%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU818^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:31:42 AM UTC 2026
% Result : Theorem 0.34s 0.43s
% Output : Refutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU818^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n019.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 14:34:18 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.30/0.34 Running higher-order theorem proving
% 0.30/0.36 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
% 0.34/0.43 % (866423)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.43 % (866429)lrs+10_16_si=on:nwc=1.5:random_seed=3492247631:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.43 % (866429)Instruction limit reached!
% 0.34/0.43 % (866429)------------------------------
% 0.34/0.43 % (866429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.43 % (866429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.43 % (866429)CaDiCaL version: 2.1.3
% 0.34/0.43 % (866429)Termination reason: Instruction limit
% 0.34/0.43 % (866429)Termination phase: Saturation
% 0.34/0.43 % (866429)Time elapsed: 0.008 s
% 0.34/0.43 % (866429)Peak memory usage: 11 MB
% 0.34/0.43 % (866429)Instructions burned: 18 (million)
% 0.34/0.43 % (866434)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.34/0.43 % (866434)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
% 0.34/0.43 % (866430)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1770292828:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.34/0.43 % (866428)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=992090140:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.34/0.43 % (866432)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1368604560:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.34/0.43 % (866431)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=1773129687: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)
% 0.34/0.43 % (866434)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=1561461012:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.34/0.43 % (866433)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1306571520:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.34/0.43 % (866430)Instruction limit reached!
% 0.34/0.43 % (866430)------------------------------
% 0.34/0.43 % (866430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.43 % (866430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.43 % (866430)CaDiCaL version: 2.1.3
% 0.34/0.43 % (866430)Termination reason: Instruction limit
% 0.34/0.43 % (866430)Termination phase: Function definition elimination
% 0.34/0.43 % (866430)Time elapsed: 0.003 s
% 0.34/0.43 % (866430)Peak memory usage: 10 MB
% 0.34/0.43 % (866430)Instructions burned: 3 (million)
% 0.34/0.43 % (866431) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-866423-866431"...
% 0.34/0.43 % (866432) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-866423-866432"...
% 0.34/0.43 % (866432)...printing done.
% 0.34/0.43 % (866431)...printing done.
% 0.34/0.43 % (866432)Refutation found. Thanks to Tanya!
% 0.34/0.43 % SZS status Theorem for theBenchmark
% 0.34/0.43 % SZS output start Proof for theBenchmark
% 0.34/0.43 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.34/0.43 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.34/0.43 thf(func_def_2, type, powerset: ($i > $i)).
% 0.34/0.43 thf(func_def_3, type, nonempty: ($i > $o)).
% 0.34/0.43 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.34/0.43 thf(func_def_5, type, subsetI1: $o).
% 0.34/0.43 thf(func_def_7, type, transitiveset: ($i > $o)).
% 0.34/0.43 thf(func_def_8, type, stricttotalorderedByIn: ($i > $o)).
% 0.34/0.43 thf(func_def_9, type, wellorderedByIn: ($i > $o)).
% 0.34/0.43 thf(func_def_10, type, ordinal: ($i > $o)).
% 0.34/0.43 thf(func_def_11, type, ordinalTransSet: $o).
% 0.34/0.43 thf(func_def_12, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.34/0.43 thf(func_def_13, type, vIMP: ($o > $o > $o)).
% 0.34/0.43 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.34/0.43 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.34/0.43 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.34/0.43 thf(func_def_17, type, vAND: ($o > $o > $o)).
% 0.34/0.43 thf(func_def_18, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.34/0.43 thf(func_def_19, type, db2: !>[X0: $tType]:(X0)).
% 0.34/0.43 thf(func_def_20, type, vOR: ($o > $o > $o)).
% 0.34/0.43 thf(func_def_21, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.34/0.43 thf(func_def_24, type, vNOT: ($o > $o)).
% 0.34/0.43 thf(func_def_25, type, db3: !>[X0: $tType]:(X0)).
% 0.34/0.43 thf(func_def_26, type, sK0: ($i > $i > $i)).
% 0.34/0.43 thf(func_def_34, type, sK8: ($i > $i)).
% 0.34/0.43 thf(f2,axiom,(
% 0.34/0.43 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.34/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.34/0.43 thf(f7,axiom,(
% 0.34/0.43 (! [X0 : $i] : ((ordinal @ X0) => ! [X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0)))) = ordinalTransSet)),
% 0.34/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet)).
% 0.34/0.43 thf(f8,conjecture,(
% 0.34/0.43 subsetI1 => (ordinalTransSet => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0))))),
% 0.34/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet1)).
% 0.34/0.43 thf(f9,negated_conjecture,(
% 0.34/0.43 ~(subsetI1 => (ordinalTransSet => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 0.34/0.43 inference(negated_conjecture,[status(cth)],[f8])).
% 0.34/0.43 thf(f14,plain,(
% 0.34/0.43 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.34/0.43 inference(rectify,[],[f2])).
% 0.34/0.43 thf(f15,plain,(
% 0.34/0.43 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
% 0.34/0.43 inference(fool_elimination,[],[f14])).
% 0.34/0.43 thf(f16,plain,(
% 0.34/0.43 (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))) = ordinalTransSet)),
% 0.34/0.43 inference(rectify,[],[f7])).
% 0.34/0.43 thf(f17,plain,(
% 0.34/0.43 ! [X0 : $i] : ((((ordinal @ X0)) = $true) => ! [X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)))) <=> (ordinalTransSet = $true)),
% 0.34/0.43 inference(fool_elimination,[],[f16])).
% 0.34/0.43 thf(f18,plain,(
% 0.34/0.43 ~(subsetI1 => (ordinalTransSet => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 0.34/0.43 inference(rectify,[],[f9])).
% 0.34/0.43 thf(f19,plain,(
% 0.34/0.43 ~((subsetI1 = $true) => ((ordinalTransSet = $true) => ! [X0 : $i] : ((((ordinal @ X0)) = $true) => ! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((subset @ X1 @ X0)) = $true)))))),
% 0.34/0.43 inference(fool_elimination,[],[f18])).
% 0.34/0.43 thf(f25,plain,(
% 0.34/0.43 (? [X0 : $i] : ((((ordinal @ X0)) = $true) & ? [X1 : $i] : ((((subset @ X1 @ X0)) != $true) & (((in @ X1 @ X0)) = $true))) & (ordinalTransSet = $true)) & (subsetI1 = $true)),
% 0.34/0.43 inference(ennf_transformation,[],[f19])).
% 0.34/0.43 thf(f26,plain,(
% 0.34/0.43 ? [X0 : $i] : ((((ordinal @ X0)) = $true) & ? [X1 : $i] : ((((subset @ X1 @ X0)) != $true) & (((in @ X1 @ X0)) = $true))) & (ordinalTransSet = $true) & (subsetI1 = $true)),
% 0.34/0.43 inference(flattening,[],[f25])).
% 0.34/0.43 thf(f27,plain,(
% 0.34/0.43 ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) <=> (subsetI1 = $true)),
% 0.34/0.43 inference(ennf_transformation,[],[f15])).
% 0.34/0.43 thf(f28,plain,(
% 0.34/0.43 ! [X0 : $i] : (! [X2 : $i,X1 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ X0)) != $true)) | (((ordinal @ X0)) != $true)) <=> (ordinalTransSet = $true)),
% 0.34/0.43 inference(ennf_transformation,[],[f17])).
% 0.34/0.43 thf(f29,plain,(
% 0.34/0.43 (ordinalTransSet = $true) <=> ! [X0 : $i] : (! [X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((ordinal @ X0)) != $true))),
% 0.34/0.43 inference(flattening,[],[f28])).
% 0.34/0.43 thf(f30,plain,(
% 0.34/0.43 (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))))),
% 0.34/0.43 inference(nnf_transformation,[],[f27])).
% 0.34/0.43 thf(f31,plain,(
% 0.34/0.43 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (($true != ((subset @ X3 @ X4))) & ! [X5 : $i] : (($true != ((in @ X5 @ X3))) | ($true = ((in @ X5 @ X4))))))),
% 0.34/0.43 inference(rectify,[],[f30])).
% 0.34/0.43 thf(f32,plain,(
% 0.34/0.43 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) & ($true != ((in @ (sK0 @ X1 @ X0) @ X1))))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != ((subset @ sK1 @ sK2))) & ! [X5 : $i] : (($true != ((in @ X5 @ sK1))) | ($true = ((in @ X5 @ sK2))))))),
% 0.34/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f31])).
% 0.34/0.43 thf(f33,plain,(
% 0.34/0.43 ((((ordinal @ sK3)) = $true) & (($true != ((subset @ sK4 @ sK3))) & ($true = ((in @ sK4 @ sK3))))) & (ordinalTransSet = $true) & (subsetI1 = $true)),
% 0.34/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f26])).
% 0.34/0.43 thf(f34,plain,(
% 0.34/0.43 ((ordinalTransSet = $true) | ? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) & (((ordinal @ X0)) = $true))) & (! [X0 : $i] : (! [X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((ordinal @ X0)) != $true)) | (ordinalTransSet != $true))),
% 0.34/0.43 inference(nnf_transformation,[],[f29])).
% 0.34/0.43 thf(f35,plain,(
% 0.34/0.43 ((ordinalTransSet = $true) | ? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) & (((ordinal @ X0)) = $true))) & (! [X3 : $i] : (! [X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true != ((in @ X5 @ X4))) | ($true = ((in @ X5 @ X3)))) | ($true != ((ordinal @ X3)))) | (ordinalTransSet != $true))),
% 0.34/0.43 inference(rectify,[],[f34])).
% 0.34/0.43 thf(f36,plain,(
% 0.34/0.43 ((ordinalTransSet = $true) | ((($true = ((in @ sK6 @ sK5))) & ($true = ((in @ sK7 @ sK6))) & ($true != ((in @ sK7 @ sK5)))) & ($true = ((ordinal @ sK5))))) & (! [X3 : $i] : (! [X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true != ((in @ X5 @ X4))) | ($true = ((in @ X5 @ X3)))) | ($true != ((ordinal @ X3)))) | (ordinalTransSet != $true))),
% 0.34/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f35])).
% 0.34/0.43 thf(f41,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | (subsetI1 != $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.34/0.43 inference(cnf_transformation,[],[f32])).
% 0.34/0.43 thf(f42,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (subsetI1 != $true)) )),
% 0.34/0.43 inference(cnf_transformation,[],[f32])).
% 0.34/0.43 thf(f44,plain,(
% 0.34/0.43 (subsetI1 = $true)),
% 0.34/0.43 inference(cnf_transformation,[],[f33])).
% 0.34/0.43 thf(f45,plain,(
% 0.34/0.43 (ordinalTransSet = $true)),
% 0.34/0.43 inference(cnf_transformation,[],[f33])).
% 0.34/0.43 thf(f46,plain,(
% 0.34/0.43 ($true = ((in @ sK4 @ sK3)))),
% 0.34/0.43 inference(cnf_transformation,[],[f33])).
% 0.34/0.43 thf(f47,plain,(
% 0.34/0.43 ($true != ((subset @ sK4 @ sK3)))),
% 0.34/0.43 inference(cnf_transformation,[],[f33])).
% 0.34/0.43 thf(f48,plain,(
% 0.34/0.43 (((ordinal @ sK3)) = $true)),
% 0.34/0.43 inference(cnf_transformation,[],[f33])).
% 0.34/0.43 thf(f51,plain,(
% 0.34/0.43 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((ordinal @ X3))) | ($true != ((in @ X5 @ X4))) | ($true = ((in @ X5 @ X3))) | (ordinalTransSet != $true) | ($true != ((in @ X4 @ X3)))) )),
% 0.34/0.43 inference(cnf_transformation,[],[f36])).
% 0.34/0.43 thf(f89,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.34/0.43 inference(forward_subsumption_resolution,[],[f41,f44])).
% 0.34/0.43 thf(f90,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.34/0.43 inference(forward_subsumption_resolution,[],[f42,f44])).
% 0.34/0.43 thf(f94,plain,(
% 0.34/0.43 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X4))) | ($true != ((in @ X4 @ X3))) | ($true != ((ordinal @ X3))) | ($true = ((in @ X5 @ X3)))) )),
% 0.34/0.43 inference(forward_subsumption_resolution,[],[f51,f45])).
% 0.34/0.43 thf(f96,plain,(
% 0.34/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ X0 @ X1) @ X2))) | (((subset @ X1 @ X0)) = $true) | (((in @ X1 @ X2)) != $true) | ($true != $true) | ($true != ((ordinal @ X2)))) )),
% 0.34/0.43 inference(superposition,[],[f94,f90])).
% 0.34/0.43 thf(f98,plain,(
% 0.34/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ X0 @ X1) @ X2))) | (((subset @ X1 @ X0)) = $true) | (((in @ X1 @ X2)) != $true) | ($true != ((ordinal @ X2)))) )),
% 0.34/0.43 inference(trivial_inequality_removal,[],[f96])).
% 0.34/0.43 thf(f115,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((in @ X1 @ X0)) != $true) | ($true != $true) | (((ordinal @ X0)) != $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.34/0.43 inference(superposition,[],[f89,f98])).
% 0.34/0.43 thf(f120,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((ordinal @ X0)) != $true) | (((in @ X1 @ X0)) != $true) | ($true != $true)) )),
% 0.34/0.43 inference(duplicate_literal_removal,[],[f115])).
% 0.34/0.43 thf(f121,plain,(
% 0.34/0.43 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((in @ X1 @ X0)) != $true) | (((ordinal @ X0)) != $true)) )),
% 0.34/0.43 inference(trivial_inequality_removal,[],[f120])).
% 0.34/0.43 thf(f123,plain,(
% 0.34/0.43 ($true != $true) | ($true != ((in @ sK4 @ sK3))) | (((ordinal @ sK3)) != $true)),
% 0.34/0.43 inference(superposition,[],[f47,f121])).
% 0.34/0.43 thf(f124,plain,(
% 0.34/0.43 (((ordinal @ sK3)) != $true) | ($true != ((in @ sK4 @ sK3)))),
% 0.34/0.43 inference(trivial_inequality_removal,[],[f123])).
% 0.34/0.43 thf(f125,plain,(
% 0.34/0.43 ($true != ((in @ sK4 @ sK3)))),
% 0.34/0.43 inference(forward_subsumption_resolution,[],[f124,f48])).
% 0.34/0.43 thf(f126,plain,(
% 0.34/0.43 $false),
% 0.34/0.43 inference(forward_subsumption_resolution,[],[f125,f46])).
% 0.34/0.43 % SZS output end Proof for theBenchmark
% 0.34/0.43 % (866432)------------------------------
% 0.34/0.43 % (866432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.43 % (866432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.43 % (866432)CaDiCaL version: 2.1.3
% 0.34/0.43 % (866432)Termination reason: Refutation
% 0.34/0.43 % (866432)Time elapsed: 0.012 s
% 0.34/0.43 % (866432)Peak memory usage: 12 MB
% 0.34/0.43 % (866432)Instructions burned: 11 (million)
% 0.34/0.43 % (866423)Success in time 0.06 s
% 0.34/0.43 % Vampire exiting
%------------------------------------------------------------------------------