%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:38:13 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:32:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.32 % (2999110)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (2999121)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (2999121)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
% 0.22/0.32 % (2999117)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3861593572:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (2999116)lrs+10_16_si=on:nwc=1.5:random_seed=1592092193:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (2999120)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3170455327:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (2999115)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=40676231:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (2999118)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=2978067379: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)
% 0.22/0.32 % (2999121)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=2935459735:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (2999119)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1959431543:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (2999117)Instruction limit reached!
% 0.22/0.32 % (2999117)------------------------------
% 0.22/0.32 % (2999117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2999117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2999117)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2999117)Termination reason: Instruction limit
% 0.22/0.32 % (2999117)Termination phase: Saturation
% 0.22/0.32 % (2999117)Time elapsed: 0.014 s
% 0.22/0.32 % (2999117)Peak memory usage: 12 MB
% 0.22/0.32 % (2999117)Instructions burned: 3 (million)
% 0.22/0.32 % (2999115) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2999110-2999115"...
% 0.22/0.32 % (2999115)...printing done.
% 0.22/0.32 % (2999116)Instruction limit reached!
% 0.22/0.32 % (2999116)------------------------------
% 0.22/0.32 % (2999116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2999116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2999116)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2999116)Termination reason: Instruction limit
% 0.22/0.32 % (2999116)Termination phase: Saturation
% 0.22/0.32 % (2999116)Time elapsed: 0.022 s
% 0.22/0.32 % (2999116)Peak memory usage: 12 MB
% 0.22/0.32 % (2999116)Instructions burned: 19 (million)
% 0.22/0.32 % (2999115)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_0, type, cONE: (($i > $o) > $o)).
% 0.22/0.32 thf(func_def_1, type, cSUCC: ((($i > $o) > $o) > ($i > $o) > $o)).
% 0.22/0.32 thf(func_def_2, type, cZERO: (($i > $o) > $o)).
% 0.22/0.32 thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.32 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_10, type, vAND: ($o > $o > $o)).
% 0.22/0.32 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_12, type, sK0: (($i > $i) > ($i > $i) > $i)).
% 0.22/0.32 thf(func_def_15, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_16, type, sK1: ($i > $o)).
% 0.22/0.32 thf(func_def_17, type, sK2: ($i > $i)).
% 0.22/0.32 thf(func_def_21, type, sK6: ($i > $i)).
% 0.22/0.32 thf(f1,axiom,(
% 0.22/0.32 ((^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.22/0.32 thf(f2,axiom,(
% 0.22/0.32 ((^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2))))))) = cSUCC)),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 (cONE = ((cSUCC @ cZERO)))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cONE_def)).
% 0.22/0.32 thf(f4,conjecture,(
% 0.22/0.32 ! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => ((^[X3 : ($i > $o)] : (? [X4 : $i] : ((((^[X2 : $i, X4 : $i] : ((X2 = X4))) @ X4)) = X3))) = cONE)),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_EXT_pme)).
% 0.22/0.32 thf(f5,negated_conjecture,(
% 0.22/0.32 ~(! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => ((^[X3 : ($i > $o)] : (? [X4 : $i] : ((((^[X2 : $i, X4 : $i] : ((X2 = X4))) @ X4)) = X3))) = cONE))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.32 thf(f6,plain,(
% 0.22/0.32 ~(! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => ((^[X3 : ($i > $o)] : (? [X4 : $i] : ((((^[X5 : $i, X6 : $i] : ((X5 = X6))) @ X4)) = X3))) = cONE))),
% 0.22/0.32 inference(rectify,[],[f5])).
% 0.22/0.32 thf(f7,plain,(
% 0.22/0.32 ~(! [X1 : ($i > $i),X0 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => (cONE = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0))))))),
% 0.22/0.32 inference(fool_elimination,[],[f6])).
% 0.22/0.32 thf(f8,plain,(
% 0.22/0.32 ((^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 0.22/0.32 inference(rectify,[],[f1])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.32 inference(fool_elimination,[],[f8])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 ((^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2))))))) = cSUCC)),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f10])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ! [X0 : ($i > $i),X1 : ($i > $i)] : (? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2))) | (X0 = X1)) & (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 0.22/0.32 inference(ennf_transformation,[],[f7])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ! [X0 : ($i > $i),X1 : ($i > $i)] : ((((X1 @ (sK0 @ X1 @ X0))) != ((X0 @ (sK0 @ X1 @ X0)))) | (X0 = X1)) & (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f12])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.32 inference(cnf_transformation,[],[f9])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 0.22/0.32 inference(cnf_transformation,[],[f13])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 0.22/0.32 inference(cnf_transformation,[],[f11])).
% 0.22/0.32 thf(f18,plain,(
% 0.22/0.32 (cONE = ((cSUCC @ cZERO)))),
% 0.22/0.32 inference(cnf_transformation,[],[f3])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 (cONE = (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 0.22/0.32 inference(definition_unfolding,[],[f18,f17,f14])).
% 0.22/0.32 thf(f22,plain,(
% 0.22/0.32 ((((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 0.22/0.32 inference(definition_unfolding,[],[f15,f21])).
% 0.22/0.32 thf(f23,plain,(
% 0.22/0.32 ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))))),
% 0.22/0.32 inference(beta-eta_normalization,[],[f22])).
% 0.22/0.32 thf(f25,plain,(
% 0.22/0.32 ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1)) != (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))) @ sK1)))),
% 0.22/0.32 inference(negative_extensionality,[],[f23])).
% 0.22/0.32 thf(f26,plain,(
% 0.22/0.32 ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))) @ sK1)) = $true) | ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1)) = $true)),
% 0.22/0.32 inference(xor_proxy_clausification,[],[f25])).
% 0.22/0.32 thf(f27,plain,(
% 0.22/0.32 ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1)) = $false) | ($false = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))) @ sK1)))),
% 0.22/0.32 inference(xor_proxy_clausification,[],[f25])).
% 0.22/0.32 thf(f28,plain,(
% 0.22/0.32 ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0)))))) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK1)))))),
% 0.22/0.32 inference(beta-eta_normalization,[],[f27])).
% 0.22/0.32 thf(f29,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))) @ X1))) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK1)))))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f28])).
% 0.22/0.32 thf(f30,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))) @ X1))) | ($false = (((^[Y0 : $i]: ((= @ Y0) = sK1)) @ X2)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f29])).
% 0.22/0.32 thf(f31,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (((((~ (?? @ $i @ (^[Y0 : $i]: ((~ (X1 = Y0)) & (sK1 @ Y0))))) & (sK1 @ X1))) = $false) | ((((= @ X2) = sK1)) = $false)) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f30])).
% 0.22/0.32 thf(f32,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (X1 = Y0)) & (sK1 @ Y0))))))) | ((((= @ X2) = sK1)) = $false) | (((sK1 @ X1)) = $false)) )),
% 0.22/0.32 inference(and_proxy_clausification,[],[f31])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | (((?? @ $i @ (^[Y0 : $i]: ((~ (X1 = Y0)) & (sK1 @ Y0))))) = $true) | ((((= @ X2) = sK1)) = $false)) )),
% 0.22/0.32 inference(not_proxy_clausification,[],[f32])).
% 0.22/0.32 thf(f34,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((~ (X1 = Y0)) & (sK1 @ Y0))) @ (sK2 @ X1)))) | ((((= @ X2) = sK1)) = $false)) )),
% 0.22/0.32 inference(sigma_proxy_clausification,[],[f33])).
% 0.22/0.32 thf(f35,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((~ (X1 = Y0)) & (sK1 @ Y0))) @ (sK2 @ X1)))) | (((= @ X2)) != sK1)) )),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f34])).
% 0.22/0.32 thf(f36,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((= @ X2)) != sK1) | ($true = (((~ (X1 = (sK2 @ X1))) & (sK1 @ (sK2 @ X1))))) | (((sK1 @ X1)) = $false)) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f35])).
% 0.22/0.32 thf(f37,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | (((= @ X2)) != sK1) | (((sK1 @ (sK2 @ X1))) = $true)) )),
% 0.22/0.32 inference(and_proxy_clausification,[],[f36])).
% 0.22/0.32 thf(f38,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((~ (X1 = (sK2 @ X1)))) = $true) | (((sK1 @ X1)) = $false) | (((= @ X2)) != sK1)) )),
% 0.22/0.32 inference(and_proxy_clausification,[],[f36])).
% 0.22/0.32 thf(f39,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | (((X1 = (sK2 @ X1))) = $false) | (((= @ X2)) != sK1)) )),
% 0.22/0.32 inference(not_proxy_clausification,[],[f38])).
% 0.22/0.32 thf(f40,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $false) | (((= @ X2)) != sK1) | (((sK2 @ X1)) != X1)) )),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f39])).
% 0.22/0.32 thf(f41,plain,(
% 0.22/0.32 ($true = ((?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK1))))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))))))),
% 0.22/0.32 inference(beta-eta_normalization,[],[f26])).
% 0.22/0.32 thf(f42,plain,(
% 0.22/0.32 ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0)))))) | ((((^[Y0 : $i]: ((= @ Y0) = sK1)) @ sK3)) = $true)),
% 0.22/0.32 inference(sigma_proxy_clausification,[],[f41])).
% 0.22/0.32 thf(f43,plain,(
% 0.22/0.32 ($true = (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))) @ sK4))) | ((((^[Y0 : $i]: ((= @ Y0) = sK1)) @ sK3)) = $true)),
% 0.22/0.32 inference(sigma_proxy_clausification,[],[f42])).
% 0.22/0.32 thf(f44,plain,(
% 0.22/0.32 ($true = (((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))))) & (sK1 @ sK4)))) | ((((= @ sK3) = sK1)) = $true)),
% 0.22/0.32 inference(beta-eta_normalization,[],[f43])).
% 0.22/0.32 thf(f45,plain,(
% 0.22/0.32 (((sK1 @ sK4)) = $true) | ((((= @ sK3) = sK1)) = $true)),
% 0.22/0.32 inference(and_proxy_clausification,[],[f44])).
% 0.22/0.32 thf(f46,plain,(
% 0.22/0.32 ((((= @ sK3) = sK1)) = $true) | ($true = ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0)))))))),
% 0.22/0.32 inference(and_proxy_clausification,[],[f44])).
% 0.22/0.32 thf(f47,plain,(
% 0.22/0.32 ($true = ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))))))) | (((= @ sK3)) = sK1)),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f46])).
% 0.22/0.32 thf(f48,plain,(
% 0.22/0.32 ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0)))))) | (((= @ sK3)) = sK1)),
% 0.22/0.32 inference(not_proxy_clausification,[],[f47])).
% 0.22/0.32 thf(f49,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))) @ X1))) | (((= @ sK3)) = sK1)) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f48])).
% 0.22/0.32 thf(f50,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((= @ sK3)) = sK1) | ($false = (((~ (sK4 = X1)) & (sK1 @ X1))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f49])).
% 0.22/0.32 thf(f51,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((= @ sK3)) = sK1) | (((~ (sK4 = X1))) = $false) | (((sK1 @ X1)) = $false)) )),
% 0.22/0.32 inference(and_proxy_clausification,[],[f50])).
% 0.22/0.32 thf(f52,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (((= @ sK3)) = sK1) | ($true = ((sK4 = X1)))) )),
% 0.22/0.32 inference(not_proxy_clausification,[],[f51])).
% 0.22/0.32 thf(f53,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (sK4 = X1) | (((= @ sK3)) = sK1)) )),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f52])).
% 0.22/0.32 thf(f54,plain,(
% 0.22/0.32 (((= @ sK3)) = sK1) | (((sK1 @ sK4)) = $true)),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f45])).
% 0.22/0.32 thf(f56,definition,(
% 0.22/0.32 spl5_1 <=> ! [X2 : $i] : (((= @ X2)) != sK1)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.32 thf(f57,plain,(
% 0.22/0.32 ( ! [X2 : $i] : ((((= @ X2)) != sK1)) ) | ~spl5_1),
% 0.22/0.32 inference(avatar_component_clause,[],[f56])).
% 0.22/0.32 thf(f59,definition,(
% 0.22/0.32 spl5_2 <=> ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (((sK2 @ X1)) != X1))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.22/0.32 thf(f60,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK2 @ X1)) != X1) | (((sK1 @ X1)) = $false)) ) | ~spl5_2),
% 0.22/0.32 inference(avatar_component_clause,[],[f59])).
% 0.22/0.32 thf(f61,plain,(
% 0.22/0.32 spl5_1 | spl5_2),
% 0.22/0.32 inference(avatar_split_clause,[],[f40,f59,f56])).
% 0.22/0.32 thf(f63,definition,(
% 0.22/0.32 spl5_3 <=> ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (((sK1 @ (sK2 @ X1))) = $true))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.22/0.32 thf(f64,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ (sK2 @ X1))) = $true) | (((sK1 @ X1)) = $false)) ) | ~spl5_3),
% 0.22/0.32 inference(avatar_component_clause,[],[f63])).
% 0.22/0.32 thf(f65,plain,(
% 0.22/0.32 spl5_1 | spl5_3),
% 0.22/0.32 inference(avatar_split_clause,[],[f37,f63,f56])).
% 0.22/0.32 thf(f67,definition,(
% 0.22/0.32 spl5_4 <=> ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (sK4 = X1))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.22/0.32 thf(f68,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (sK4 = X1)) ) | ~spl5_4),
% 0.22/0.32 inference(avatar_component_clause,[],[f67])).
% 0.22/0.32 thf(f70,definition,(
% 0.22/0.32 spl5_5 <=> (((= @ sK3)) = sK1)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.22/0.32 thf(f72,plain,(
% 0.22/0.32 (((= @ sK3)) = sK1) | ~spl5_5),
% 0.22/0.32 inference(avatar_component_clause,[],[f70])).
% 0.22/0.32 thf(f73,plain,(
% 0.22/0.32 spl5_4 | spl5_5),
% 0.22/0.32 inference(avatar_split_clause,[],[f53,f70,f67])).
% 0.22/0.32 thf(f75,definition,(
% 0.22/0.32 spl5_6 <=> (((sK1 @ sK4)) = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.22/0.32 thf(f77,plain,(
% 0.22/0.32 (((sK1 @ sK4)) = $true) | ~spl5_6),
% 0.22/0.32 inference(avatar_component_clause,[],[f75])).
% 0.22/0.32 thf(f78,plain,(
% 0.22/0.32 spl5_6 | spl5_5),
% 0.22/0.32 inference(avatar_split_clause,[],[f54,f70,f75])).
% 0.22/0.32 thf(f79,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK3 = X1)) = ((sK1 @ X1)))) ) | ~spl5_5),
% 0.22/0.32 inference(argument_congruence,[],[f72])).
% 0.22/0.32 thf(f80,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (((sK3 = X1)) = $true)) ) | ~spl5_5),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f79])).
% 0.22/0.32 thf(f81,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | (((sK3 = X1)) = $false)) ) | ~spl5_5),
% 0.22/0.32 inference(iff_proxy_clausification,[],[f79])).
% 0.22/0.32 thf(f82,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((sK3 != X1) | (((sK1 @ X1)) = $true)) ) | ~spl5_5),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f81])).
% 0.22/0.32 thf(f83,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((sK1 @ X1)) = $false) | (sK3 = X1)) ) | ~spl5_5),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f80])).
% 0.22/0.32 thf(f84,plain,(
% 0.22/0.32 (((sK1 @ sK3)) = $true) | (sK3 != sK3) | ~spl5_5),
% 0.22/0.32 inference(imitation,[],[f82])).
% 0.22/0.32 thf(f86,plain,(
% 0.22/0.32 (((sK1 @ sK3)) = $true) | ~spl5_5),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.32 thf(f88,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((sK2 @ X0)) = sK3) | ($false = $true) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(constrained_superposition,[],[f64,f83])).
% 0.22/0.32 thf(f90,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((sK2 @ X0)) = sK3) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f88])).
% 0.22/0.32 thf(f93,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | ($false = ((sK1 @ X0))) | (sK3 != X0)) ) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(constrained_superposition,[],[f60,f90])).
% 0.22/0.32 thf(f95,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | (sK3 != X0)) ) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f93])).
% 0.22/0.32 thf(f96,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f95,f83])).
% 0.22/0.32 thf(f97,plain,(
% 0.22/0.32 ($false = $true) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(constrained_superposition,[],[f96,f86])).
% 0.22/0.32 thf(f104,plain,(
% 0.22/0.32 $false | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f97])).
% 0.22/0.32 thf(f105,plain,(
% 0.22/0.32 ~spl5_2 | ~spl5_3 | ~spl5_5),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f104])).
% 0.22/0.32 thf(f107,plain,(
% 0.22/0.32 ( ! [X2 : $i] : ((((sK1 @ (sK6 @ X2))) != ((X2 = (sK6 @ X2))))) ) | ~spl5_1),
% 0.22/0.32 inference(negative_extensionality,[],[f57])).
% 0.22/0.32 thf(f108,plain,(
% 0.22/0.32 (sK1 != sK1) | (~spl5_1 | ~spl5_5)),
% 0.22/0.32 inference(constrained_superposition,[],[f57,f72])).
% 0.22/0.32 thf(f109,plain,(
% 0.22/0.32 $false | (~spl5_1 | ~spl5_5)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f108])).
% 0.22/0.32 thf(f110,plain,(
% 0.22/0.32 ~spl5_1 | ~spl5_5),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f109])).
% 0.22/0.32 thf(f111,plain,(
% 0.22/0.32 ( ! [X2 : $i] : (($true = ((sK1 @ (sK6 @ X2)))) | ($true = ((X2 = (sK6 @ X2))))) ) | ~spl5_1),
% 0.22/0.32 inference(xor_proxy_clausification,[],[f107])).
% 0.22/0.32 thf(f112,plain,(
% 0.22/0.32 ( ! [X2 : $i] : (($false = ((sK1 @ (sK6 @ X2)))) | ($false = ((X2 = (sK6 @ X2))))) ) | ~spl5_1),
% 0.22/0.32 inference(xor_proxy_clausification,[],[f107])).
% 0.22/0.32 thf(f113,plain,(
% 0.22/0.32 ( ! [X2 : $i] : ((((sK6 @ X2)) != X2) | ($false = ((sK1 @ (sK6 @ X2))))) ) | ~spl5_1),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f112])).
% 0.22/0.32 thf(f114,plain,(
% 0.22/0.32 ( ! [X2 : $i] : (($true = ((sK1 @ (sK6 @ X2)))) | (((sK6 @ X2)) = X2)) ) | ~spl5_1),
% 0.22/0.32 inference(equality_proxy_clausification,[],[f111])).
% 0.22/0.32 thf(f117,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = $true) | (((sK6 @ X0)) = sK4) | (((sK6 @ X0)) = X0)) ) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(constrained_superposition,[],[f68,f114])).
% 0.22/0.32 thf(f118,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((sK6 @ X0)) = X0) | (((sK6 @ X0)) = sK4)) ) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f117])).
% 0.22/0.32 thf(f123,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((sK4 != X0) | (((sK6 @ X0)) = sK4)) ) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(equality_factoring,[],[f118])).
% 0.22/0.32 thf(f128,plain,(
% 0.22/0.32 (((sK6 @ sK4)) = sK4) | (sK4 != sK4) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(imitation,[],[f123])).
% 0.22/0.32 thf(f130,plain,(
% 0.22/0.32 (((sK6 @ sK4)) = sK4) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f128])).
% 0.22/0.32 thf(f131,plain,(
% 0.22/0.32 (((sK1 @ sK4)) = $false) | (sK4 != sK4) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(constrained_superposition,[],[f113,f130])).
% 0.22/0.32 thf(f132,plain,(
% 0.22/0.32 (((sK1 @ sK4)) = $false) | (~spl5_1 | ~spl5_4)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f131])).
% 0.22/0.32 thf(f133,plain,(
% 0.22/0.32 ($false = $true) | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 0.22/0.32 inference(forward_demodulation,[],[f132,f77])).
% 0.22/0.32 thf(f134,plain,(
% 0.22/0.32 $false | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f133])).
% 0.22/0.32 thf(f135,plain,(
% 0.22/0.32 ~spl5_1 | ~spl5_4 | ~spl5_6),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f134])).
% 0.22/0.32 thf(f156,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | (((sK2 @ X0)) = sK4) | ($false = $true)) ) | (~spl5_3 | ~spl5_4)),
% 0.22/0.32 inference(constrained_superposition,[],[f64,f68])).
% 0.22/0.32 thf(f158,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((sK2 @ X0)) = sK4) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_4)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f156])).
% 0.22/0.32 thf(f161,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((sK4 != X0) | ($false = ((sK1 @ X0))) | ($false = ((sK1 @ X0)))) ) | (~spl5_2 | ~spl5_3 | ~spl5_4)),
% 0.22/0.32 inference(constrained_superposition,[],[f60,f158])).
% 0.22/0.32 thf(f162,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((sK4 != X0) | ($false = ((sK1 @ X0)))) ) | (~spl5_2 | ~spl5_3 | ~spl5_4)),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f161])).
% 0.22/0.32 thf(f164,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | (~spl5_2 | ~spl5_3 | ~spl5_4)),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f162,f68])).
% 0.22/0.32 thf(f168,plain,(
% 0.22/0.32 ($false = $true) | (~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_6)),
% 0.22/0.32 inference(constrained_superposition,[],[f77,f164])).
% 0.22/0.32 thf(f172,plain,(
% 0.22/0.32 $false | (~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_6)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f168])).
% 0.22/0.32 thf(f173,plain,(
% 0.22/0.32 ~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_6),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f172])).
% 0.22/0.32 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f61])).
% 0.22/0.32 cnf(s2, plain, spl5_1 | spl5_3, inference(sat_conversion,[],[f65])).
% 0.22/0.32 cnf(s3, plain, spl5_4 | spl5_5, inference(sat_conversion,[],[f73])).
% 0.22/0.32 cnf(s4, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f78])).
% 0.22/0.32 cnf(s6, plain, ~spl5_2 | ~spl5_3 | ~spl5_5, inference(sat_conversion,[],[f105])).
% 0.22/0.32 cnf(s7, plain, ~spl5_1 | ~spl5_5, inference(sat_conversion,[],[f110])).
% 0.22/0.32 cnf(s8, plain, ~spl5_1 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f135])).
% 0.22/0.32 cnf(s12, plain, ~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f173])).
% 0.22/0.32 cnf(s13, plain, ~spl5_2 | ~spl5_3, inference(rat,[],[s12,s3,s4,s6])).
% 0.22/0.32 cnf(s14, plain, spl5_1, inference(rat,[],[s13,s1,s2])).
% 0.22/0.32 cnf(s15, plain, ~spl5_5, inference(rat,[],[s7,s14])).
% 0.22/0.32 cnf(s16, plain, spl5_6, inference(rat,[],[s4,s15])).
% 0.22/0.32 cnf(s17, plain, spl5_4, inference(rat,[],[s3,s15])).
% 0.22/0.32 cnf(s18, plain, $false, inference(rat,[],[s8,s14,s16,s17])).
% 0.22/0.32 thf(f175,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(avatar_sat_refutation,[],[s18])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (2999115)------------------------------
% 0.22/0.32 % (2999115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2999115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2999115)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2999115)Termination reason: Refutation
% 0.22/0.32 % (2999115)Time elapsed: 0.019 s
% 0.22/0.32 % (2999115)Peak memory usage: 13 MB
% 0.22/0.32 % (2999115)Instructions burned: 12 (million)
% 0.22/0.32 % (2999110)Success in time 0.064 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------