%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT036_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:48:00 AM UTC 2026
% Result : Theorem 2.66s 0.78s
% Output : Refutation 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT036_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.22 % Computer : n011.cluster.edu
% 0.13/0.22 % Model : x86_64 x86_64
% 0.13/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.22 % Memory : 8046.5625MB
% 0.13/0.22 % OS : Linux 6.8.0-71-generic
% 0.13/0.23 % CPULimit : 300
% 0.13/0.23 % WCLimit : 300
% 0.13/0.23 % DateTime : Tue Sep 29 00:06:17 UTC 2026
% 0.13/0.23 % CPUTime :
% 0.13/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.28 Running first-order model finding
% 0.13/0.28 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
% 2.66/0.78 % (3912205)Will run a generic schedule for satisfiability detection.
% 2.66/0.78 % (3912211)% WARNING: option uhcvi not known.
% 2.66/0.78 % (3912211)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1947446783:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.66/0.78 % (3912210)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3726250832_2999 on theBenchmark for (2999ds/0Mi)
% 2.66/0.78 % (3912210)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.66/0.78 % (3912210)Terminated due to inappropriate strategy.
% 2.66/0.78 % (3912210)------------------------------
% 2.66/0.78 % (3912210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912210)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912210)Termination reason: Inappropriate
% 2.66/0.78 % (3912210)Time elapsed: 0.001 s
% 2.66/0.78 % (3912210)Peak memory usage: 10 MB
% 2.66/0.78 % (3912210)Instructions burned: 1 (million)
% 2.66/0.78 % (3912210)------------------------------
% 2.66/0.78 % (3912210)------------------------------
% 2.66/0.78 % (3912212)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1970442047:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.66/0.78 % (3912213)dis+10_1_sil=32000:sp=arity:random_seed=3932705385:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.66/0.78 % (3912216)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=749486339:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.66/0.78 % (3912215)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3041352084:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.66/0.78 % (3912214)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2086116534:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.66/0.78 % (3912220)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=534865466:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.66/0.78 % (3912220)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.66/0.78 % (3912220)Terminated due to inappropriate strategy.
% 2.66/0.78 % (3912220)------------------------------
% 2.66/0.78 % (3912220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912220)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912220)Termination reason: Inappropriate
% 2.66/0.78 % (3912220)Time elapsed: 0.002 s
% 2.66/0.78 % (3912220)Peak memory usage: 10 MB
% 2.66/0.78 % (3912220)Instructions burned: 1 (million)
% 2.66/0.78 % (3912220)------------------------------
% 2.66/0.78 % (3912220)------------------------------
% 2.66/0.78 % (3912230)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=903291126:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.66/0.78 % (3912214)Instruction limit reached!
% 2.66/0.78 % (3912214)------------------------------
% 2.66/0.78 % (3912214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912214)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912214)Termination reason: Instruction limit
% 2.66/0.78 % (3912214)Termination phase: Saturation
% 2.66/0.78 % (3912214)Time elapsed: 0.107 s
% 2.66/0.78 % (3912214)Peak memory usage: 12 MB
% 2.66/0.78 % (3912214)Instructions burned: 116 (million)
% 2.66/0.78 % (3912213)Instruction limit reached!
% 2.66/0.78 % (3912213)------------------------------
% 2.66/0.78 % (3912213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912213)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912213)Termination reason: Instruction limit
% 2.66/0.78 % (3912213)Termination phase: Saturation
% 2.66/0.78 % (3912213)Time elapsed: 0.109 s
% 2.66/0.78 % (3912213)Peak memory usage: 12 MB
% 2.66/0.78 % (3912213)Instructions burned: 104 (million)
% 2.66/0.78 % (3912233)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=1678870585:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.66/0.78 % (3912215)Instruction limit reached!
% 2.66/0.78 % (3912215)------------------------------
% 2.66/0.78 % (3912215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912215)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912215)Termination reason: Instruction limit
% 2.66/0.78 % (3912215)Termination phase: Saturation
% 2.66/0.78 % (3912215)Time elapsed: 0.135 s
% 2.66/0.78 % (3912215)Peak memory usage: 13 MB
% 2.66/0.78 % (3912215)Instructions burned: 132 (million)
% 2.66/0.78 % (3912234)ott-21_1_sil=16000:fs=off:random_seed=1573373718:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.66/0.78 % (3912216)Instruction limit reached!
% 2.66/0.78 % (3912216)------------------------------
% 2.66/0.78 % (3912216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912216)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912216)Termination reason: Instruction limit
% 2.66/0.78 % (3912216)Termination phase: Saturation
% 2.66/0.78 % (3912216)Time elapsed: 0.169 s
% 2.66/0.78 % (3912216)Peak memory usage: 13 MB
% 2.66/0.78 % (3912216)Instructions burned: 159 (million)
% 2.66/0.78 % (3912237)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4149268122:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.66/0.78 % (3912240)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1545349326:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.66/0.78 % (3912230)Instruction limit reached!
% 2.66/0.78 % (3912230)------------------------------
% 2.66/0.78 % (3912230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912230)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912230)Termination reason: Instruction limit
% 2.66/0.78 % (3912230)Termination phase: Saturation
% 2.66/0.78 % (3912230)Time elapsed: 0.136 s
% 2.66/0.78 % (3912230)Peak memory usage: 13 MB
% 2.66/0.78 % (3912230)Instructions burned: 132 (million)
% 2.66/0.78 % (3912240)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.66/0.78 % (3912240)Terminated due to inappropriate strategy.
% 2.66/0.78 % (3912240)------------------------------
% 2.66/0.78 % (3912240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912240)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912240)Termination reason: Inappropriate
% 2.66/0.78 % (3912240)Time elapsed: 0.002 s
% 2.66/0.78 % (3912240)Peak memory usage: 10 MB
% 2.66/0.78 % (3912240)------------------------------
% 2.66/0.78 % (3912240)------------------------------
% 2.66/0.78 % (3912244)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2697258166:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.66/0.78 % (3912245)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2322738778:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.66/0.78 % (3912245)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.66/0.78 % (3912245)Terminated due to inappropriate strategy.
% 2.66/0.78 % (3912245)------------------------------
% 2.66/0.78 % (3912245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912245)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912245)Termination reason: Inappropriate
% 2.66/0.78 % (3912245)Time elapsed: 0.002 s
% 2.66/0.78 % (3912245)Peak memory usage: 10 MB
% 2.66/0.78 % (3912245)Instructions burned: 1 (million)
% 2.66/0.78 % (3912245)------------------------------
% 2.66/0.78 % (3912245)------------------------------
% 2.66/0.78 % (3912251)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=790812077:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 2.66/0.78 % (3912234)Instruction limit reached!
% 2.66/0.78 % (3912234)------------------------------
% 2.66/0.78 % (3912234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912234)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912234)Termination reason: Instruction limit
% 2.66/0.78 % (3912234)Termination phase: Saturation
% 2.66/0.78 % (3912234)Time elapsed: 0.146 s
% 2.66/0.78 % (3912234)Peak memory usage: 12 MB
% 2.66/0.78 % (3912234)Instructions burned: 180 (million)
% 2.66/0.78 % (3912255)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1586477079:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.66/0.78 % (3912244) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3912205-3912244"...
% 2.66/0.78 % (3912244)...printing done.
% 2.66/0.78 % (3912244)Refutation found. Thanks to Tanya!
% 2.66/0.78 % SZS status Theorem for theBenchmark
% 2.66/0.78 % SZS output start Proof for theBenchmark
% 2.66/0.78 tff(type_def_5, type, collection: $tType).
% 2.66/0.78 tff(func_def_0, type, empty: collection).
% 2.66/0.78 tff(func_def_1, type, add: ($int * collection) > collection).
% 2.66/0.78 tff(func_def_2, type, remove: ($int * collection) > collection).
% 2.66/0.78 tff(func_def_3, type, count: collection > $int).
% 2.66/0.78 tff(func_def_9, type, sK0: collection).
% 2.66/0.78 tff(func_def_10, type, sK1: $int).
% 2.66/0.78 tff(func_def_11, type, sK2: $int).
% 2.66/0.78 tff(func_def_12, type, sF3: $int).
% 2.66/0.78 tff(func_def_13, type, sF4: $int).
% 2.66/0.78 tff(func_def_14, type, sF5: collection).
% 2.66/0.78 tff(func_def_15, type, sF6: collection).
% 2.66/0.78 tff(func_def_16, type, sF7: $int).
% 2.66/0.78 tff(pred_def_1, type, in: ($int * collection) > $o).
% 2.66/0.78 tff(f4,axiom,(
% 2.66/0.78 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 2.66/0.78 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax4)).
% 2.66/0.78 tff(f8,axiom,(
% 2.66/0.78 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 2.66/0.78 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax3)).
% 2.66/0.78 tff(f9,axiom,(
% 2.66/0.78 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 2.66/0.78 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax4)).
% 2.66/0.78 tff(f13,conjecture,(
% 2.66/0.78 ! [X0 : collection,X1 : $int,X2 : $int] : ($greater(X2,0) => $greatereq($sum(count(X0),X2),count(add(X1,add(X1,X0)))))),
% 2.66/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 2.66/0.78 tff(f14,negated_conjecture,(
% 2.66/0.78 ~ ! [X0 : collection,X1 : $int,X2 : $int] : ($greater(X2,0) => $greatereq($sum(count(X0),X2),count(add(X1,add(X1,X0)))))),
% 2.66/0.78 inference(negated_conjecture,[status(cth)],[f13])).
% 2.66/0.78 tff(f17,plain,(
% 2.66/0.78 ~ ! [X0 : collection,X1 : $int,X2 : $int] : ($less(0,X2) => ~$less($sum(count(X0),X2),count(add(X1,add(X1,X0)))))),
% 2.66/0.78 inference(theory_normalization,[],[f14])).
% 2.66/0.78 tff(f18,definition,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 2.66/0.78 introduced(theory,[tha_commutativity])).
% 2.66/0.78 tff(f19,definition,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 2.66/0.78 introduced(theory,[tha_associativity])).
% 2.66/0.78 tff(f20,definition,(
% 2.66/0.78 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 2.66/0.78 introduced(theory,[tha_right_identity])).
% 2.66/0.78 tff(f22,definition,(
% 2.66/0.78 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 2.66/0.78 introduced(theory,[tha_inverse_op_unit])).
% 2.66/0.78 tff(f23,definition,(
% 2.66/0.78 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 2.66/0.78 introduced(theory,[tha_non-reflexivity])).
% 2.66/0.78 tff(f24,definition,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 2.66/0.78 introduced(theory,[tha_transitivity])).
% 2.66/0.78 tff(f26,definition,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 2.66/0.78 introduced(theory,[tha_order_monotonicity])).
% 2.66/0.78 tff(f29,definition,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 2.66/0.78 introduced(theory,[tha_extra_integer_ordering])).
% 2.66/0.78 tff(f31,plain,(
% 2.66/0.78 ? [X0 : collection,X1 : $int,X2 : $int] : ($less($sum(count(X0),X2),count(add(X1,add(X1,X0)))) & $less(0,X2))),
% 2.66/0.78 inference(ennf_transformation,[],[f17])).
% 2.66/0.78 tff(f32,plain,(
% 2.66/0.78 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) | X0 = X2) | ~in(X0,add(X2,X1))) & (in(X0,add(X2,X1)) | (~in(X0,X1) & X0 != X2)))),
% 2.66/0.78 inference(nnf_transformation,[],[f4])).
% 2.66/0.78 tff(f33,plain,(
% 2.66/0.78 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2 | ~in(X0,add(X2,X1))) & (in(X0,add(X2,X1)) | (~in(X0,X1) & X0 != X2)))),
% 2.66/0.78 inference(flattening,[],[f32])).
% 2.66/0.78 tff(f37,plain,(
% 2.66/0.78 ! [X0 : $int,X1 : collection] : ((~in(X0,X1) | count(add(X0,X1)) != $sum(count(X1),1)) & (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)))),
% 2.66/0.78 inference(nnf_transformation,[],[f8])).
% 2.66/0.78 tff(f38,plain,(
% 2.66/0.78 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(add(X0,X1)) != count(X1)) & (count(add(X0,X1)) = count(X1) | ~in(X0,X1)))),
% 2.66/0.78 inference(nnf_transformation,[],[f9])).
% 2.66/0.78 tff(f41,plain,(
% 2.66/0.78 $less($sum(count(sK0),sK2),count(add(sK1,add(sK1,sK0)))) & $less(0,sK2)),
% 2.66/0.78 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f31])).
% 2.66/0.78 tff(f45,plain,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,add(X2,X1)) | X0 != X2) )),
% 2.66/0.78 inference(cnf_transformation,[],[f33])).
% 2.66/0.78 tff(f54,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = $sum(count(X1),1)) )),
% 2.66/0.78 inference(cnf_transformation,[],[f37])).
% 2.66/0.78 tff(f56,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 2.66/0.78 inference(cnf_transformation,[],[f38])).
% 2.66/0.78 tff(f63,plain,(
% 2.66/0.78 $less(0,sK2)),
% 2.66/0.78 inference(cnf_transformation,[],[f41])).
% 2.66/0.78 tff(f64,plain,(
% 2.66/0.78 $less($sum(count(sK0),sK2),count(add(sK1,add(sK1,sK0))))),
% 2.66/0.78 inference(cnf_transformation,[],[f41])).
% 2.66/0.78 tff(f65,plain,(
% 2.66/0.78 ( ! [X2 : $int,X1 : collection] : (in(X2,add(X2,X1))) )),
% 2.66/0.78 inference(equality_resolution,[],[f45])).
% 2.66/0.78 tff(f68,definition,(
% 2.66/0.78 sF3 = count(sK0)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 2.66/0.78 tff(f69,plain,(
% 2.66/0.78 count(sK0) = sF3),
% 2.66/0.78 inference(reorient_equations,[],[f68])).
% 2.66/0.78 tff(f70,definition,(
% 2.66/0.78 sF4 = $sum(sF3,sK2)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 2.66/0.78 tff(f71,plain,(
% 2.66/0.78 $sum(sF3,sK2) = sF4),
% 2.66/0.78 inference(reorient_equations,[],[f70])).
% 2.66/0.78 tff(f72,definition,(
% 2.66/0.78 sF5 = add(sK1,sK0)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 2.66/0.78 tff(f73,plain,(
% 2.66/0.78 add(sK1,sK0) = sF5),
% 2.66/0.78 inference(reorient_equations,[],[f72])).
% 2.66/0.78 tff(f74,definition,(
% 2.66/0.78 sF6 = add(sK1,sF5)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 2.66/0.78 tff(f75,plain,(
% 2.66/0.78 add(sK1,sF5) = sF6),
% 2.66/0.78 inference(reorient_equations,[],[f74])).
% 2.66/0.78 tff(f76,definition,(
% 2.66/0.78 sF7 = count(sF6)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 2.66/0.78 tff(f77,plain,(
% 2.66/0.78 count(sF6) = sF7),
% 2.66/0.78 inference(reorient_equations,[],[f76])).
% 2.66/0.78 tff(f78,plain,(
% 2.66/0.78 $less(sF4,sF7)),
% 2.66/0.78 inference(definition_folding,[],[f64,f77,f75,f73,f71,f69])).
% 2.66/0.78 tff(f84,plain,(
% 2.66/0.78 $less($sum(sF3,sK2),sF7)),
% 2.66/0.78 inference(superposition,[],[f78,f71])).
% 2.66/0.78 tff(f85,plain,(
% 2.66/0.78 in(sK1,sF5)),
% 2.66/0.78 inference(superposition,[],[f65,f73])).
% 2.66/0.78 tff(f125,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 2.66/0.78 inference(superposition,[],[f29,f18])).
% 2.66/0.78 tff(f136,plain,(
% 2.66/0.78 ( ! [X0 : $int] : (~$less(X0,$sum(sF3,sK2)) | $less(X0,sF7)) )),
% 2.66/0.78 inference(resolution,[],[f24,f84])).
% 2.66/0.78 tff(f181,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(0,$sum(X1,$uminus(X0)))) )),
% 2.66/0.78 inference(superposition,[],[f26,f22])).
% 2.66/0.78 tff(f183,plain,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X1),$sum(X2,X0)) | ~$less(X1,X2)) )),
% 2.66/0.78 inference(superposition,[],[f26,f18])).
% 2.66/0.78 tff(f187,plain,(
% 2.66/0.78 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X2,X0),$sum(X0,X1)) | ~$less(X2,X1)) )),
% 2.66/0.78 inference(superposition,[],[f26,f18])).
% 2.66/0.78 tff(f193,plain,(
% 2.66/0.78 count(add(sK1,sF5)) = count(sF5)),
% 2.66/0.78 inference(resolution,[],[f56,f85])).
% 2.66/0.78 tff(f196,plain,(
% 2.66/0.78 count(sF6) = count(sF5)),
% 2.66/0.78 inference(forward_demodulation,[],[f193,f75])).
% 2.66/0.78 tff(f197,plain,(
% 2.66/0.78 sF7 = count(sF5)),
% 2.66/0.78 inference(forward_demodulation,[],[f196,f77])).
% 2.66/0.78 tff(f212,definition,(
% 2.66/0.78 spl8_6 <=> sF3 = sF7),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 2.66/0.78 tff(f213,plain,(
% 2.66/0.78 sF3 = sF7 | ~spl8_6),
% 2.66/0.78 inference(avatar_component_clause,[],[f212])).
% 2.66/0.78 tff(f214,plain,(
% 2.66/0.78 sF3 != sF7 | spl8_6),
% 2.66/0.78 inference(avatar_component_clause,[],[f212])).
% 2.66/0.78 tff(f237,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 2.66/0.78 inference(superposition,[],[f19,f22])).
% 2.66/0.78 tff(f256,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 2.66/0.78 inference(evaluation,[],[f237])).
% 2.66/0.78 tff(f287,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | count(add(X0,X1)) = count(X1)) )),
% 2.66/0.78 inference(resolution,[],[f54,f56])).
% 2.66/0.78 tff(f296,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 2.66/0.78 inference(forward_demodulation,[],[f287,f18])).
% 2.66/0.78 tff(f315,definition,(
% 2.66/0.78 spl8_7 <=> sF7 = $sum(1,sF3)),
% 2.66/0.78 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 2.66/0.78 tff(f316,plain,(
% 2.66/0.78 sF7 = $sum(1,sF3) | ~spl8_7),
% 2.66/0.78 inference(avatar_component_clause,[],[f315])).
% 2.66/0.78 tff(f734,plain,(
% 2.66/0.78 ( ! [X0 : $int,X1 : $int] : (~$less(0,X1) | $less(X0,$sum(X1,X0))) )),
% 2.66/0.78 inference(superposition,[],[f183,f20])).
% 2.66/0.78 tff(f757,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less($sum(X0,sF3),sF7) | ~$less(X0,sK2)) )),
% 2.66/0.78 inference(resolution,[],[f187,f136])).
% 2.66/0.78 tff(f1094,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less($sum(sF3,X0),sF7) | ~$less(X0,sK2)) )),
% 2.66/0.78 inference(superposition,[],[f757,f18])).
% 2.66/0.78 tff(f1115,plain,(
% 2.66/0.78 $less(sF3,sF7) | ~$less(0,sK2)),
% 2.66/0.78 inference(superposition,[],[f1094,f20])).
% 2.66/0.78 tff(f1119,plain,(
% 2.66/0.78 $less(sF3,sF7)),
% 2.66/0.78 inference(forward_subsumption_resolution,[],[f1115,f63])).
% 2.66/0.78 tff(f1208,plain,(
% 2.66/0.78 $less(0,$sum(sF7,$uminus(sF3)))),
% 2.66/0.78 inference(resolution,[],[f1119,f181])).
% 2.66/0.78 tff(f2103,plain,(
% 2.66/0.78 count(sF5) = $sum(1,count(sK0)) | count(sK0) = count(sF5)),
% 2.66/0.78 inference(superposition,[],[f296,f73])).
% 2.66/0.78 tff(f2122,plain,(
% 2.66/0.78 $sum(1,sF3) = count(sF5) | count(sK0) = count(sF5)),
% 2.66/0.78 inference(forward_demodulation,[],[f2103,f69])).
% 2.66/0.78 tff(f3477,plain,(
% 2.66/0.78 sF7 = $sum(1,sF3) | count(sK0) = count(sF5)),
% 2.66/0.78 inference(forward_demodulation,[],[f2122,f197])).
% 2.66/0.78 tff(f3527,plain,(
% 2.66/0.78 count(sK0) = sF7 | sF7 = $sum(1,sF3)),
% 2.66/0.78 inference(forward_demodulation,[],[f3477,f197])).
% 2.66/0.78 tff(f3531,plain,(
% 2.66/0.78 sF3 = sF7 | sF7 = $sum(1,sF3)),
% 2.66/0.78 inference(forward_demodulation,[],[f3527,f69])).
% 2.66/0.78 tff(f3533,plain,(
% 2.66/0.78 sF7 = $sum(1,sF3) | spl8_6),
% 2.66/0.78 inference(forward_subsumption_resolution,[],[f3531,f214])).
% 2.66/0.78 tff(f3535,plain,(
% 2.66/0.78 spl8_7 | spl8_6),
% 2.66/0.78 inference(avatar_split_clause,[],[f3533,f212,f315])).
% 2.66/0.78 tff(f3589,plain,(
% 2.66/0.78 $less($sum(sF3,sK2),$sum(1,sF3)) | ~spl8_7),
% 2.66/0.78 inference(superposition,[],[f84,f316])).
% 2.66/0.78 tff(f3631,plain,(
% 2.66/0.78 ~$less(sF3,$sum(sF3,sK2)) | ~spl8_7),
% 2.66/0.78 inference(resolution,[],[f3589,f125])).
% 2.66/0.78 tff(f4541,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,$sum($sum(sF7,$uminus(sF3)),X0))) )),
% 2.66/0.78 inference(resolution,[],[f734,f1208])).
% 2.66/0.78 tff(f4545,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,$sum(sK2,X0))) )),
% 2.66/0.78 inference(resolution,[],[f734,f63])).
% 2.66/0.78 tff(f4578,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,$sum(sF7,$sum($uminus(sF3),X0)))) )),
% 2.66/0.78 inference(forward_demodulation,[],[f4541,f19])).
% 2.66/0.78 tff(f4627,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,$sum(X0,sK2))) )),
% 2.66/0.78 inference(superposition,[],[f4545,f18])).
% 2.66/0.78 tff(f4779,plain,(
% 2.66/0.78 $false | ~spl8_7),
% 2.66/0.78 inference(resolution,[],[f4627,f3631])).
% 2.66/0.78 tff(f4786,plain,(
% 2.66/0.78 ~spl8_7),
% 2.66/0.78 inference(avatar_contradiction_clause,[],[f4779])).
% 2.66/0.78 tff(f4839,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,$sum(sF3,$sum($uminus(sF3),X0)))) ) | ~spl8_6),
% 2.66/0.78 inference(forward_demodulation,[],[f4578,f213])).
% 2.66/0.78 tff(f4870,plain,(
% 2.66/0.78 ( ! [X0 : $int] : ($less(X0,X0)) ) | ~spl8_6),
% 2.66/0.78 inference(forward_demodulation,[],[f4839,f256])).
% 2.66/0.78 tff(f4882,plain,(
% 2.66/0.78 $false | ~spl8_6),
% 2.66/0.78 inference(forward_subsumption_resolution,[],[f4870,f23])).
% 2.66/0.78 tff(f4883,plain,(
% 2.66/0.78 ~spl8_6),
% 2.66/0.78 inference(avatar_contradiction_clause,[],[f4882])).
% 2.66/0.78 cnf(s22, plain, spl8_6 | spl8_7, inference(sat_conversion,[],[f3535])).
% 2.66/0.78 cnf(s34, plain, ~spl8_7, inference(sat_conversion,[],[f4786])).
% 2.66/0.78 cnf(s39, plain, ~spl8_6, inference(sat_conversion,[],[f4883])).
% 2.66/0.78 cnf(s41, plain, $false, inference(rat,[],[s22,s34,s39])).
% 2.66/0.78 tff(f4884,plain,(
% 2.66/0.78 $false),
% 2.66/0.78 inference(avatar_sat_refutation,[],[s41])).
% 2.66/0.78 % SZS output end Proof for theBenchmark
% 2.66/0.78 % (3912244)------------------------------
% 2.66/0.78 % (3912244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.78 % (3912244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.78 % (3912244)CaDiCaL version: 2.1.3
% 2.66/0.78 % (3912244)Termination reason: Refutation
% 2.66/0.78 % (3912244)Time elapsed: 0.196 s
% 2.66/0.78 % (3912244)Peak memory usage: 14 MB
% 2.66/0.78 % (3912244)Instructions burned: 217 (million)
% 2.66/0.78 % (3912205)Success in time 0.485 s
% 2.66/0.78 % Vampire exiting
%------------------------------------------------------------------------------