%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU897^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:31:54 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU897^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:44:46 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (179018)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (179026)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=578344734:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.28 % (179026)Refutation not found, incomplete strategy
% 0.19/0.28 % (179026)------------------------------
% 0.19/0.28 % (179026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179026)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179026)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (179026)Time elapsed: 0.002 s
% 0.19/0.28 % (179026)Peak memory usage: 12 MB
% 0.19/0.28 % (179026)Instructions burned: 4 (million)
% 0.19/0.28 % (179026)------------------------------
% 0.19/0.28 % (179026)------------------------------
% 0.19/0.28 % (179029)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (179029)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.28 % (179023)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4037762763:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (179024)lrs+10_16_si=on:nwc=1.5:random_seed=3783878628:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (179025)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1120954949:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (179027)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=514779548:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (179029)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=66969373:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (179025)Refutation not found, incomplete strategy
% 0.19/0.28 % (179025)------------------------------
% 0.19/0.28 % (179025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179023)Refutation not found, incomplete strategy
% 0.19/0.28 % (179023)------------------------------
% 0.19/0.28 % (179023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179025)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179025)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (179025)Time elapsed: 0.002 s
% 0.19/0.28 % (179025)Peak memory usage: 12 MB
% 0.19/0.28 % (179023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179025)Instructions burned: 2 (million)
% 0.19/0.28 % (179023)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179023)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (179023)Time elapsed: 0.002 s
% 0.19/0.28 % (179023)Peak memory usage: 12 MB
% 0.19/0.28 % (179023)Instructions burned: 2 (million)
% 0.19/0.28 % (179025)------------------------------
% 0.19/0.28 % (179025)------------------------------
% 0.19/0.28 % (179023)------------------------------
% 0.19/0.28 % (179023)------------------------------
% 0.19/0.28 % (179027)Refutation not found, incomplete strategy
% 0.19/0.28 % (179027)------------------------------
% 0.19/0.28 % (179027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179027)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179027)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (179027)Time elapsed: 0.005 s
% 0.19/0.28 % (179027)Peak memory usage: 12 MB
% 0.19/0.28 % (179027)Instructions burned: 7 (million)
% 0.19/0.28 % (179027)------------------------------
% 0.19/0.28 % (179027)------------------------------
% 0.19/0.28 % (179031)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3433729854:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (179031)Instruction limit reached!
% 0.19/0.28 % (179031)------------------------------
% 0.19/0.28 % (179031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179031)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179031)Termination reason: Instruction limit
% 0.19/0.28 % (179031)Termination phase: Saturation
% 0.19/0.28 % (179031)Time elapsed: 0.001 s
% 0.19/0.28 % (179031)Peak memory usage: 12 MB
% 0.19/0.28 % (179031)Instructions burned: 2 (million)
% 0.19/0.28 % (179024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-179018-179024"...
% 0.19/0.28 % (179024)...printing done.
% 0.19/0.28 % (179024)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, a: $tType).
% 0.19/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, cS: (a > $o)).
% 0.19/0.28 thf(func_def_1, type, cR: (a > $o)).
% 0.19/0.28 thf(func_def_5, type, sK0: a).
% 0.19/0.28 thf(func_def_6, type, sK1: (a > a)).
% 0.19/0.28 thf(func_def_7, type, sK2: a).
% 0.19/0.28 thf(func_def_8, type, sK3: a).
% 0.19/0.28 thf(func_def_9, type, sK4: ((a > a) > a > a)).
% 0.19/0.28 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(f1,conjecture,(
% 0.19/0.28 ! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X0 : a,X1 : (a > a)] : (? [X2 : a] : ((X0 = ((X1 @ X2))) & (cR @ X2)) => ? [X2 : a] : ((cS @ X2) & (X0 = ((X1 @ X2)))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM30_pme)).
% 0.19/0.28 thf(f2,negated_conjecture,(
% 0.19/0.28 ~(! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X0 : a,X1 : (a > a)] : (? [X2 : a] : ((X0 = ((X1 @ X2))) & (cR @ X2)) => ? [X2 : a] : ((cS @ X2) & (X0 = ((X1 @ X2))))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 thf(f3,plain,(
% 0.19/0.28 ~(! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X1 : a,X2 : (a > a)] : (? [X3 : a] : ((((X2 @ X3)) = X1) & (cR @ X3)) => ? [X4 : a] : ((cS @ X4) & (((X2 @ X4)) = X1))))),
% 0.19/0.28 inference(rectify,[],[f2])).
% 0.19/0.28 thf(f4,plain,(
% 0.19/0.28 ~(! [X0 : a] : ((((cR @ X0)) = $true) => (((cS @ X0)) = $true)) <=> ! [X2 : (a > a),X1 : a] : (? [X3 : a] : ((((X2 @ X3)) = X1) & (((cR @ X3)) = $true)) => ? [X4 : a] : ((((cS @ X4)) = $true) & (((X2 @ X4)) = X1))))),
% 0.19/0.28 inference(fool_elimination,[],[f3])).
% 0.19/0.28 thf(f5,plain,(
% 0.19/0.28 ! [X0 : a] : ((((cS @ X0)) = $true) | (((cR @ X0)) != $true)) <~> ! [X1 : a,X2 : (a > a)] : (! [X3 : a] : ((((cR @ X3)) != $true) | (((X2 @ X3)) != X1)) | ? [X4 : a] : ((((cS @ X4)) = $true) & (((X2 @ X4)) = X1)))),
% 0.19/0.28 inference(ennf_transformation,[],[f4])).
% 0.19/0.28 thf(f6,plain,(
% 0.19/0.28 (? [X1 : a,X2 : (a > a)] : (? [X3 : a] : ((((cR @ X3)) = $true) & (((X2 @ X3)) = X1)) & ! [X4 : a] : ((((cS @ X4)) != $true) | (((X2 @ X4)) != X1))) | ? [X0 : a] : ((((cS @ X0)) != $true) & (((cR @ X0)) = $true))) & (! [X1 : a,X2 : (a > a)] : (! [X3 : a] : ((((cR @ X3)) != $true) | (((X2 @ X3)) != X1)) | ? [X4 : a] : ((((cS @ X4)) = $true) & (((X2 @ X4)) = X1))) | ! [X0 : a] : ((((cS @ X0)) = $true) | (((cR @ X0)) != $true)))),
% 0.19/0.28 inference(nnf_transformation,[],[f5])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 (? [X0 : a,X1 : (a > a)] : (? [X2 : a] : ((((cR @ X2)) = $true) & (((X1 @ X2)) = X0)) & ! [X3 : a] : ((((cS @ X3)) != $true) | (((X1 @ X3)) != X0))) | ? [X4 : a] : ((((cS @ X4)) != $true) & ($true = ((cR @ X4))))) & (! [X5 : a,X6 : (a > a)] : (! [X7 : a] : ((((cR @ X7)) != $true) | (((X6 @ X7)) != X5)) | ? [X8 : a] : ((((cS @ X8)) = $true) & (((X6 @ X8)) = X5))) | ! [X9 : a] : ((((cS @ X9)) = $true) | (((cR @ X9)) != $true)))),
% 0.19/0.28 inference(rectify,[],[f6])).
% 0.19/0.28 thf(f8,plain,(
% 0.19/0.28 ((((((cR @ sK2)) = $true) & (((sK1 @ sK2)) = sK0)) & ! [X3 : a] : ((((cS @ X3)) != $true) | (sK0 != ((sK1 @ X3))))) | (($true != ((cS @ sK3))) & (((cR @ sK3)) = $true))) & (! [X5 : a,X6 : (a > a)] : (! [X7 : a] : ((((cR @ X7)) != $true) | (((X6 @ X7)) != X5)) | (($true = ((cS @ (sK4 @ X6 @ X5)))) & (((X6 @ (sK4 @ X6 @ X5))) = X5))) | ! [X9 : a] : ((((cS @ X9)) = $true) | (((cR @ X9)) != $true)))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3),skolemize(X8,sK4 @ X6 @ X5)],[f7])).
% 0.19/0.28 thf(f9,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X9 : a,X7 : a,X5 : a] : ((((cR @ X7)) != $true) | (((X6 @ X7)) != X5) | (((X6 @ (sK4 @ X6 @ X5))) = X5) | (((cS @ X9)) = $true) | (((cR @ X9)) != $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X9 : a,X7 : a,X5 : a] : ((((cR @ X7)) != $true) | (((X6 @ X7)) != X5) | ($true = ((cS @ (sK4 @ X6 @ X5)))) | (((cS @ X9)) = $true) | (((cR @ X9)) != $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 ( ! [X3 : a] : ((((cR @ sK3)) = $true) | (((cS @ X3)) != $true) | (sK0 != ((sK1 @ X3)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f12,plain,(
% 0.19/0.28 ( ! [X3 : a] : (($true != ((cS @ sK3))) | (sK0 != ((sK1 @ X3))) | (((cS @ X3)) != $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f13,plain,(
% 0.19/0.28 (((sK1 @ sK2)) = sK0) | (((cR @ sK3)) = $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f14,plain,(
% 0.19/0.28 (((sK1 @ sK2)) = sK0) | ($true != ((cS @ sK3)))),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f15,plain,(
% 0.19/0.28 (((cR @ sK3)) = $true) | (((cR @ sK2)) = $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f16,plain,(
% 0.19/0.28 ($true != ((cS @ sK3))) | (((cR @ sK2)) = $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f19,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X9 : a,X7 : a] : ((((cR @ X7)) != $true) | (((cR @ X9)) != $true) | (((cS @ (sK4 @ X6 @ (X6 @ X7)))) = $true) | (((cS @ X9)) = $true)) )),
% 0.19/0.28 inference(equality_resolution,[],[f10])).
% 0.19/0.28 thf(f20,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X9 : a,X7 : a] : ((((X6 @ (sK4 @ X6 @ (X6 @ X7)))) = ((X6 @ X7))) | (((cR @ X9)) != $true) | (((cS @ X9)) = $true) | (((cR @ X7)) != $true)) )),
% 0.19/0.28 inference(equality_resolution,[],[f9])).
% 0.19/0.28 thf(f22,definition,(
% 0.19/0.28 spl5_1 <=> (((cR @ sK2)) = $true)),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.28 thf(f24,plain,(
% 0.19/0.28 (((cR @ sK2)) = $true) | ~spl5_1),
% 0.19/0.28 inference(avatar_component_clause,[],[f22])).
% 0.19/0.28 thf(f26,definition,(
% 0.19/0.28 spl5_2 <=> (((cR @ sK3)) = $true)),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.28 thf(f28,plain,(
% 0.19/0.28 (((cR @ sK3)) = $true) | ~spl5_2),
% 0.19/0.28 inference(avatar_component_clause,[],[f26])).
% 0.19/0.28 thf(f29,plain,(
% 0.19/0.28 spl5_1 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f15,f26,f22])).
% 0.19/0.28 thf(f31,definition,(
% 0.19/0.28 spl5_3 <=> ($true = ((cS @ sK3)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.28 thf(f33,plain,(
% 0.19/0.28 ($true != ((cS @ sK3))) | spl5_3),
% 0.19/0.28 inference(avatar_component_clause,[],[f31])).
% 0.19/0.28 thf(f34,plain,(
% 0.19/0.28 ~spl5_3 | spl5_1),
% 0.19/0.28 inference(avatar_split_clause,[],[f16,f22,f31])).
% 0.19/0.28 thf(f36,definition,(
% 0.19/0.28 spl5_4 <=> ! [X6 : (a > a),X7 : a] : ((((cR @ X7)) != $true) | (((cS @ (sK4 @ X6 @ (X6 @ X7)))) = $true))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.19/0.28 thf(f37,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X7 : a] : ((((cR @ X7)) != $true) | (((cS @ (sK4 @ X6 @ (X6 @ X7)))) = $true)) ) | ~spl5_4),
% 0.19/0.28 inference(avatar_component_clause,[],[f36])).
% 0.19/0.28 thf(f39,definition,(
% 0.19/0.28 spl5_5 <=> ! [X9 : a] : ((((cR @ X9)) != $true) | (((cS @ X9)) = $true))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.19/0.28 thf(f40,plain,(
% 0.19/0.28 ( ! [X9 : a] : ((((cR @ X9)) != $true) | (((cS @ X9)) = $true)) ) | ~spl5_5),
% 0.19/0.28 inference(avatar_component_clause,[],[f39])).
% 0.19/0.28 thf(f41,plain,(
% 0.19/0.28 spl5_4 | spl5_5),
% 0.19/0.28 inference(avatar_split_clause,[],[f19,f39,f36])).
% 0.19/0.28 thf(f43,definition,(
% 0.19/0.28 spl5_6 <=> (((sK1 @ sK2)) = sK0)),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.19/0.28 thf(f45,plain,(
% 0.19/0.28 (((sK1 @ sK2)) = sK0) | ~spl5_6),
% 0.19/0.28 inference(avatar_component_clause,[],[f43])).
% 0.19/0.28 thf(f46,plain,(
% 0.19/0.28 ~spl5_3 | spl5_6),
% 0.19/0.28 inference(avatar_split_clause,[],[f14,f43,f31])).
% 0.19/0.28 thf(f48,definition,(
% 0.19/0.28 spl5_7 <=> ! [X3 : a] : ((((cS @ X3)) != $true) | (sK0 != ((sK1 @ X3))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.19/0.28 thf(f49,plain,(
% 0.19/0.28 ( ! [X3 : a] : ((sK0 != ((sK1 @ X3))) | (((cS @ X3)) != $true)) ) | ~spl5_7),
% 0.19/0.28 inference(avatar_component_clause,[],[f48])).
% 0.19/0.28 thf(f50,plain,(
% 0.19/0.28 spl5_7 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f11,f26,f48])).
% 0.19/0.28 thf(f51,plain,(
% 0.19/0.28 ~spl5_3 | spl5_7),
% 0.19/0.28 inference(avatar_split_clause,[],[f12,f48,f31])).
% 0.19/0.28 thf(f52,plain,(
% 0.19/0.28 spl5_6 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f13,f26,f43])).
% 0.19/0.28 thf(f54,definition,(
% 0.19/0.28 spl5_8 <=> ! [X6 : (a > a),X7 : a] : ((((X6 @ (sK4 @ X6 @ (X6 @ X7)))) = ((X6 @ X7))) | (((cR @ X7)) != $true))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.19/0.28 thf(f55,plain,(
% 0.19/0.28 ( ! [X6 : (a > a),X7 : a] : ((((cR @ X7)) != $true) | (((X6 @ (sK4 @ X6 @ (X6 @ X7)))) = ((X6 @ X7)))) ) | ~spl5_8),
% 0.19/0.28 inference(avatar_component_clause,[],[f54])).
% 0.19/0.28 thf(f56,plain,(
% 0.19/0.28 spl5_5 | spl5_8),
% 0.19/0.28 inference(avatar_split_clause,[],[f20,f54,f39])).
% 0.19/0.28 thf(f57,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((cS @ sK3))) | (~spl5_2 | ~spl5_5)),
% 0.19/0.28 inference(constrained_superposition,[],[f40,f28])).
% 0.19/0.28 thf(f58,plain,(
% 0.19/0.28 ($true = ((cS @ sK3))) | (~spl5_2 | ~spl5_5)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f57])).
% 0.19/0.28 thf(f59,plain,(
% 0.19/0.28 $false | (~spl5_2 | spl5_3 | ~spl5_5)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f58,f33])).
% 0.19/0.28 thf(f60,plain,(
% 0.19/0.28 ~spl5_2 | spl5_3 | ~spl5_5),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f59])).
% 0.19/0.28 thf(f61,plain,(
% 0.19/0.28 ($true != $true) | (((cS @ sK2)) = $true) | (~spl5_1 | ~spl5_5)),
% 0.19/0.28 inference(constrained_superposition,[],[f40,f24])).
% 0.19/0.28 thf(f62,plain,(
% 0.19/0.28 (((cS @ sK2)) = $true) | (~spl5_1 | ~spl5_5)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f61])).
% 0.19/0.28 thf(f63,plain,(
% 0.19/0.28 (sK0 != sK0) | (((cS @ sK2)) != $true) | (~spl5_6 | ~spl5_7)),
% 0.19/0.28 inference(constrained_superposition,[],[f49,f45])).
% 0.19/0.28 thf(f64,plain,(
% 0.19/0.28 (((cS @ sK2)) != $true) | (~spl5_6 | ~spl5_7)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f63])).
% 0.19/0.28 thf(f65,plain,(
% 0.19/0.28 $false | (~spl5_1 | ~spl5_5 | ~spl5_6 | ~spl5_7)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f64,f62])).
% 0.19/0.28 thf(f66,plain,(
% 0.19/0.28 ~spl5_1 | ~spl5_5 | ~spl5_6 | ~spl5_7),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f65])).
% 0.19/0.28 thf(f67,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : (($true != $true) | (((cS @ (sK4 @ X0 @ (X0 @ sK3)))) = $true)) ) | (~spl5_2 | ~spl5_4)),
% 0.19/0.28 inference(constrained_superposition,[],[f37,f28])).
% 0.19/0.28 thf(f68,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((cS @ (sK4 @ X0 @ (X0 @ sK2)))) = $true) | ($true != $true)) ) | (~spl5_1 | ~spl5_4)),
% 0.19/0.28 inference(constrained_superposition,[],[f37,f24])).
% 0.19/0.28 thf(f69,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((cS @ (sK4 @ X0 @ (X0 @ sK2)))) = $true)) ) | (~spl5_1 | ~spl5_4)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f68])).
% 0.19/0.28 thf(f70,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((cS @ (sK4 @ X0 @ (X0 @ sK3)))) = $true)) ) | (~spl5_2 | ~spl5_4)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f67])).
% 0.19/0.28 thf(f77,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((X0 @ (sK4 @ X0 @ (X0 @ sK3)))) = ((X0 @ sK3))) | ($true != $true)) ) | (~spl5_2 | ~spl5_8)),
% 0.19/0.28 inference(constrained_superposition,[],[f55,f28])).
% 0.19/0.28 thf(f78,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : (($true != $true) | (((X0 @ (sK4 @ X0 @ (X0 @ sK2)))) = ((X0 @ sK2)))) ) | (~spl5_1 | ~spl5_8)),
% 0.19/0.28 inference(constrained_superposition,[],[f55,f24])).
% 0.19/0.28 thf(f79,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((X0 @ (sK4 @ X0 @ (X0 @ sK2)))) = ((X0 @ sK2)))) ) | (~spl5_1 | ~spl5_8)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f78])).
% 0.19/0.28 thf(f80,plain,(
% 0.19/0.28 ( ! [X0 : (a > a)] : ((((X0 @ (sK4 @ X0 @ (X0 @ sK3)))) = ((X0 @ sK3)))) ) | (~spl5_2 | ~spl5_8)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f77])).
% 0.19/0.28 thf(f92,plain,(
% 0.19/0.28 (((cS @ ((^[Y0 : a]: (Y0)) @ sK2))) = $true) | (~spl5_1 | ~spl5_4 | ~spl5_8)),
% 0.19/0.28 inference(constrained_superposition,[],[f69,f79])).
% 0.19/0.28 thf(f99,plain,(
% 0.19/0.28 (((cS @ sK2)) = $true) | (~spl5_1 | ~spl5_4 | ~spl5_8)),
% 0.19/0.28 inference(beta-eta_normalization,[],[f92])).
% 0.19/0.28 thf(f110,plain,(
% 0.19/0.28 $false | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7 | ~spl5_8)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f99,f64])).
% 0.19/0.28 thf(f111,plain,(
% 0.19/0.28 ~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7 | ~spl5_8),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f110])).
% 0.19/0.28 thf(f137,plain,(
% 0.19/0.28 (((cS @ ((^[Y0 : a]: (Y0)) @ sK3))) = $true) | (~spl5_2 | ~spl5_4 | ~spl5_8)),
% 0.19/0.28 inference(constrained_superposition,[],[f70,f80])).
% 0.19/0.28 thf(f140,plain,(
% 0.19/0.28 ($true = ((cS @ sK3))) | (~spl5_2 | ~spl5_4 | ~spl5_8)),
% 0.19/0.28 inference(beta-eta_normalization,[],[f137])).
% 0.19/0.28 thf(f154,plain,(
% 0.19/0.28 $false | (~spl5_2 | spl5_3 | ~spl5_4 | ~spl5_8)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f140,f33])).
% 0.19/0.28 thf(f155,plain,(
% 0.19/0.28 ~spl5_2 | spl5_3 | ~spl5_4 | ~spl5_8),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f154])).
% 0.19/0.28 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f29])).
% 0.19/0.28 cnf(s2, plain, spl5_1 | ~spl5_3, inference(sat_conversion,[],[f34])).
% 0.19/0.28 cnf(s3, plain, spl5_4 | spl5_5, inference(sat_conversion,[],[f41])).
% 0.19/0.28 cnf(s4, plain, ~spl5_3 | spl5_6, inference(sat_conversion,[],[f46])).
% 0.19/0.28 cnf(s5, plain, spl5_2 | spl5_7, inference(sat_conversion,[],[f50])).
% 0.19/0.28 cnf(s6, plain, ~spl5_3 | spl5_7, inference(sat_conversion,[],[f51])).
% 0.19/0.28 cnf(s7, plain, spl5_2 | spl5_6, inference(sat_conversion,[],[f52])).
% 0.19/0.28 cnf(s8, plain, spl5_5 | spl5_8, inference(sat_conversion,[],[f56])).
% 0.19/0.28 cnf(s9, plain, ~spl5_2 | spl5_3 | ~spl5_5, inference(sat_conversion,[],[f60])).
% 0.19/0.28 cnf(s10, plain, ~spl5_1 | ~spl5_5 | ~spl5_6 | ~spl5_7, inference(sat_conversion,[],[f66])).
% 0.19/0.28 cnf(s11, plain, ~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7 | ~spl5_8, inference(sat_conversion,[],[f111])).
% 0.19/0.28 cnf(s12, plain, ~spl5_2 | spl5_3 | ~spl5_4 | ~spl5_8, inference(sat_conversion,[],[f155])).
% 0.19/0.28 cnf(s13, plain, ~spl5_2 | spl5_3, inference(rat,[],[s12,s3,s8,s9])).
% 0.19/0.28 cnf(s14, plain, spl5_1, inference(rat,[],[s13,s1,s2])).
% 0.19/0.28 cnf(s15, plain, ~spl5_6 | ~spl5_7, inference(rat,[],[s11,s3,s8,s10,s14])).
% 0.19/0.28 cnf(s16, plain, ~spl5_3, inference(rat,[],[s15,s4,s6])).
% 0.19/0.28 cnf(s17, plain, ~spl5_2, inference(rat,[],[s13,s16])).
% 0.19/0.28 cnf(s18, plain, spl5_6, inference(rat,[],[s7,s17])).
% 0.19/0.28 cnf(s19, plain, spl5_7, inference(rat,[],[s5,s17])).
% 0.19/0.28 cnf(s20, plain, $false, inference(rat,[],[s15,s19,s18])).
% 0.19/0.28 thf(f169,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(avatar_sat_refutation,[],[s20])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (179024)------------------------------
% 0.19/0.28 % (179024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (179024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (179024)CaDiCaL version: 2.1.3
% 0.19/0.28 % (179024)Termination reason: Refutation
% 0.19/0.28 % (179024)Time elapsed: 0.011 s
% 0.19/0.28 % (179024)Peak memory usage: 13 MB
% 0.19/0.28 % (179024)Instructions burned: 18 (million)
% 0.19/0.28 % (179018)Success in time 0.052 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------