%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU695^2 : 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 : 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 : Wed Sep 30 08:30:49 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU695^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:11:33 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.29 % (2914663)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2914668)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1600817740:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2914670)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2125250833:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2914669)lrs+10_16_si=on:nwc=1.5:random_seed=2047751684:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2914672)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=331655528:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2914671)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=1602831305: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)
% 0.20/0.29 % (2914673)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=617432966:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (2914670)Instruction limit reached!
% 0.20/0.29 % (2914670)------------------------------
% 0.20/0.29 % (2914670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2914670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2914670)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2914670)Termination reason: Instruction limit
% 0.20/0.29 % (2914670)Termination phase: Saturation
% 0.20/0.29 % (2914670)Time elapsed: 0.002 s
% 0.20/0.29 % (2914670)Peak memory usage: 11 MB
% 0.20/0.29 % (2914670)Instructions burned: 3 (million)
% 0.20/0.29 % (2914674)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2914674)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
% 0.20/0.29 % (2914669)Instruction limit reached!
% 0.20/0.29 % (2914669)------------------------------
% 0.20/0.29 % (2914669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2914669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2914669)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2914669)Termination reason: Instruction limit
% 0.20/0.29 % (2914669)Termination phase: Saturation
% 0.20/0.29 % (2914669)Time elapsed: 0.010 s
% 0.20/0.29 % (2914669)Peak memory usage: 12 MB
% 0.20/0.29 % (2914669)Instructions burned: 19 (million)
% 0.20/0.29 % (2914672) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2914663-2914672"...
% 0.20/0.29 % (2914674)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=2394037808:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (2914671) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2914663-2914671"...
% 0.20/0.29 % (2914672)...printing done.
% 0.20/0.29 % (2914672)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.29 thf(func_def_1, type, kpair: ($i > $i > $i)).
% 0.20/0.29 thf(func_def_2, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 0.20/0.29 thf(func_def_3, type, dpsetconstrI: $o).
% 0.20/0.29 thf(func_def_5, type, func: ($i > $i > $i > $o)).
% 0.20/0.29 thf(func_def_6, type, ap: ($i > $i > $i > $i > $i)).
% 0.20/0.29 thf(func_def_7, type, lam: ($i > $i > ($i > $i) > $i)).
% 0.20/0.29 thf(func_def_8, type, lamp: $o).
% 0.20/0.29 thf(func_def_9, type, funcGraphProp2: $o).
% 0.20/0.29 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_18, type, sK1: ($i > $i > $o)).
% 0.20/0.29 thf(func_def_28, type, sK11: ($i > $i)).
% 0.20/0.29 thf(func_def_33, type, sK16: ($i > $i)).
% 0.20/0.29 thf(func_def_34, type, sK17: (($i > $i) > $i > $i > $i)).
% 0.20/0.29 thf(func_def_35, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 (dpsetconstrI = ! [X1 : $i,X0 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6)))))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 (lam = (^[X0 : $i, X1 : $i, X2 : ($i > $i)] : ((dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam)).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 (lamp = ! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp)).
% 0.20/0.29 thf(f4,axiom,(
% 0.20/0.29 (funcGraphProp2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X0 @ X1 @ X2 @ X3)) = X4))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2)).
% 0.20/0.29 thf(f5,conjecture,(
% 0.20/0.29 dpsetconstrI => (lamp => (funcGraphProp2 => ! [X2 : ($i > $i),X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3)))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1)).
% 0.20/0.29 thf(f6,negated_conjecture,(
% 0.20/0.29 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X2 : ($i > $i),X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3))))))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 (funcGraphProp2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (((ap @ X2 @ X1 @ X0 @ X3)) = X4))))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X2 : $i,X0 : $i,X1 : $i] : ((((func @ X2 @ X1 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => (($true = ((in @ (kpair @ X3 @ X4) @ X0))) => (((ap @ X2 @ X1 @ X0 @ X3)) = X4))))) <=> (funcGraphProp2 = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X0) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6)))))))))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ! [X3 : $i,X2 : ($i > $i > $o),X0 : $i,X1 : $i] : ((((in @ X3 @ X1)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((X2 @ X3 @ X4)) = $true) => (((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) = $true)))) <=> (dpsetconstrI = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => ! [X4 : $i] : ((in @ X4 @ X1) => (((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[X5 : $i] : ((X0 @ X5)))) @ X4)) = ((X0 @ X4))))))))),
% 0.20/0.29 inference(rectify,[],[f6])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ~((dpsetconstrI = $true) => ((lamp = $true) => ((funcGraphProp2 = $true) => ! [X2 : $i,X1 : $i,X0 : ($i > $i)] : (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((in @ (X0 @ X3) @ X2)) = $true)) => ! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => (((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4)) = ((X0 @ X4))))))))),
% 0.20/0.29 inference(fool_elimination,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 (lam = (^[X0 : $i, X1 : $i, X2 : ($i > $i)] : ((dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.20/0.29 inference(fool_elimination,[],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 (lamp = ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X4 : $i] : ((X0 @ X4)))))))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 (lamp = $true) <=> ! [X0 : ($i > $i),X2 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) = $true) => ($true = ((in @ (X0 @ X3) @ X1)))) => (((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f15])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((((ap @ X2 @ X1 @ X0 @ X3)) = X4) | ($true != ((in @ (kpair @ X3 @ X4) @ X0)))) | (((in @ X4 @ X1)) != $true)) | (((in @ X3 @ X2)) != $true)) | (((func @ X2 @ X1 @ X0)) != $true)) <=> (funcGraphProp2 = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f8])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 (funcGraphProp2 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ($true != ((in @ (kpair @ X3 @ X4) @ X0))) | (((ap @ X2 @ X1 @ X0 @ X3)) = X4))) | (((func @ X2 @ X1 @ X0)) != $true))),
% 0.20/0.29 inference(flattening,[],[f17])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ! [X3 : $i,X2 : ($i > $i > $o),X0 : $i,X1 : $i] : (! [X4 : $i] : (((((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) = $true) | (((X2 @ X3 @ X4)) != $true)) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true)) <=> (dpsetconstrI = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f10])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [X1 : $i,X2 : ($i > $i > $o),X3 : $i,X0 : $i] : (! [X4 : $i] : ((((X2 @ X3 @ X4)) != $true) | (((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) = $true) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true)) <=> (dpsetconstrI = $true)),
% 0.20/0.29 inference(flattening,[],[f19])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 (lamp = $true) <=> ! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : (($true != ((in @ (X0 @ X3) @ X1))) & (((in @ X3 @ X2)) = $true)) | (((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true))),
% 0.20/0.29 inference(ennf_transformation,[],[f16])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ((? [X1 : $i,X0 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((((in @ (X0 @ X3) @ X2)) = $true) | (((in @ X3 @ X1)) != $true)) & ? [X4 : $i] : ((((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4)) != ((X0 @ X4))) & (((in @ X4 @ X1)) = $true))) & (funcGraphProp2 = $true)) & (lamp = $true)) & (dpsetconstrI = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f12])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 (lamp = $true) & ? [X1 : $i,X0 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((((in @ (X0 @ X3) @ X2)) = $true) | (((in @ X3 @ X1)) != $true)) & ? [X4 : $i] : ((((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4)) != ((X0 @ X4))) & (((in @ X4 @ X1)) = $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 0.20/0.29 inference(flattening,[],[f22])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 (! [X1 : $i,X2 : ($i > $i > $o),X3 : $i,X0 : $i] : (! [X4 : $i] : ((((X2 @ X3 @ X4)) != $true) | (((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) = $true) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true)) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | ? [X1 : $i,X2 : ($i > $i > $o),X3 : $i,X0 : $i] : (? [X4 : $i] : ((((X2 @ X3 @ X4)) = $true) & (((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) != $true) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true)))),
% 0.20/0.29 inference(nnf_transformation,[],[f20])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i] : (! [X4 : $i] : ((((X1 @ X2 @ X4)) != $true) | (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) = $true) | (((in @ X4 @ X3)) != $true)) | (((in @ X2 @ X0)) != $true)) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | ? [X5 : $i,X6 : ($i > $i > $o),X7 : $i,X8 : $i] : (? [X9 : $i] : ((((X6 @ X7 @ X9)) = $true) & ($true != ((in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X5 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X6 @ Y0 @ Y1)))))))) & (((in @ X9 @ X8)) = $true)) & ($true = ((in @ X7 @ X5)))))),
% 0.20/0.29 inference(rectify,[],[f24])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i] : (! [X4 : $i] : ((((X1 @ X2 @ X4)) != $true) | (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) = $true) | (((in @ X4 @ X3)) != $true)) | (((in @ X2 @ X0)) != $true)) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | ((($true = ((sK1 @ sK2 @ sK4))) & (((in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) != $true) & (((in @ sK4 @ sK3)) = $true)) & (((in @ sK2 @ sK0)) = $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X5,sK0),skolemize(X6,sK1),skolemize(X7,sK2),skolemize(X8,sK3),skolemize(X9,sK4)],[f25])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ((funcGraphProp2 = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ($true = ((in @ (kpair @ X3 @ X4) @ X0))) & (((ap @ X2 @ X1 @ X0 @ X3)) != X4))) & (((func @ X2 @ X1 @ X0)) = $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ($true != ((in @ (kpair @ X3 @ X4) @ X0))) | (((ap @ X2 @ X1 @ X0 @ X3)) = X4))) | (((func @ X2 @ X1 @ X0)) != $true)) | (funcGraphProp2 != $true))),
% 0.20/0.29 inference(nnf_transformation,[],[f18])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & ($true = ((in @ (kpair @ X3 @ X4) @ X0))) & (((ap @ X1 @ X2 @ X0 @ X3)) != X4))) & (((func @ X1 @ X2 @ X0)) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : ((((in @ X8 @ X6)) != $true) | ! [X9 : $i] : ((((in @ X9 @ X7)) != $true) | (((in @ (kpair @ X8 @ X9) @ X5)) != $true) | (((ap @ X6 @ X7 @ X5 @ X8)) = X9))) | (((func @ X6 @ X7 @ X5)) != $true)) | (funcGraphProp2 != $true))),
% 0.20/0.29 inference(rectify,[],[f27])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ((funcGraphProp2 = $true) | (((((in @ sK8 @ sK6)) = $true) & (($true = ((in @ sK9 @ sK7))) & (((in @ (kpair @ sK8 @ sK9) @ sK5)) = $true) & (sK9 != ((ap @ sK6 @ sK7 @ sK5 @ sK8))))) & (((func @ sK6 @ sK7 @ sK5)) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : ((((in @ X8 @ X6)) != $true) | ! [X9 : $i] : ((((in @ X9 @ X7)) != $true) | (((in @ (kpair @ X8 @ X9) @ X5)) != $true) | (((ap @ X6 @ X7 @ X5 @ X8)) = X9))) | (((func @ X6 @ X7 @ X5)) != $true)) | (funcGraphProp2 != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9)],[f28])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 (lamp = $true) & ? [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : (($true = ((in @ (X1 @ X3) @ X2))) | (((in @ X3 @ X0)) != $true)) & ? [X4 : $i] : ((((ap @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))) @ X4)) != ((X1 @ X4))) & (((in @ X4 @ X0)) = $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 0.20/0.29 inference(rectify,[],[f23])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 (lamp = $true) & (! [X3 : $i] : ((((in @ (sK11 @ X3) @ sK12)) = $true) | (((in @ X3 @ sK10)) != $true)) & ((((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ (^[Y0 : $i]: (sK11 @ Y0))) @ sK13)) != ((sK11 @ sK13))) & (((in @ sK13 @ sK10)) = $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X4,sK13)],[f30])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ((lamp = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $i)] : (! [X3 : $i] : (($true = ((in @ (X0 @ X3) @ X1))) | (((in @ X3 @ X2)) != $true)) & (((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true))) & (! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : (($true != ((in @ (X0 @ X3) @ X1))) & (((in @ X3 @ X2)) = $true)) | (((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)) | (lamp != $true))),
% 0.20/0.29 inference(nnf_transformation,[],[f21])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ((lamp = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((((in @ (X2 @ X3) @ X0)) = $true) | (((in @ X3 @ X1)) != $true)) & (((func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) != $true))) & (! [X4 : $i,X5 : $i,X6 : ($i > $i)] : (? [X7 : $i] : ((((in @ (X6 @ X7) @ X4)) != $true) & ($true = ((in @ X7 @ X5)))) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))))) = $true)) | (lamp != $true))),
% 0.20/0.29 inference(rectify,[],[f32])).
% 0.20/0.29 thf(f34,plain,(
% 0.20/0.29 ((lamp = $true) | (! [X3 : $i] : ((((in @ (sK16 @ X3) @ sK14)) = $true) | ($true != ((in @ X3 @ sK15)))) & (((func @ sK15 @ sK14 @ (lam @ sK15 @ sK14 @ (^[Y0 : $i]: (sK16 @ Y0))))) != $true))) & (! [X4 : $i,X5 : $i,X6 : ($i > $i)] : (((((in @ (X6 @ (sK17 @ X6 @ X5 @ X4)) @ X4)) != $true) & (((in @ (sK17 @ X6 @ X5 @ X4) @ X5)) = $true)) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))))) = $true)) | (lamp != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,vAPP]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X7,sK17 @ X6 @ X5 @ X4)],[f33])).
% 0.20/0.29 thf(f39,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $i > $o),X4 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X4 @ X3)) != $true) | (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) = $true) | (((X1 @ X2 @ X4)) != $true) | (dpsetconstrI != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f26])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : ((((ap @ X6 @ X7 @ X5 @ X8)) = X9) | (((in @ X9 @ X7)) != $true) | (funcGraphProp2 != $true) | (((in @ (kpair @ X8 @ X9) @ X5)) != $true) | (((func @ X6 @ X7 @ X5)) != $true) | (((in @ X8 @ X6)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f29])).
% 0.20/0.29 thf(f47,plain,(
% 0.20/0.29 (dpsetconstrI = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 (funcGraphProp2 = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f49,plain,(
% 0.20/0.29 (((in @ sK13 @ sK10)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ (^[Y0 : $i]: (sK11 @ Y0))) @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 ( ! [X3 : $i] : ((((in @ (sK11 @ X3) @ sK12)) = $true) | (((in @ X3 @ sK10)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 (lamp = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f31])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((lamp != $true) | (((in @ (sK17 @ X6 @ X5 @ X4) @ X5)) = $true) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f34])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((((in @ (X6 @ (sK17 @ X6 @ X5 @ X4)) @ X4)) != $true) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))))) = $true) | (lamp != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f34])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $i > $o),X4 : $i] : ((((in @ X4 @ X3)) != $true) | (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ X1))) = $true) | (((X1 @ X2 @ X4)) != $true) | (dpsetconstrI != $true) | (((in @ X2 @ X0)) != $true)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f39])).
% 0.20/0.29 thf(f59,plain,(
% 0.20/0.29 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (Y2 @ Y3))))))))))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f40])).
% 0.20/0.29 thf(f62,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((((func @ X5 @ X4 @ (lam @ X5 @ X4 @ X6))) = $true) | (((in @ (sK17 @ X6 @ X5 @ X4) @ X5)) = $true) | (lamp != $true)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f53])).
% 0.20/0.29 thf(f63,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((((in @ (X6 @ (sK17 @ X6 @ X5 @ X4)) @ X4)) != $true) | (lamp != $true) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ X6))) = $true)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f54])).
% 0.20/0.29 thf(f64,plain,(
% 0.20/0.29 (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f50])).
% 0.20/0.29 thf(f68,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((((func @ X5 @ X4 @ (lam @ X5 @ X4 @ X6))) = $true) | (((in @ (sK17 @ X6 @ X5 @ X4) @ X5)) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f62,f52])).
% 0.20/0.29 thf(f69,plain,(
% 0.20/0.29 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (Y2 @ Y3))))))))) @ X1)) = ((lam @ X1)))) )),
% 0.20/0.29 inference(argument_congruence,[],[f59])).
% 0.20/0.29 thf(f70,plain,(
% 0.20/0.29 ( ! [X1 : $i] : (((^[Y0 : $i]: ((^[Y1 : $i > $i]: (dpsetconstr @ X1 @ Y0 @ (^[Y2 : $i]: (= @ (Y1 @ Y2))))))) = ((lam @ X1)))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f69])).
% 0.20/0.29 thf(f71,plain,(
% 0.20/0.29 ( ! [X6 : ($i > $i),X4 : $i,X5 : $i] : ((((in @ (X6 @ (sK17 @ X6 @ X5 @ X4)) @ X4)) != $true) | (((func @ X5 @ X4 @ (lam @ X5 @ X4 @ X6))) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f63,f52])).
% 0.20/0.29 thf(f72,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != $true) | (((func @ X0 @ sK12 @ (lam @ X0 @ sK12 @ sK11))) = $true) | (((in @ (sK17 @ sK11 @ X0 @ sK12) @ sK10)) != $true)) )),
% 0.20/0.29 inference(superposition,[],[f71,f51])).
% 0.20/0.29 thf(f73,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((((func @ X0 @ sK12 @ (lam @ X0 @ sK12 @ sK11))) = $true) | (((in @ (sK17 @ sK11 @ X0 @ sK12) @ sK10)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f72])).
% 0.20/0.29 thf(f74,plain,(
% 0.20/0.29 ( ! [X2 : $i,X1 : $i] : ((((lam @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i > $i]: (dpsetconstr @ X1 @ Y0 @ (^[Y2 : $i]: (= @ (Y1 @ Y2))))))) @ X2)))) )),
% 0.20/0.29 inference(argument_congruence,[],[f70])).
% 0.20/0.29 thf(f75,plain,(
% 0.20/0.29 ( ! [X2 : $i,X1 : $i] : (((^[Y0 : $i > $i]: (dpsetconstr @ X1 @ X2 @ (^[Y1 : $i]: (= @ (Y0 @ Y1))))) = ((lam @ X1 @ X2)))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f74])).
% 0.20/0.29 thf(f76,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : ($i > $i),X1 : $i] : (((((^[Y0 : $i > $i]: (dpsetconstr @ X1 @ X2 @ (^[Y1 : $i]: (= @ (Y0 @ Y1))))) @ X3)) = ((lam @ X1 @ X2 @ X3)))) )),
% 0.20/0.29 inference(argument_congruence,[],[f75])).
% 0.20/0.29 thf(f77,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : ($i > $i),X1 : $i] : ((((dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = ((lam @ X1 @ X2 @ X3)))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f76])).
% 0.20/0.29 thf(f78,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $i > $o),X4 : $i] : ((((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ X1))) = $true) | (((in @ X4 @ X3)) != $true) | (((X1 @ X2 @ X4)) != $true) | (((in @ X2 @ X0)) != $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f58,f47])).
% 0.20/0.29 thf(f82,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X1)) != $true) | ((((^[Y0 : $i]: (= @ (X2 @ Y0))) @ X3 @ X4)) != $true) | (((in @ X3 @ X0)) != $true) | (((in @ (kpair @ X3 @ X4) @ (lam @ X0 @ X1 @ X2))) = $true)) )),
% 0.20/0.29 inference(superposition,[],[f78,f77])).
% 0.20/0.29 thf(f83,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (lam @ X0 @ X1 @ X2))) = $true) | (((in @ X3 @ X0)) != $true) | ((((X2 @ X3) = X4)) != $true) | (((in @ X4 @ X1)) != $true)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f82])).
% 0.20/0.29 thf(f84,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (lam @ X0 @ X1 @ X2))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X4 @ X1)) != $true) | (((X2 @ X3)) != X4)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f83])).
% 0.20/0.29 thf(f89,plain,(
% 0.20/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : ((((in @ (kpair @ X8 @ X9) @ X5)) != $true) | (((ap @ X6 @ X7 @ X5 @ X8)) = X9) | (((in @ X9 @ X7)) != $true) | (((in @ X8 @ X6)) != $true) | (((func @ X6 @ X7 @ X5)) != $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f41,f48])).
% 0.20/0.29 thf(f91,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X6 : $i,X4 : ($i > $i),X5 : $i] : (($true != $true) | (((X4 @ X0)) != X1) | (((in @ X0 @ X2)) != $true) | (((func @ X5 @ X6 @ (lam @ X2 @ X3 @ X4))) != $true) | (((in @ X1 @ X6)) != $true) | (((in @ X0 @ X5)) != $true) | (((in @ X1 @ X3)) != $true) | (((ap @ X5 @ X6 @ (lam @ X2 @ X3 @ X4) @ X0)) = X1)) )),
% 0.20/0.29 inference(superposition,[],[f89,f84])).
% 0.20/0.29 thf(f93,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X6 : $i,X4 : ($i > $i),X5 : $i] : ((((func @ X5 @ X6 @ (lam @ X2 @ X3 @ X4))) != $true) | (((in @ X1 @ X3)) != $true) | (((in @ X0 @ X2)) != $true) | (((in @ X1 @ X6)) != $true) | (((ap @ X5 @ X6 @ (lam @ X2 @ X3 @ X4) @ X0)) = X1) | (((in @ X0 @ X5)) != $true) | (((X4 @ X0)) != X1)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f91])).
% 0.20/0.29 thf(f94,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4)) = X3) | (((in @ X4 @ X0)) != $true) | ($true != $true) | (((in @ X3 @ X1)) != $true) | (((in @ (sK17 @ X2 @ X0 @ X1) @ X0)) = $true) | (((in @ X4 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((X2 @ X4)) != X3)) )),
% 0.20/0.29 inference(superposition,[],[f93,f68])).
% 0.20/0.29 thf(f95,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK11 @ X2)) != X1) | (((in @ X1 @ sK12)) != $true) | (((ap @ X0 @ sK12 @ (lam @ X0 @ sK12 @ sK11) @ X2)) = X1) | (((in @ (sK17 @ sK11 @ X0 @ sK12) @ sK10)) != $true) | (((in @ X2 @ X0)) != $true) | (((in @ X1 @ sK12)) != $true) | (((in @ X2 @ X0)) != $true) | ($true != $true)) )),
% 0.20/0.29 inference(superposition,[],[f93,f73])).
% 0.20/0.29 thf(f96,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X3 @ X1)) != $true) | ($true != $true) | (((X2 @ X4)) != X3) | (((in @ X4 @ X0)) != $true) | (((in @ (sK17 @ X2 @ X0 @ X1) @ X0)) = $true) | (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4)) = X3)) )),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f94])).
% 0.20/0.29 thf(f97,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X4 @ X0)) != $true) | (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4)) = X3) | (((in @ (sK17 @ X2 @ X0 @ X1) @ X0)) = $true) | (((X2 @ X4)) != X3)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f96])).
% 0.20/0.29 thf(f98,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ sK12)) != $true) | (((sK11 @ X2)) != X1) | (((ap @ X0 @ sK12 @ (lam @ X0 @ sK12 @ sK11) @ X2)) = X1) | (((in @ (sK17 @ sK11 @ X0 @ sK12) @ sK10)) != $true) | (((in @ X2 @ X0)) != $true) | ($true != $true)) )),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f95])).
% 0.20/0.29 thf(f99,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ sK11 @ X0 @ sK12) @ sK10)) != $true) | (((in @ X1 @ sK12)) != $true) | (((ap @ X0 @ sK12 @ (lam @ X0 @ sK12 @ sK11) @ X2)) = X1) | (((sK11 @ X2)) != X1) | (((in @ X2 @ X0)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f98])).
% 0.20/0.29 thf(f101,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : ($i > $i),X0 : $i,X1 : $i] : ((((sK11 @ X0)) != ((X3 @ X1))) | ($true != ((in @ X0 @ sK10))) | (((ap @ X2 @ sK12 @ (lam @ X2 @ sK12 @ X3) @ X1)) = ((sK11 @ X0))) | ($true != $true) | (((in @ X1 @ X2)) != $true) | ($true = ((in @ (sK17 @ X3 @ X2 @ sK12) @ X2)))) )),
% 0.20/0.29 inference(superposition,[],[f97,f51])).
% 0.20/0.29 thf(f105,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : ($i > $i),X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK10))) | (((in @ X1 @ X2)) != $true) | (((sK11 @ X0)) != ((X3 @ X1))) | (((ap @ X2 @ sK12 @ (lam @ X2 @ sK12 @ X3) @ X1)) = ((sK11 @ X0))) | ($true = ((in @ (sK17 @ X3 @ X2 @ sK12) @ X2)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f101])).
% 0.20/0.29 thf(f112,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((ap @ X1 @ sK12 @ (lam @ X1 @ sK12 @ X2) @ X0)) = ((sK11 @ sK13))) | (((in @ (sK17 @ X2 @ X1 @ sK12) @ X1)) = $true) | (((X2 @ X0)) != ((sK11 @ sK13))) | ($true != $true)) )),
% 0.20/0.29 inference(superposition,[],[f105,f49])).
% 0.20/0.29 thf(f113,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((ap @ X1 @ sK12 @ (lam @ X1 @ sK12 @ X2) @ X0)) = ((sK11 @ sK13))) | (((in @ (sK17 @ X2 @ X1 @ sK12) @ X1)) = $true) | (((X2 @ X0)) != ((sK11 @ sK13))) | (((in @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f112])).
% 0.20/0.29 thf(f114,plain,(
% 0.20/0.29 (((in @ sK13 @ sK10)) != $true) | ($true = ((in @ (sK17 @ sK11 @ sK10 @ sK12) @ sK10))) | (((sK11 @ sK13)) != ((sK11 @ sK13))) | (((sK11 @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.29 inference(superposition,[],[f64,f113])).
% 0.20/0.29 thf(f116,plain,(
% 0.20/0.29 ($true = ((in @ (sK17 @ sK11 @ sK10 @ sK12) @ sK10))) | (((in @ sK13 @ sK10)) != $true) | (((sK11 @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f114])).
% 0.20/0.29 thf(f117,plain,(
% 0.20/0.29 (((in @ sK13 @ sK10)) != $true) | ($true = ((in @ (sK17 @ sK11 @ sK10 @ sK12) @ sK10)))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f116])).
% 0.20/0.29 thf(f118,plain,(
% 0.20/0.29 ($true = ((in @ (sK17 @ sK11 @ sK10 @ sK12) @ sK10)))),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f117,f49])).
% 0.20/0.29 thf(f119,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ sK12)) != $true) | (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X1)) = X0) | ($true != $true) | (((sK11 @ X1)) != X0) | (((in @ X1 @ sK10)) != $true)) )),
% 0.20/0.29 inference(superposition,[],[f99,f118])).
% 0.20/0.29 thf(f123,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ sK12)) != $true) | (((in @ X1 @ sK10)) != $true) | (((sK11 @ X1)) != X0) | (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X1)) = X0)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f119])).
% 0.20/0.29 thf(f128,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ sK10)) != $true) | (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X1)) = ((sK11 @ X0))) | ($true != ((in @ X0 @ sK10))) | (((sK11 @ X1)) != ((sK11 @ X0))) | ($true != $true)) )),
% 0.20/0.30 inference(superposition,[],[f123,f51])).
% 0.20/0.30 thf(f129,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK10))) | (((in @ X1 @ sK10)) != $true) | (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X1)) = ((sK11 @ X0))) | (((sK11 @ X1)) != ((sK11 @ X0)))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f128])).
% 0.20/0.30 thf(f130,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK10))) | (((sK11 @ X0)) != ((sK11 @ sK13))) | (((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X0)) = ((sK11 @ sK13)))) )),
% 0.20/0.30 inference(superposition,[],[f129,f49])).
% 0.20/0.30 thf(f133,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((ap @ sK10 @ sK12 @ (lam @ sK10 @ sK12 @ sK11) @ X0)) = ((sK11 @ sK13))) | ($true != ((in @ X0 @ sK10))) | (((sK11 @ X0)) != ((sK11 @ sK13)))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f130])).
% 0.20/0.30 thf(f134,plain,(
% 0.20/0.30 (((in @ sK13 @ sK10)) != $true) | (((sK11 @ sK13)) != ((sK11 @ sK13))) | (((sK11 @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.30 inference(superposition,[],[f64,f133])).
% 0.20/0.30 thf(f136,plain,(
% 0.20/0.30 (((in @ sK13 @ sK10)) != $true) | (((sK11 @ sK13)) != ((sK11 @ sK13)))),
% 0.20/0.30 inference(duplicate_literal_removal,[],[f134])).
% 0.20/0.30 thf(f137,plain,(
% 0.20/0.30 (((in @ sK13 @ sK10)) != $true)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f136])).
% 0.20/0.30 thf(f138,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f137,f49])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (2914672)------------------------------
% 0.20/0.30 % (2914672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2914672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2914672)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2914672)Termination reason: Refutation
% 0.20/0.30 % (2914672)Time elapsed: 0.016 s
% 0.20/0.30 % (2914672)Peak memory usage: 12 MB
% 0.20/0.30 % (2914672)Instructions burned: 27 (million)
% 0.20/0.30 % (2914663)Success in time 0.053 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------