%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV448^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:38:39 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV448^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:49:08 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.30 % (3326994)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (3327003)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3348832031:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (3327005)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (3327005)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
% 0.21/0.30 % (3327001)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3857045339:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (3326999)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3363494124:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (3327002)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=3757703291: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)
% 0.21/0.30 % (3327005)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=1452023157:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (3327004)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1573615242:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (3327001)Refutation not found, incomplete strategy
% 0.21/0.30 % (3327001)------------------------------
% 0.21/0.30 % (3327001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3327001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3327001)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3327001)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (3327001)Time elapsed: 0.002 s
% 0.21/0.30 % (3327001)Peak memory usage: 12 MB
% 0.21/0.30 % (3327001)Instructions burned: 2 (million)
% 0.21/0.30 % (3327001)------------------------------
% 0.21/0.30 % (3327001)------------------------------
% 0.21/0.30 % (3327003)Instruction limit reached!
% 0.21/0.30 % (3327003)------------------------------
% 0.21/0.30 % (3327003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3327003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3327003)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3327003)Termination reason: Instruction limit
% 0.21/0.30 % (3327003)Termination phase: Saturation
% 0.21/0.30 % (3327003)Time elapsed: 0.009 s
% 0.21/0.30 % (3327003)Peak memory usage: 12 MB
% 0.21/0.30 % (3327003)Instructions burned: 25 (million)
% 0.21/0.30 % (3326999) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3326994-3326999"...
% 0.21/0.30 % (3327002) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3326994-3327002"...
% 0.21/0.30 % (3327000)lrs+10_16_si=on:nwc=1.5:random_seed=1781416657:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (3327004) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3326994-3327004"...
% 0.21/0.30 % (3326999)...printing done.
% 0.21/0.30 % (3327002)...printing done.
% 0.21/0.30 % (3326999)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(type_def_6, type, sK1: $tType).
% 0.21/0.30 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_5, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.30 thf(func_def_6, type, sK2: (sK1 > $o)).
% 0.21/0.30 thf(func_def_7, type, sK3: (sK1 > $o)).
% 0.21/0.30 thf(func_def_8, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.30 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_13, type, sK6: sK1).
% 0.21/0.30 thf(f1,axiom,(
% 0.21/0.30 ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = ((X1 @ X2)))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_')).
% 0.21/0.30 thf(f3,axiom,(
% 0.21/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 0.21/0.30 thf(f4,conjecture,(
% 0.21/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) = ('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/SUBSET' @ X0 @ X2 @ X1))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_ANTISYM_EQ_')).
% 0.21/0.30 thf(f5,negated_conjecture,(
% 0.21/0.30 ~ ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) = ('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/SUBSET' @ X0 @ X2 @ X1))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/sets/IN' @ X0 @ X3 @ X1)))),
% 0.21/0.30 inference(rectify,[],[f3])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) <=> ! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) => ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)))),
% 0.21/0.30 inference(fool_elimination,[],[f6])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((X1 = X2) = ('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 0.21/0.30 inference(rectify,[],[f5])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ~ ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) <=> (X1 = X2))),
% 0.21/0.30 inference(fool_elimination,[],[f8])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ X2)) = ((X2 @ X1)))),
% 0.21/0.30 inference(rectify,[],[f1])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) <=> ! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)))),
% 0.21/0.30 inference(ennf_transformation,[],[f7])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) <~> (X1 = X2))),
% 0.21/0.30 inference(ennf_transformation,[],[f9])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 != X2) | (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true))) & ((X1 = X2) | (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true))))),
% 0.21/0.30 inference(nnf_transformation,[],[f14])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 != X2) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & ((X1 = X2) | (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true))))),
% 0.21/0.30 inference(flattening,[],[f18])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ((sK2 != sK3) | ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) != $true) | ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) != $true)) & ((sK2 = sK3) | (((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) = $true) & ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) = $true)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f19])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = ((X1 @ X2)))),
% 0.21/0.30 inference(rectify,[],[f12])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true))) & (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true)))),
% 0.21/0.30 inference(nnf_transformation,[],[f13])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) & ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true))) & (! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)))),
% 0.21/0.30 inference(rectify,[],[f22])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1)) = $true) & ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)) != $true))) & (! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f23])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 (sK2 = sK3) | ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 (sK2 = sK3) | ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) != $true) | (sK2 != sK3) | ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) != $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f30,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X1)) = ((X1 @ X2)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f21])).
% 0.21/0.30 thf(f31,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X4 : X0] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f24])).
% 0.21/0.30 thf(f32,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)) != $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f24])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1)) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f24])).
% 0.21/0.30 thf(f37,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) | (((X1 @ X2)) = $false)) )),
% 0.21/0.30 inference(iff_proxy_clausification,[],[f30])).
% 0.21/0.30 thf(f38,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X1)) = $false) | (((X1 @ X2)) = $true)) )),
% 0.21/0.30 inference(iff_proxy_clausification,[],[f30])).
% 0.21/0.30 thf(f44,definition,(
% 0.21/0.30 spl5_1 <=> ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.21/0.30 thf(f45,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) != $true) | spl5_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f44])).
% 0.21/0.30 thf(f46,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK3 @ sK2)) = $true) | ~spl5_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f44])).
% 0.21/0.30 thf(f48,definition,(
% 0.21/0.30 spl5_2 <=> (sK2 = sK3)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.21/0.30 thf(f49,plain,(
% 0.21/0.30 (sK2 != sK3) | spl5_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f48])).
% 0.21/0.30 thf(f50,plain,(
% 0.21/0.30 (sK2 = sK3) | ~spl5_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f48])).
% 0.21/0.30 thf(f51,plain,(
% 0.21/0.30 spl5_1 | spl5_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f28,f48,f44])).
% 0.21/0.30 thf(f53,definition,(
% 0.21/0.30 spl5_3 <=> ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) != $true) | spl5_3),
% 0.21/0.30 inference(avatar_component_clause,[],[f53])).
% 0.21/0.30 thf(f55,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)) = $true) | ~spl5_3),
% 0.21/0.30 inference(avatar_component_clause,[],[f53])).
% 0.21/0.30 thf(f56,plain,(
% 0.21/0.30 spl5_3 | spl5_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f27,f48,f53])).
% 0.21/0.30 thf(f57,plain,(
% 0.21/0.30 ~spl5_3 | ~spl5_2 | ~spl5_1),
% 0.21/0.30 inference(avatar_split_clause,[],[f29,f44,f48,f53])).
% 0.21/0.30 thf(f61,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK2)) != $true) | (~spl5_2 | spl5_3)),
% 0.21/0.30 inference(constrained_superposition,[],[f54,f50])).
% 0.21/0.30 thf(f94,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X1)) = $true) | ($true != $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X1)) = $true)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f32,f33])).
% 0.21/0.30 thf(f97,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X1)) = $true) | ($true != $true)) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f94])).
% 0.21/0.30 thf(f98,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X1)) = $true)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f97])).
% 0.21/0.30 thf(f99,plain,(
% 0.21/0.30 ($true != $true) | (~spl5_2 | spl5_3)),
% 0.21/0.30 inference(constrained_superposition,[],[f61,f98])).
% 0.21/0.30 thf(f100,plain,(
% 0.21/0.30 $false | (~spl5_2 | spl5_3)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f99])).
% 0.21/0.30 thf(f101,plain,(
% 0.21/0.30 ~spl5_2 | spl5_3),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f100])).
% 0.21/0.30 thf(f103,plain,(
% 0.21/0.30 ((('const/sets/SUBSET' @ sK1 @ sK2 @ sK2)) != $true) | (spl5_1 | ~spl5_2)),
% 0.21/0.30 inference(forward_demodulation,[],[f45,f50])).
% 0.21/0.30 thf(f104,plain,(
% 0.21/0.30 $false | (spl5_1 | ~spl5_2)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f103,f98])).
% 0.21/0.30 thf(f105,plain,(
% 0.21/0.30 spl5_1 | ~spl5_2),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f104])).
% 0.21/0.30 thf(f106,plain,(
% 0.21/0.30 (((sK2 @ sK6)) != ((sK3 @ sK6))) | spl5_2),
% 0.21/0.30 inference(negative_extensionality,[],[f49])).
% 0.21/0.30 thf(f107,plain,(
% 0.21/0.30 (((sK2 @ sK6)) = $true) | (((sK3 @ sK6)) = $true) | spl5_2),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f106])).
% 0.21/0.30 thf(f108,plain,(
% 0.21/0.30 ($false = ((sK3 @ sK6))) | ($false = ((sK2 @ sK6))) | spl5_2),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f106])).
% 0.21/0.30 thf(f110,definition,(
% 0.21/0.30 spl5_4 <=> ($false = ((sK3 @ sK6)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.21/0.30 thf(f112,plain,(
% 0.21/0.30 ($false = ((sK3 @ sK6))) | ~spl5_4),
% 0.21/0.30 inference(avatar_component_clause,[],[f110])).
% 0.21/0.30 thf(f114,definition,(
% 0.21/0.30 spl5_5 <=> ($false = ((sK2 @ sK6)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.21/0.30 thf(f115,plain,(
% 0.21/0.30 ($false != ((sK2 @ sK6))) | spl5_5),
% 0.21/0.30 inference(avatar_component_clause,[],[f114])).
% 0.21/0.30 thf(f116,plain,(
% 0.21/0.30 ($false = ((sK2 @ sK6))) | ~spl5_5),
% 0.21/0.30 inference(avatar_component_clause,[],[f114])).
% 0.21/0.30 thf(f117,plain,(
% 0.21/0.30 spl5_4 | spl5_5 | spl5_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f108,f48,f114,f110])).
% 0.21/0.30 thf(f119,definition,(
% 0.21/0.30 spl5_6 <=> (((sK3 @ sK6)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.21/0.30 thf(f121,plain,(
% 0.21/0.30 (((sK3 @ sK6)) = $true) | ~spl5_6),
% 0.21/0.30 inference(avatar_component_clause,[],[f119])).
% 0.21/0.30 thf(f123,definition,(
% 0.21/0.30 spl5_7 <=> (((sK2 @ sK6)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.21/0.30 thf(f125,plain,(
% 0.21/0.30 (((sK2 @ sK6)) = $true) | ~spl5_7),
% 0.21/0.30 inference(avatar_component_clause,[],[f123])).
% 0.21/0.30 thf(f126,plain,(
% 0.21/0.30 spl5_6 | spl5_7 | spl5_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f107,f48,f123,f119])).
% 0.21/0.30 thf(f157,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK2)) = $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | ($true != $true)) ) | ~spl5_1),
% 0.21/0.30 inference(constrained_superposition,[],[f31,f46])).
% 0.21/0.30 thf(f158,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (($true != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK2)) != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) = $true)) ) | ~spl5_3),
% 0.21/0.30 inference(constrained_superposition,[],[f31,f55])).
% 0.21/0.30 thf(f162,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK2)) = $true)) ) | ~spl5_1),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f157])).
% 0.21/0.30 thf(f165,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK2)) != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) = $true)) ) | ~spl5_3),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f158])).
% 0.21/0.30 thf(f169,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : ((((sK3 @ X0)) = $false) | ($true != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK2)) = $true)) ) | ~spl5_1),
% 0.21/0.30 inference(constrained_superposition,[],[f162,f37])).
% 0.21/0.30 thf(f172,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK2)) = $true) | (((sK3 @ X0)) = $false)) ) | ~spl5_1),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f169])).
% 0.21/0.30 thf(f174,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : ((((sK2 @ X0)) = $true) | ($false = $true) | (((sK3 @ X0)) = $false)) ) | ~spl5_1),
% 0.21/0.30 inference(constrained_superposition,[],[f38,f172])).
% 0.21/0.30 thf(f176,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : ((((sK3 @ X0)) = $false) | (((sK2 @ X0)) = $true)) ) | ~spl5_1),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f174])).
% 0.21/0.30 thf(f181,plain,(
% 0.21/0.30 (((sK2 @ sK6)) = $true) | ($false = $true) | (~spl5_1 | ~spl5_6)),
% 0.21/0.30 inference(constrained_superposition,[],[f121,f176])).
% 0.21/0.30 thf(f185,plain,(
% 0.21/0.30 (((sK2 @ sK6)) = $true) | (~spl5_1 | ~spl5_6)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f181])).
% 0.21/0.30 thf(f190,plain,(
% 0.21/0.30 ($false = $true) | (~spl5_1 | ~spl5_5 | ~spl5_6)),
% 0.21/0.30 inference(forward_demodulation,[],[f185,f116])).
% 0.21/0.30 thf(f191,plain,(
% 0.21/0.30 $false | (~spl5_1 | ~spl5_5 | ~spl5_6)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f190])).
% 0.21/0.30 thf(f192,plain,(
% 0.21/0.30 ~spl5_1 | ~spl5_5 | ~spl5_6),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f191])).
% 0.21/0.30 thf(f193,plain,(
% 0.21/0.30 ($false = $true) | (~spl5_5 | ~spl5_7)),
% 0.21/0.30 inference(forward_demodulation,[],[f125,f116])).
% 0.21/0.30 thf(f194,plain,(
% 0.21/0.30 $false | (~spl5_5 | ~spl5_7)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f193])).
% 0.21/0.30 thf(f195,plain,(
% 0.21/0.30 ~spl5_5 | ~spl5_7),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f194])).
% 0.21/0.30 thf(f201,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (($false = ((sK2 @ X0))) | ($true != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) = $true)) ) | ~spl5_3),
% 0.21/0.30 inference(constrained_superposition,[],[f165,f37])).
% 0.21/0.30 thf(f205,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) = $true) | ($false = ((sK2 @ X0)))) ) | ~spl5_3),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f201])).
% 0.21/0.30 thf(f208,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : ((((sK3 @ X0)) = $true) | ($false = $true) | ($false = ((sK2 @ X0)))) ) | ~spl5_3),
% 0.21/0.30 inference(constrained_superposition,[],[f38,f205])).
% 0.21/0.30 thf(f210,plain,(
% 0.21/0.30 ( ! [X0 : sK1] : ((((sK3 @ X0)) = $true) | ($false = ((sK2 @ X0)))) ) | ~spl5_3),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f208])).
% 0.21/0.30 thf(f219,plain,(
% 0.21/0.30 ($false = ((sK2 @ sK6))) | ($false = $true) | (~spl5_3 | ~spl5_4)),
% 0.21/0.30 inference(constrained_superposition,[],[f112,f210])).
% 0.21/0.30 thf(f224,plain,(
% 0.21/0.30 ($false = ((sK2 @ sK6))) | (~spl5_3 | ~spl5_4)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f219])).
% 0.21/0.30 thf(f230,plain,(
% 0.21/0.30 $false | (~spl5_3 | ~spl5_4 | spl5_5)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f224,f115])).
% 0.21/0.30 thf(f231,plain,(
% 0.21/0.30 ~spl5_3 | ~spl5_4 | spl5_5),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f230])).
% 0.21/0.30 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f51])).
% 0.21/0.30 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f56])).
% 0.21/0.30 cnf(s3, plain, ~spl5_1 | ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f57])).
% 0.21/0.30 cnf(s4, plain, ~spl5_2 | spl5_3, inference(sat_conversion,[],[f101])).
% 0.21/0.30 cnf(s5, plain, spl5_1 | ~spl5_2, inference(sat_conversion,[],[f105])).
% 0.21/0.30 cnf(s6, plain, spl5_2 | spl5_4 | spl5_5, inference(sat_conversion,[],[f117])).
% 0.21/0.30 cnf(s7, plain, spl5_2 | spl5_6 | spl5_7, inference(sat_conversion,[],[f126])).
% 0.21/0.30 cnf(s9, plain, ~spl5_1 | ~spl5_5 | ~spl5_6, inference(sat_conversion,[],[f192])).
% 0.21/0.30 cnf(s10, plain, ~spl5_5 | ~spl5_7, inference(sat_conversion,[],[f195])).
% 0.21/0.30 cnf(s13, plain, ~spl5_3 | ~spl5_4 | spl5_5, inference(sat_conversion,[],[f231])).
% 0.21/0.30 cnf(s14, plain, spl5_1, inference(rat,[],[s1,s5])).
% 0.21/0.30 cnf(s15, plain, ~spl5_5 | spl5_2, inference(rat,[],[s7,s9,s10,s14])).
% 0.21/0.30 cnf(s16, plain, spl5_2, inference(rat,[],[s13,s6,s15,s2])).
% 0.21/0.30 cnf(s17, plain, spl5_3, inference(rat,[],[s4,s16])).
% 0.21/0.30 cnf(s18, plain, $false, inference(rat,[],[s3,s14,s17,s16])).
% 0.21/0.30 thf(f232,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s18])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (3326999)------------------------------
% 0.21/0.30 % (3326999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3326999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3326999)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3326999)Termination reason: Refutation
% 0.21/0.30 % (3326999)Time elapsed: 0.012 s
% 0.21/0.30 % (3326999)Peak memory usage: 13 MB
% 0.21/0.30 % (3326999)Instructions burned: 18 (million)
% 0.21/0.30 % (3326994)Success in time 0.048 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------