : $int] : ($product(2,X1) = X0 & pow2(X1))))) => ? [X0 : $int,X1 : $int] : (pow2(X0) & pow2(X1) & $sum(X0,X1) = 10))),
% 0.09/0.18 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.18 tff(f3,plain,(
% 0.09/0.18 ~(! [X0 : $int] : (pow2(X0) <=> (X0 = 1 | (~$less(X0,2) & ? [X1 : $int] : ($product(2,X1) = X0 & pow2(X1))))) => ? [X0 : $int,X1 : $int] : (pow2(X0) & pow2(X1) & $sum(X0,X1) = 10))),
% 0.09/0.18 inference(theory_normalization,[],[f2])).
% 0.09/0.18 tff(f4,definition,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.09/0.18 introduced(theory,[tha_commutativity])).
% 0.09/0.18 tff(f5,definition,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.09/0.18 introduced(theory,[tha_associativity])).
% 0.09/0.18 tff(f8,definition,(
% 0.09/0.18 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.09/0.18 introduced(theory,[tha_inverse_op_unit])).
% 0.09/0.18 tff(f15,definition,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 0.09/0.18 introduced(theory,[tha_commutativity])).
% 0.09/0.18 tff(f16,definition,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 0.09/0.18 introduced(theory,[tha_associativity])).
% 0.09/0.18 tff(f17,definition,(
% 0.09/0.18 ( ! [X0 : $int] : ($product(X0,1) = X0) )),
% 0.09/0.18 introduced(theory,[tha_right_identity])).
% 0.09/0.18 tff(f22,plain,(
% 0.09/0.18 ~(! [X0 : $int] : (pow2(X0) <=> (X0 = 1 | (~$less(X0,2) & ? [X1 : $int] : ($product(2,X1) = X0 & pow2(X1))))) => ? [X2 : $int,X3 : $int] : (pow2(X2) & pow2(X3) & 10 = $sum(X2,X3)))),
% 0.09/0.18 inference(rectify,[],[f3])).
% 0.09/0.18 tff(f23,plain,(
% 0.09/0.18 ! [X2 : $int,X3 : $int] : (~pow2(X2) | ~pow2(X3) | 10 != $sum(X2,X3)) & ! [X0 : $int] : (pow2(X0) <=> (X0 = 1 | (~$less(X0,2) & ? [X1 : $int] : ($product(2,X1) = X0 & pow2(X1)))))),
% 0.09/0.18 inference(ennf_transformation,[],[f22])).
% 0.09/0.18 tff(f25,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (~pow2(X0) | 1 = X0 | $product(2,sK0(X0)) = X0) )),
% 0.09/0.18 inference(cnf_transformation,[],[f23])).
% 0.09/0.18 tff(f26,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : (~pow2(X1) | $product(2,X1) != X0 | $less(X0,2) | pow2(X0)) )),
% 0.09/0.18 inference(cnf_transformation,[],[f23])).
% 0.09/0.18 tff(f28,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (1 != X0 | pow2(X0)) )),
% 0.09/0.18 inference(cnf_transformation,[],[f23])).
% 0.09/0.18 tff(f29,plain,(
% 0.09/0.18 ( ! [X2 : $int,X3 : $int] : (10 != $sum(X2,X3) | ~pow2(X3) | ~pow2(X2)) )),
% 0.09/0.18 inference(cnf_transformation,[],[f23])).
% 0.09/0.18 tff(f31,plain,(
% 0.09/0.18 pow2(1)),
% 0.09/0.18 inference(equality_resolution,[],[f28])).
% 0.09/0.18 tff(f32,plain,(
% 0.09/0.18 ( ! [X1 : $int] : (pow2($product(2,X1)) | $less($product(2,X1),2) | ~pow2(X1)) )),
% 0.09/0.18 inference(equality_resolution,[],[f26])).
% 0.09/0.18 tff(f35,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (~pow2(X0) | $less($product(2,X0),2) | 1 = $product(2,X0) | $product(2,X0) = $product(2,sK0($product(2,X0)))) )),
% 0.09/0.18 inference(resolution,[],[f32,f25])).
% 0.09/0.18 tff(f45,plain,(
% 0.09/0.18 pow2(2) | $less(2,2) | ~pow2(1)),
% 0.09/0.18 inference(superposition,[],[f32,f17])).
% 0.09/0.18 tff(f46,plain,(
% 0.09/0.18 pow2(2) | ~pow2(1)),
% 0.09/0.18 inference(evaluation,[],[f45])).
% 0.09/0.18 tff(f47,plain,(
% 0.09/0.18 pow2(2)),
% 0.09/0.18 inference(forward_subsumption_resolution,[],[f46,f31])).
% 0.09/0.18 tff(f61,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (pow2($product(X0,2)) | $less($product(X0,2),2) | ~pow2(X0)) )),
% 0.09/0.18 inference(superposition,[],[f32,f15])).
% 0.09/0.18 tff(f70,plain,(
% 0.09/0.18 1 = 2 | 2 = $product(2,sK0(2))),
% 0.09/0.18 inference(resolution,[],[f47,f25])).
% 0.09/0.18 tff(f71,plain,(
% 0.09/0.18 2 = $product(2,sK0(2))),
% 0.09/0.18 inference(evaluation,[],[f70])).
% 0.09/0.18 tff(f108,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.09/0.18 inference(superposition,[],[f5,f8])).
% 0.09/0.18 tff(f123,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.09/0.18 inference(evaluation,[],[f108])).
% 0.09/0.18 tff(f134,plain,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product(X1,$product(X2,X0))) )),
% 0.09/0.18 inference(superposition,[],[f16,f15])).
% 0.09/0.18 tff(f139,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : (~pow2($product(X0,X1)) | $less($product(X0,$product(X1,2)),2) | pow2($product(X0,$product(X1,2)))) )),
% 0.09/0.18 inference(superposition,[],[f61,f16])).
% 0.09/0.18 tff(f220,plain,(
% 0.09/0.18 $less($product(2,2),2) | 1 = $product(2,2) | $product(2,2) = $product(2,sK0($product(2,2)))),
% 0.09/0.18 inference(resolution,[],[f35,f47])).
% 0.09/0.18 tff(f224,plain,(
% 0.09/0.18 4 = $product(2,sK0(4))),
% 0.09/0.18 inference(evaluation,[],[f220])).
% 0.09/0.18 tff(f270,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : (10 != X0 | ~pow2($sum($uminus(X1),X0)) | ~pow2(X1)) )),
% 0.09/0.18 inference(superposition,[],[f29,f123])).
% 0.09/0.18 tff(f395,definition,(
% 0.09/0.18 spl1_6 <=> pow2(4)),
% 0.09/0.18 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 0.09/0.18 tff(f667,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (~pow2($sum($uminus(X0),10)) | ~pow2(X0)) )),
% 0.09/0.18 inference(equality_resolution,[],[f270])).
% 0.09/0.18 tff(f668,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (~pow2(X0) | ~pow2($sum(10,$uminus(X0)))) )),
% 0.09/0.18 inference(forward_demodulation,[],[f667,f4])).
% 0.09/0.18 tff(f747,plain,(
% 0.09/0.18 ~pow2($sum(10,$uminus(2)))),
% 0.09/0.18 inference(resolution,[],[f668,f47])).
% 0.09/0.18 tff(f751,plain,(
% 0.09/0.18 ~pow2(8)),
% 0.09/0.18 inference(evaluation,[],[f747])).
% 0.09/0.18 tff(f1954,plain,(
% 0.09/0.18 ~pow2(2) | $less($product(2,$product(sK0(2),2)),2) | pow2($product(2,$product(sK0(2),2)))),
% 0.09/0.18 inference(superposition,[],[f139,f71])).
% 0.09/0.18 tff(f1955,plain,(
% 0.09/0.18 ~pow2(4) | $less($product(2,$product(sK0(4),2)),2) | pow2($product(2,$product(sK0(4),2)))),
% 0.09/0.18 inference(superposition,[],[f139,f224])).
% 0.09/0.18 tff(f1969,plain,(
% 0.09/0.18 $less($product(2,$product(sK0(2),2)),2) | pow2($product(2,$product(sK0(2),2)))),
% 0.09/0.18 inference(forward_subsumption_resolution,[],[f1954,f47])).
% 0.09/0.18 tff(f1976,plain,(
% 0.09/0.18 $less($product(2,$product(2,sK0(2))),2) | pow2($product(2,$product(sK0(2),2)))),
% 0.09/0.18 inference(forward_demodulation,[],[f1969,f134])).
% 0.09/0.18 tff(f1983,plain,(
% 0.09/0.18 $less($product(2,2),2) | pow2($product(2,$product(sK0(2),2)))),
% 0.09/0.18 inference(forward_demodulation,[],[f1976,f71])).
% 0.09/0.18 tff(f1984,plain,(
% 0.09/0.18 pow2($product(2,$product(sK0(2),2)))),
% 0.09/0.18 inference(evaluation,[],[f1983])).
% 0.09/0.18 tff(f1989,plain,(
% 0.09/0.18 pow2($product(2,$product(2,sK0(2))))),
% 0.09/0.18 inference(forward_demodulation,[],[f1984,f134])).
% 0.09/0.18 tff(f1991,plain,(
% 0.09/0.18 pow2($product(2,2))),
% 0.09/0.18 inference(forward_demodulation,[],[f1989,f71])).
% 0.09/0.18 tff(f1992,plain,(
% 0.09/0.18 pow2(4)),
% 0.09/0.18 inference(evaluation,[],[f1991])).
% 0.09/0.18 tff(f2018,plain,(
% 0.09/0.18 $less($product(2,$product(2,sK0(4))),2) | ~pow2(4) | pow2($product(2,$product(sK0(4),2)))),
% 0.09/0.18 inference(forward_demodulation,[],[f1955,f134])).
% 0.09/0.18 tff(f2019,plain,(
% 0.09/0.18 spl1_6),
% 0.09/0.18 inference(avatar_split_clause,[],[f1992,f395])).
% 0.09/0.18 tff(f2021,plain,(
% 0.09/0.18 $less($product(2,4),2) | ~pow2(4) | pow2($product(2,$product(sK0(4),2)))),
% 0.09/0.18 inference(forward_demodulation,[],[f2018,f224])).
% 0.09/0.18 tff(f2022,plain,(
% 0.09/0.18 ~pow2(4) | pow2($product(2,$product(sK0(4),2)))),
% 0.09/0.18 inference(evaluation,[],[f2021])).
% 0.09/0.18 tff(f2032,plain,(
% 0.09/0.18 pow2($product(2,$product(2,sK0(4)))) | ~pow2(4)),
% 0.09/0.18 inference(forward_demodulation,[],[f2022,f134])).
% 0.09/0.18 tff(f2033,plain,(
% 0.09/0.18 pow2($product(2,4)) | ~pow2(4)),
% 0.09/0.18 inference(forward_demodulation,[],[f2032,f224])).
% 0.09/0.18 tff(f2034,plain,(
% 0.09/0.18 pow2(8) | ~pow2(4)),
% 0.09/0.18 inference(evaluation,[],[f2033])).
% 0.09/0.18 tff(f2035,plain,(
% 0.09/0.18 ~pow2(4)),
% 0.09/0.18 inference(forward_subsumption_resolution,[],[f2034,f751])).
% 0.09/0.18 tff(f2036,plain,(
% 0.09/0.18 ~spl1_6),
% 0.09/0.18 inference(avatar_split_clause,[],[f2035,f395])).
% 0.09/0.18 cnf(s24, plain, spl1_6, inference(sat_conversion,[],[f2019])).
% 0.09/0.18 cnf(s26, plain, ~spl1_6, inference(sat_conversion,[],[f2036])).
% 0.09/0.18 cnf(s27, plain, $false, inference(rat,[],[s24,s26])).
% 0.09/0.18 tff(f2037,plain,(
% 0.09/0.18 $false),
% 0.09/0.18 inference(avatar_sat_refutation,[],[s27])).
% 0.09/0.18 % SZS output end Proof for theBenchmark
% 0.09/0.18 % (3751407)------------------------------
% 0.09/0.18 % (3751407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3751407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3751407)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3751407)Termination reason: Refutation
% 0.09/0.18 % (3751407)Time elapsed: 0.031 s
% 0.09/0.18 % (3751407)Peak memory usage: 13 MB
% 0.09/0.18 % (3751407)Instructions burned: 98 (million)
% 0.09/0.18 % (3751401)Success in time 0.054 s
% 0.09/0.18 % Vampire exiting
%------------------------------------------------------------------------------