%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT048_1 : TPTP v9.3.1. Released v5.0.0.
% 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 09:48:01 AM UTC 2026
% Result : Theorem 1.23s 0.44s
% Output : Refutation 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT048_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.16 % Computer : n010.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 00:07:35 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 1.23/0.44 % (2480935)Will run a generic schedule for satisfiability detection.
% 1.23/0.44 % (2480946)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4267918503:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.23/0.44 % (2480941)% WARNING: option uhcvi not known.
% 1.23/0.44 % (2480943)dis+10_1_sil=32000:sp=arity:random_seed=791736321:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.23/0.44 % (2480941)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1673761391:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.23/0.44 % (2480942)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3800832:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.23/0.44 % (2480944)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1161995601:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.23/0.44 % (2480945)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2322900219:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.44 % (2480940)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2111638893_2999 on theBenchmark for (2999ds/0Mi)
% 1.23/0.44 % (2480940)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.23/0.44 % (2480940)Terminated due to inappropriate strategy.
% 1.23/0.44 % (2480940)------------------------------
% 1.23/0.44 % (2480940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480940)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480940)Termination reason: Inappropriate
% 1.23/0.44 % (2480940)Time elapsed: 0.002 s
% 1.23/0.44 % (2480940)Peak memory usage: 10 MB
% 1.23/0.44 % (2480940)Instructions burned: 1 (million)
% 1.23/0.44 % (2480940)------------------------------
% 1.23/0.44 % (2480940)------------------------------
% 1.23/0.44 % (2480954)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=334309491:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.23/0.44 % (2480954)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.23/0.44 % (2480954)Terminated due to inappropriate strategy.
% 1.23/0.44 % (2480954)------------------------------
% 1.23/0.44 % (2480954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480954)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480954)Termination reason: Inappropriate
% 1.23/0.44 % (2480954)Time elapsed: 0.001 s
% 1.23/0.44 % (2480954)Peak memory usage: 10 MB
% 1.23/0.44 % (2480954)Instructions burned: 1 (million)
% 1.23/0.44 % (2480954)------------------------------
% 1.23/0.44 % (2480954)------------------------------
% 1.23/0.44 % (2480946)Instruction limit reached!
% 1.23/0.44 % (2480946)------------------------------
% 1.23/0.44 % (2480946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480946)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480946)Termination reason: Instruction limit
% 1.23/0.44 % (2480946)Termination phase: Saturation
% 1.23/0.44 % (2480946)Time elapsed: 0.057 s
% 1.23/0.44 % (2480946)Peak memory usage: 13 MB
% 1.23/0.44 % (2480946)Instructions burned: 160 (million)
% 1.23/0.44 % (2480956)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3968756555:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.44 % (2480957)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=4156067953:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.23/0.44 % (2480943)Instruction limit reached!
% 1.23/0.44 % (2480943)------------------------------
% 1.23/0.44 % (2480943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480943)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480943)Termination reason: Instruction limit
% 1.23/0.44 % (2480943)Termination phase: Saturation
% 1.23/0.44 % (2480943)Time elapsed: 0.064 s
% 1.23/0.44 % (2480943)Peak memory usage: 12 MB
% 1.23/0.44 % (2480943)Instructions burned: 103 (million)
% 1.23/0.44 % (2480944)Instruction limit reached!
% 1.23/0.44 % (2480944)------------------------------
% 1.23/0.44 % (2480944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480944)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480944)Termination reason: Instruction limit
% 1.23/0.44 % (2480944)Termination phase: Saturation
% 1.23/0.44 % (2480944)Time elapsed: 0.071 s
% 1.23/0.44 % (2480944)Peak memory usage: 12 MB
% 1.23/0.44 % (2480944)Instructions burned: 117 (million)
% 1.23/0.44 % (2480945)Instruction limit reached!
% 1.23/0.44 % (2480945)------------------------------
% 1.23/0.44 % (2480945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480945)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480945)Termination reason: Instruction limit
% 1.23/0.44 % (2480945)Termination phase: Saturation
% 1.23/0.44 % (2480945)Time elapsed: 0.085 s
% 1.23/0.44 % (2480945)Peak memory usage: 13 MB
% 1.23/0.44 % (2480945)Instructions burned: 132 (million)
% 1.23/0.44 % (2480961)ott-21_1_sil=16000:fs=off:random_seed=2189105223:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.23/0.44 % (2480967)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4081173861:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.23/0.44 % (2480970)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3094727703:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.23/0.44 % (2480970)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.23/0.44 % (2480970)Terminated due to inappropriate strategy.
% 1.23/0.44 % (2480970)------------------------------
% 1.23/0.44 % (2480970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480970)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480970)Termination reason: Inappropriate
% 1.23/0.44 % (2480970)Time elapsed: 0.001 s
% 1.23/0.44 % (2480970)Peak memory usage: 10 MB
% 1.23/0.44 % (2480970)------------------------------
% 1.23/0.44 % (2480970)------------------------------
% 1.23/0.44 % (2480974)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3622130036:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.23/0.44 % (2480956)Instruction limit reached!
% 1.23/0.44 % (2480956)------------------------------
% 1.23/0.44 % (2480956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480956)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480956)Termination reason: Instruction limit
% 1.23/0.44 % (2480956)Termination phase: Saturation
% 1.23/0.44 % (2480956)Time elapsed: 0.126 s
% 1.23/0.44 % (2480956)Peak memory usage: 13 MB
% 1.23/0.44 % (2480956)Instructions burned: 132 (million)
% 1.23/0.44 % (2480974) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2480935-2480974"...
% 1.23/0.44 % (2480974)...printing done.
% 1.23/0.44 % (2480976)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1017163310:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.23/0.44 % (2480974)Refutation found. Thanks to Tanya!
% 1.23/0.44 % SZS status Theorem for theBenchmark
% 1.23/0.44 % SZS output start Proof for theBenchmark
% 1.23/0.44 tff(type_def_5, type, collection: $tType).
% 1.23/0.44 tff(func_def_0, type, empty: collection).
% 1.23/0.44 tff(func_def_1, type, add: ($int * collection) > collection).
% 1.23/0.44 tff(func_def_2, type, remove: ($int * collection) > collection).
% 1.23/0.44 tff(func_def_3, type, count: collection > $int).
% 1.23/0.44 tff(func_def_12, type, sF0: collection).
% 1.23/0.44 tff(func_def_13, type, sF1: collection).
% 1.23/0.44 tff(func_def_14, type, sF2: collection).
% 1.23/0.44 tff(func_def_15, type, sF3: collection).
% 1.23/0.44 tff(func_def_16, type, sF4: $int).
% 1.23/0.44 tff(pred_def_1, type, in: ($int * collection) > $o).
% 1.23/0.44 tff(f1,axiom,(
% 1.23/0.44 ! [X0 : $int] : ~in(X0,empty)),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1)).
% 1.23/0.44 tff(f4,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4)).
% 1.23/0.44 tff(f5,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) & X0 != X2) <=> in(X0,remove(X2,X1)))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5)).
% 1.23/0.44 tff(f7,axiom,(
% 1.23/0.44 ! [X0 : collection] : (X0 = empty <=> count(X0) = 0)),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2)).
% 1.23/0.44 tff(f8,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3)).
% 1.23/0.44 tff(f9,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 1.23/0.44 tff(f10,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5)).
% 1.23/0.44 tff(f11,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(remove(X0,X1)) = count(X1))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6)).
% 1.23/0.44 tff(f12,axiom,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (in(X0,X1) => X1 = add(X0,remove(X0,X1)))),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7)).
% 1.23/0.44 tff(f13,conjecture,(
% 1.23/0.44 count(add(1,add(5,remove(3,add(2,empty))))) = 3),
% 1.23/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 1.23/0.44 tff(f14,negated_conjecture,(
% 1.23/0.44 ~ count(add(1,add(5,remove(3,add(2,empty))))) = 3),
% 1.23/0.44 inference(negated_conjecture,[status(cth)],[f13])).
% 1.23/0.44 tff(f16,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 1.23/0.44 inference(theory_normalization,[],[f10])).
% 1.23/0.44 tff(f17,definition,(
% 1.23/0.44 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 1.23/0.44 introduced(theory,[tha_commutativity])).
% 1.23/0.44 tff(f29,plain,(
% 1.23/0.44 3 != count(add(1,add(5,remove(3,add(2,empty)))))),
% 1.23/0.44 inference(flattening,[],[f14])).
% 1.23/0.44 tff(f30,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : (X1 = add(X0,remove(X0,X1)) | ~in(X0,X1))),
% 1.23/0.44 inference(ennf_transformation,[],[f12])).
% 1.23/0.44 tff(f31,plain,(
% 1.23/0.44 ! [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)))),
% 1.23/0.44 inference(nnf_transformation,[],[f4])).
% 1.23/0.44 tff(f32,plain,(
% 1.23/0.44 ! [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)))),
% 1.23/0.44 inference(flattening,[],[f31])).
% 1.23/0.44 tff(f33,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | (~in(X0,X1) | X0 = X2)))),
% 1.23/0.44 inference(nnf_transformation,[],[f5])).
% 1.23/0.44 tff(f34,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2))),
% 1.23/0.44 inference(flattening,[],[f33])).
% 1.23/0.44 tff(f35,plain,(
% 1.23/0.44 ! [X0 : collection] : ((X0 = empty | count(X0) != 0) & (count(X0) = 0 | empty != X0))),
% 1.23/0.44 inference(nnf_transformation,[],[f7])).
% 1.23/0.44 tff(f36,plain,(
% 1.23/0.44 ! [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)))),
% 1.23/0.44 inference(nnf_transformation,[],[f8])).
% 1.23/0.44 tff(f37,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(add(X0,X1)) != count(X1)) & (count(add(X0,X1)) = count(X1) | ~in(X0,X1)))),
% 1.23/0.44 inference(nnf_transformation,[],[f9])).
% 1.23/0.44 tff(f38,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(remove(X0,X1)) != $sum(count(X1),$uminus(1))) & (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)))),
% 1.23/0.44 inference(nnf_transformation,[],[f16])).
% 1.23/0.44 tff(f39,plain,(
% 1.23/0.44 ! [X0 : $int,X1 : collection] : ((~in(X0,X1) | count(X1) != count(remove(X0,X1))) & (count(remove(X0,X1)) = count(X1) | in(X0,X1)))),
% 1.23/0.44 inference(nnf_transformation,[],[f11])).
% 1.23/0.44 tff(f40,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f1])).
% 1.23/0.44 tff(f43,plain,(
% 1.23/0.44 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,add(X2,X1)) | X0 != X2) )),
% 1.23/0.44 inference(cnf_transformation,[],[f32])).
% 1.23/0.44 tff(f44,plain,(
% 1.23/0.44 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,add(X2,X1)) | ~in(X0,X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f32])).
% 1.23/0.44 tff(f45,plain,(
% 1.23/0.44 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,add(X2,X1)) | X0 = X2 | in(X0,X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f32])).
% 1.23/0.44 tff(f46,plain,(
% 1.23/0.44 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2) )),
% 1.23/0.44 inference(cnf_transformation,[],[f34])).
% 1.23/0.44 tff(f48,plain,(
% 1.23/0.44 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,remove(X2,X1)) | in(X0,X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f34])).
% 1.23/0.44 tff(f50,plain,(
% 1.23/0.44 ( ! [X0 : collection] : (count(X0) = 0 | empty != X0) )),
% 1.23/0.44 inference(cnf_transformation,[],[f35])).
% 1.23/0.44 tff(f51,plain,(
% 1.23/0.44 ( ! [X0 : collection] : (count(X0) != 0 | empty = X0) )),
% 1.23/0.44 inference(cnf_transformation,[],[f35])).
% 1.23/0.44 tff(f52,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = $sum(count(X1),1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f36])).
% 1.23/0.44 tff(f54,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f37])).
% 1.23/0.44 tff(f55,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f37])).
% 1.23/0.44 tff(f56,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 1.23/0.44 inference(cnf_transformation,[],[f38])).
% 1.23/0.44 tff(f58,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(X1) = count(remove(X0,X1))) )),
% 1.23/0.44 inference(cnf_transformation,[],[f39])).
% 1.23/0.44 tff(f60,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | add(X0,remove(X0,X1)) = X1) )),
% 1.23/0.44 inference(cnf_transformation,[],[f30])).
% 1.23/0.44 tff(f61,plain,(
% 1.23/0.44 3 != count(add(1,add(5,remove(3,add(2,empty)))))),
% 1.23/0.44 inference(cnf_transformation,[],[f29])).
% 1.23/0.44 tff(f62,plain,(
% 1.23/0.44 ( ! [X2 : $int,X1 : collection] : (in(X2,add(X2,X1))) )),
% 1.23/0.44 inference(equality_resolution,[],[f43])).
% 1.23/0.44 tff(f64,plain,(
% 1.23/0.44 0 = count(empty)),
% 1.23/0.44 inference(equality_resolution,[],[f50])).
% 1.23/0.44 tff(f65,definition,(
% 1.23/0.44 sF0 = add(2,empty)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 1.23/0.44 tff(f66,plain,(
% 1.23/0.44 add(2,empty) = sF0),
% 1.23/0.44 inference(reorient_equations,[],[f65])).
% 1.23/0.44 tff(f67,definition,(
% 1.23/0.44 sF1 = remove(3,sF0)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 1.23/0.44 tff(f68,plain,(
% 1.23/0.44 remove(3,sF0) = sF1),
% 1.23/0.44 inference(reorient_equations,[],[f67])).
% 1.23/0.44 tff(f69,definition,(
% 1.23/0.44 sF2 = add(5,sF1)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 1.23/0.44 tff(f70,plain,(
% 1.23/0.44 add(5,sF1) = sF2),
% 1.23/0.44 inference(reorient_equations,[],[f69])).
% 1.23/0.44 tff(f71,definition,(
% 1.23/0.44 sF3 = add(1,sF2)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 1.23/0.44 tff(f72,plain,(
% 1.23/0.44 add(1,sF2) = sF3),
% 1.23/0.44 inference(reorient_equations,[],[f71])).
% 1.23/0.44 tff(f73,definition,(
% 1.23/0.44 sF4 = count(sF3)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 1.23/0.44 tff(f74,plain,(
% 1.23/0.44 count(sF3) = sF4),
% 1.23/0.44 inference(reorient_equations,[],[f73])).
% 1.23/0.44 tff(f75,plain,(
% 1.23/0.44 3 != sF4),
% 1.23/0.44 inference(definition_folding,[],[f61,f74,f72,f70,f68,f66])).
% 1.23/0.44 tff(f76,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(count(X1),-1)) )),
% 1.23/0.44 inference(evaluation,[],[f56])).
% 1.23/0.44 tff(f80,plain,(
% 1.23/0.44 in(2,sF0)),
% 1.23/0.44 inference(superposition,[],[f62,f66])).
% 1.23/0.44 tff(f115,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF1) | in(X0,sF2)) )),
% 1.23/0.44 inference(superposition,[],[f44,f70])).
% 1.23/0.44 tff(f122,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF1) | in(X0,sF0)) )),
% 1.23/0.44 inference(superposition,[],[f48,f68])).
% 1.23/0.44 tff(f176,plain,(
% 1.23/0.44 count(sF3) != count(sF2) | in(1,sF2)),
% 1.23/0.44 inference(superposition,[],[f55,f72])).
% 1.23/0.44 tff(f177,plain,(
% 1.23/0.44 sF4 != count(sF2) | in(1,sF2)),
% 1.23/0.44 inference(forward_demodulation,[],[f176,f74])).
% 1.23/0.44 tff(f179,definition,(
% 1.23/0.44 spl5_3 <=> in(5,sF1)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 1.23/0.44 tff(f180,plain,(
% 1.23/0.44 ~in(5,sF1) | spl5_3),
% 1.23/0.44 inference(avatar_component_clause,[],[f179])).
% 1.23/0.44 tff(f181,plain,(
% 1.23/0.44 in(5,sF1) | ~spl5_3),
% 1.23/0.44 inference(avatar_component_clause,[],[f179])).
% 1.23/0.44 tff(f189,definition,(
% 1.23/0.44 spl5_5 <=> in(1,sF2)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 1.23/0.44 tff(f191,plain,(
% 1.23/0.44 in(1,sF2) | ~spl5_5),
% 1.23/0.44 inference(avatar_component_clause,[],[f189])).
% 1.23/0.44 tff(f193,definition,(
% 1.23/0.44 spl5_6 <=> sF4 = count(sF2)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 1.23/0.44 tff(f195,plain,(
% 1.23/0.44 sF4 != count(sF2) | spl5_6),
% 1.23/0.44 inference(avatar_component_clause,[],[f193])).
% 1.23/0.44 tff(f196,plain,(
% 1.23/0.44 spl5_5 | ~spl5_6),
% 1.23/0.44 inference(avatar_split_clause,[],[f177,f193,f189])).
% 1.23/0.44 tff(f198,plain,(
% 1.23/0.44 ( ! [X0 : collection,X1 : $int] : (count(X0) = count(remove(X1,X0)) | count(X0) = count(add(X1,X0))) )),
% 1.23/0.44 inference(resolution,[],[f58,f54])).
% 1.23/0.44 tff(f209,definition,(
% 1.23/0.44 spl5_7 <=> in(3,sF0)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 1.23/0.44 tff(f210,plain,(
% 1.23/0.44 in(3,sF0) | ~spl5_7),
% 1.23/0.44 inference(avatar_component_clause,[],[f209])).
% 1.23/0.44 tff(f211,plain,(
% 1.23/0.44 ~in(3,sF0) | spl5_7),
% 1.23/0.44 inference(avatar_component_clause,[],[f209])).
% 1.23/0.44 tff(f213,definition,(
% 1.23/0.44 spl5_8 <=> count(sF0) = count(sF1)),
% 1.23/0.44 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 1.23/0.44 tff(f214,plain,(
% 1.23/0.44 count(sF0) = count(sF1) | ~spl5_8),
% 1.23/0.44 inference(avatar_component_clause,[],[f213])).
% 1.23/0.44 tff(f217,plain,(
% 1.23/0.44 count(sF0) = count(remove(3,sF0)) | spl5_7),
% 1.23/0.44 inference(resolution,[],[f211,f58])).
% 1.23/0.44 tff(f218,plain,(
% 1.23/0.44 count(sF0) = count(sF1) | spl5_7),
% 1.23/0.44 inference(forward_demodulation,[],[f217,f68])).
% 1.23/0.44 tff(f219,plain,(
% 1.23/0.44 spl5_8 | spl5_7),
% 1.23/0.44 inference(avatar_split_clause,[],[f218,f209,f213])).
% 1.23/0.44 tff(f222,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (add(X0,remove(X0,X1)) = X1 | count(X1) = count(remove(X0,X1))) )),
% 1.23/0.44 inference(resolution,[],[f60,f58])).
% 1.23/0.44 tff(f260,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF0) | 2 = X0 | in(X0,empty)) )),
% 1.23/0.44 inference(superposition,[],[f45,f66])).
% 1.23/0.44 tff(f261,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF2) | 5 = X0 | in(X0,sF1)) )),
% 1.23/0.44 inference(superposition,[],[f45,f70])).
% 1.23/0.44 tff(f263,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF0) | 2 = X0) )),
% 1.23/0.44 inference(forward_subsumption_resolution,[],[f260,f40])).
% 1.23/0.44 tff(f268,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (~in(X0,sF0) | in(X0,sF1) | 3 = X0) )),
% 1.23/0.44 inference(superposition,[],[f46,f68])).
% 1.23/0.44 tff(f274,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | count(add(X0,X1)) = count(X1)) )),
% 1.23/0.44 inference(resolution,[],[f52,f54])).
% 1.23/0.44 tff(f275,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (count(add(X0,empty)) = $sum(count(empty),1)) )),
% 1.23/0.44 inference(resolution,[],[f52,f40])).
% 1.23/0.44 tff(f290,plain,(
% 1.23/0.44 ( ! [X0 : $int] : ($sum(1,count(empty)) = count(add(X0,empty))) )),
% 1.23/0.44 inference(forward_demodulation,[],[f275,f17])).
% 1.23/0.44 tff(f291,plain,(
% 1.23/0.44 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 1.23/0.44 inference(forward_demodulation,[],[f274,f17])).
% 1.23/0.44 tff(f294,plain,(
% 1.23/0.44 ( ! [X0 : $int] : ($sum(1,0) = count(add(X0,empty))) )),
% 1.23/0.44 inference(forward_demodulation,[],[f290,f64])).
% 1.23/0.44 tff(f295,plain,(
% 1.23/0.44 ( ! [X0 : $int] : (1 = count(add(X0,empty))) )),
% 1.23/0.44 inference(evaluation,[],[f294])).
% 1.23/0.44 tff(f349,plain,(
% 1.23/0.44 in(5,sF0) | ~spl5_3),
% 1.23/0.44 inference(resolution,[],[f181,f122])).
% 1.23/0.44 tff(f379,plain,(
% 1.23/0.44 5 = 2 | ~spl5_3),
% 1.23/0.44 inference(resolution,[],[f263,f349])).
% 1.23/0.44 tff(f380,plain,(
% 1.23/0.44 3 = 2 | ~spl5_7),
% 1.23/0.44 inference(resolution,[],[f263,f210])).
% 1.23/0.44 tff(f382,plain,(
% 1.23/0.44 $false | ~spl5_7),
% 1.23/0.44 inference(evaluation,[],[f380])).
% 1.23/0.44 tff(f383,plain,(
% 1.23/0.44 ~spl5_7),
% 1.23/0.44 inference(avatar_contradiction_clause,[],[f382])).
% 1.23/0.44 tff(f384,plain,(
% 1.23/0.44 $false | ~spl5_3),
% 1.23/0.44 inference(evaluation,[],[f379])).
% 1.23/0.44 tff(f385,plain,(
% 1.23/0.44 ~spl5_3),
% 1.23/0.44 inference(avatar_contradiction_clause,[],[f384])).
% 1.23/0.44 tff(f391,plain,(
% 1.23/0.44 count(add(5,sF1)) = $sum(count(sF1),1) | spl5_3),
% 1.23/0.44 inference(resolution,[],[f180,f52])).
% 1.23/0.44 tff(f394,plain,(
% 1.23/0.44 count(add(5,sF1)) = $sum(1,count(sF1)) | spl5_3),
% 1.23/0.44 inference(forward_demodulation,[],[f391,f17])).
% 1.23/0.44 tff(f395,plain,(
% 1.23/0.44 count(add(5,sF1)) = $sum(1,count(sF0)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f394,f214])).
% 1.23/0.44 tff(f396,plain,(
% 1.23/0.44 count(sF2) = $sum(1,count(sF0)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f395,f70])).
% 1.23/0.44 tff(f404,plain,(
% 1.23/0.44 1 = count(sF0)),
% 1.23/0.44 inference(superposition,[],[f295,f66])).
% 1.23/0.44 tff(f654,plain,(
% 1.23/0.44 in(2,sF1) | 3 = 2),
% 1.23/0.44 inference(resolution,[],[f268,f80])).
% 1.23/0.44 tff(f655,plain,(
% 1.23/0.44 in(2,sF1)),
% 1.23/0.44 inference(evaluation,[],[f654])).
% 1.23/0.44 tff(f726,plain,(
% 1.23/0.44 in(2,sF2)),
% 1.23/0.44 inference(resolution,[],[f655,f115])).
% 1.23/0.44 tff(f727,plain,(
% 1.23/0.44 $sum(count(sF1),-1) = count(remove(2,sF1))),
% 1.23/0.44 inference(resolution,[],[f655,f76])).
% 1.23/0.44 tff(f731,plain,(
% 1.23/0.44 $sum(-1,count(sF1)) = count(remove(2,sF1))),
% 1.23/0.44 inference(forward_demodulation,[],[f727,f17])).
% 1.23/0.44 tff(f733,plain,(
% 1.23/0.44 $sum(-1,count(sF0)) = count(remove(2,sF1)) | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f731,f214])).
% 1.23/0.44 tff(f734,plain,(
% 1.23/0.44 $sum(-1,1) = count(remove(2,sF1)) | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f733,f404])).
% 1.23/0.44 tff(f735,plain,(
% 1.23/0.44 0 = count(remove(2,sF1)) | ~spl5_8),
% 1.23/0.44 inference(evaluation,[],[f734])).
% 1.23/0.44 tff(f813,plain,(
% 1.23/0.44 $sum(count(sF2),-1) = count(remove(2,sF2))),
% 1.23/0.44 inference(resolution,[],[f726,f76])).
% 1.23/0.44 tff(f815,plain,(
% 1.23/0.44 count(sF2) = count(add(2,sF2))),
% 1.23/0.44 inference(resolution,[],[f726,f54])).
% 1.23/0.44 tff(f817,plain,(
% 1.23/0.44 $sum(1,count(sF0)) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f815,f396])).
% 1.23/0.44 tff(f818,plain,(
% 1.23/0.44 $sum(-1,count(sF2)) = count(remove(2,sF2))),
% 1.23/0.44 inference(forward_demodulation,[],[f813,f17])).
% 1.23/0.44 tff(f819,plain,(
% 1.23/0.44 $sum(1,1) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f817,f404])).
% 1.23/0.44 tff(f820,plain,(
% 1.23/0.44 2 = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f819])).
% 1.23/0.44 tff(f821,plain,(
% 1.23/0.44 count(remove(2,sF2)) = $sum(-1,$sum(1,count(sF0))) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f818,f396])).
% 1.23/0.44 tff(f822,plain,(
% 1.23/0.44 count(remove(2,sF2)) = $sum(-1,$sum(1,1)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f821,f404])).
% 1.23/0.44 tff(f823,plain,(
% 1.23/0.44 1 = count(remove(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f822])).
% 1.23/0.44 tff(f1363,plain,(
% 1.23/0.44 0 != 0 | empty = remove(2,sF1) | ~spl5_8),
% 1.23/0.44 inference(superposition,[],[f51,f735])).
% 1.23/0.44 tff(f1365,plain,(
% 1.23/0.44 empty = remove(2,sF1) | ~spl5_8),
% 1.23/0.44 inference(trivial_inequality_removal,[],[f1363])).
% 1.23/0.44 tff(f1718,plain,(
% 1.23/0.44 1 = count(sF2) | count(sF2) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(superposition,[],[f198,f823])).
% 1.23/0.44 tff(f1728,plain,(
% 1.23/0.44 1 = $sum(1,count(sF0)) | count(sF2) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1718,f396])).
% 1.23/0.44 tff(f1731,plain,(
% 1.23/0.44 1 = $sum(1,1) | count(sF2) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1728,f404])).
% 1.23/0.44 tff(f1732,plain,(
% 1.23/0.44 count(sF2) = count(add(2,sF2)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f1731])).
% 1.23/0.44 tff(f1736,plain,(
% 1.23/0.44 2 = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1732,f820])).
% 1.23/0.44 tff(f1739,plain,(
% 1.23/0.44 add(2,empty) = sF1 | count(empty) = count(sF1) | ~spl5_8),
% 1.23/0.44 inference(superposition,[],[f222,f1365])).
% 1.23/0.44 tff(f1750,plain,(
% 1.23/0.44 sF0 = sF1 | count(empty) = count(sF1) | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f1739,f66])).
% 1.23/0.44 tff(f1751,plain,(
% 1.23/0.44 count(empty) = count(sF0) | sF0 = sF1 | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f1750,f214])).
% 1.23/0.44 tff(f1752,plain,(
% 1.23/0.44 1 = count(empty) | sF0 = sF1 | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f1751,f404])).
% 1.23/0.44 tff(f1753,plain,(
% 1.23/0.44 0 = 1 | sF0 = sF1 | ~spl5_8),
% 1.23/0.44 inference(forward_demodulation,[],[f1752,f64])).
% 1.23/0.44 tff(f1754,plain,(
% 1.23/0.44 sF0 = sF1 | ~spl5_8),
% 1.23/0.44 inference(evaluation,[],[f1753])).
% 1.23/0.44 tff(f1883,plain,(
% 1.23/0.44 2 != sF4 | (spl5_3 | spl5_6 | ~spl5_8)),
% 1.23/0.44 inference(superposition,[],[f195,f1736])).
% 1.23/0.44 tff(f1937,plain,(
% 1.23/0.44 count(sF3) = $sum(1,count(sF2)) | count(sF3) = count(sF2)),
% 1.23/0.44 inference(superposition,[],[f291,f72])).
% 1.23/0.44 tff(f1971,plain,(
% 1.23/0.44 count(sF3) = $sum(1,$sum(1,count(sF0))) | count(sF3) = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1937,f396])).
% 1.23/0.44 tff(f1980,plain,(
% 1.23/0.44 count(sF3) = $sum(1,$sum(1,1)) | count(sF3) = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1971,f404])).
% 1.23/0.44 tff(f1981,plain,(
% 1.23/0.44 3 = count(sF3) | count(sF3) = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f1980])).
% 1.23/0.44 tff(f1986,plain,(
% 1.23/0.44 3 = sF4 | count(sF3) = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1981,f74])).
% 1.23/0.44 tff(f1987,plain,(
% 1.23/0.44 count(sF3) = count(sF2) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_subsumption_resolution,[],[f1986,f75])).
% 1.23/0.44 tff(f1988,plain,(
% 1.23/0.44 count(sF3) = $sum(1,count(sF0)) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1987,f396])).
% 1.23/0.44 tff(f1989,plain,(
% 1.23/0.44 count(sF3) = $sum(1,1) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f1988,f404])).
% 1.23/0.44 tff(f1990,plain,(
% 1.23/0.44 2 = count(sF3) | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f1989])).
% 1.23/0.44 tff(f1991,plain,(
% 1.23/0.44 2 = sF4 | (spl5_3 | ~spl5_8)),
% 1.23/0.44 inference(superposition,[],[f1990,f74])).
% 1.23/0.44 tff(f2007,plain,(
% 1.23/0.44 $false | (spl5_3 | spl5_6 | ~spl5_8)),
% 1.23/0.44 inference(forward_subsumption_resolution,[],[f1991,f1883])).
% 1.23/0.44 tff(f2008,plain,(
% 1.23/0.44 spl5_3 | spl5_6 | ~spl5_8),
% 1.23/0.44 inference(avatar_contradiction_clause,[],[f2007])).
% 1.23/0.44 tff(f2010,plain,(
% 1.23/0.44 1 = 5 | in(1,sF1) | ~spl5_5),
% 1.23/0.44 inference(resolution,[],[f191,f261])).
% 1.23/0.44 tff(f2017,plain,(
% 1.23/0.44 in(1,sF1) | ~spl5_5),
% 1.23/0.44 inference(evaluation,[],[f2010])).
% 1.23/0.44 tff(f2020,plain,(
% 1.23/0.44 in(1,sF0) | (~spl5_5 | ~spl5_8)),
% 1.23/0.44 inference(forward_demodulation,[],[f2017,f1754])).
% 1.23/0.44 tff(f2056,plain,(
% 1.23/0.44 1 = 2 | (~spl5_5 | ~spl5_8)),
% 1.23/0.44 inference(resolution,[],[f2020,f263])).
% 1.23/0.44 tff(f2062,plain,(
% 1.23/0.44 $false | (~spl5_5 | ~spl5_8)),
% 1.23/0.44 inference(evaluation,[],[f2056])).
% 1.23/0.44 tff(f2063,plain,(
% 1.23/0.44 ~spl5_5 | ~spl5_8),
% 1.23/0.44 inference(avatar_contradiction_clause,[],[f2062])).
% 1.23/0.44 cnf(s3, plain, spl5_5 | ~spl5_6, inference(sat_conversion,[],[f196])).
% 1.23/0.44 cnf(s5, plain, spl5_7 | spl5_8, inference(sat_conversion,[],[f219])).
% 1.23/0.44 cnf(s9, plain, ~spl5_7, inference(sat_conversion,[],[f383])).
% 1.23/0.44 cnf(s10, plain, ~spl5_3, inference(sat_conversion,[],[f385])).
% 1.23/0.44 cnf(s18, plain, spl5_3 | spl5_6 | ~spl5_8, inference(sat_conversion,[],[f2008])).
% 1.23/0.44 cnf(s19, plain, ~spl5_5 | ~spl5_8, inference(sat_conversion,[],[f2063])).
% 1.23/0.44 cnf(s20, plain, spl5_8, inference(rat,[],[s5,s9])).
% 1.23/0.44 cnf(s21, plain, ~spl5_5, inference(rat,[],[s19,s20])).
% 1.23/0.44 cnf(s23, plain, spl5_6, inference(rat,[],[s18,s10,s20])).
% 1.23/0.44 cnf(s24, plain, $false, inference(rat,[],[s3,s23,s21])).
% 1.23/0.44 tff(f2070,plain,(
% 1.23/0.44 $false),
% 1.23/0.44 inference(avatar_sat_refutation,[],[s24])).
% 1.23/0.44 % SZS output end Proof for theBenchmark
% 1.23/0.44 % (2480974)------------------------------
% 1.23/0.44 % (2480974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.44 % (2480974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.44 % (2480974)CaDiCaL version: 2.1.3
% 1.23/0.44 % (2480974)Termination reason: Refutation
% 1.23/0.44 % (2480974)Time elapsed: 0.066 s
% 1.23/0.44 % (2480974)Peak memory usage: 13 MB
% 1.23/0.44 % (2480974)Instructions burned: 84 (million)
% 1.23/0.44 % (2480935)Success in time 0.24 s
% 1.23/0.44 % Vampire exiting
%------------------------------------------------------------------------------