%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV214^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:39:09 AM UTC 2026
% Result : Theorem 0.07s 0.17s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV214^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 15:21:34 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.14 Running first-order model finding
% 0.07/0.14 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % (239830)Will run a generic schedule for satisfiability detection.
% 0.07/0.17 % (239836)% WARNING: option uhcvi not known.
% 0.07/0.17 % (239836)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1718522949:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.17 % (239837)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1032104689:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.17 % (239838)dis+10_1_sil=32000:sp=arity:random_seed=2143230325:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.17 % (239835)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1982786614_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.17 % (239836)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.17 % (239836)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.17 % Exception at run slice level
% 0.07/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.17 % (239837) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-239830-239837"...
% 0.07/0.17 % (239837)...printing done.
% 0.07/0.17 % (239837)Refutation found. Thanks to Tanya!
% 0.07/0.17 % SZS status Theorem for theBenchmark
% 0.07/0.17 % SZS output start Proof for theBenchmark
% 0.07/0.17 thf(type_def_5, type, iS: $tType).
% 0.07/0.17 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.17 thf(func_def_0, type, c0: iS).
% 0.07/0.17 thf(func_def_1, type, cP: (iS > iS > iS)).
% 0.07/0.17 thf(func_def_5, type, vOR: ($o > $o > $o)).
% 0.07/0.17 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.17 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.17 thf(func_def_8, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.17 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.17 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.17 thf(func_def_11, type, sK0: ((iS > $o) > iS)).
% 0.07/0.17 thf(func_def_12, type, sK1: ((iS > $o) > iS)).
% 0.07/0.17 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.07/0.17 thf(func_def_15, type, sK3: iS).
% 0.07/0.17 thf(func_def_16, type, sK4: iS).
% 0.07/0.17 thf(func_def_17, type, sK5: iS).
% 0.07/0.17 thf(func_def_18, type, sK6: iS).
% 0.07/0.17 thf(f1,conjecture,(
% 0.07/0.17 (! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0)) => (((^[X1 : iS] : (? [X0 : iS] : (c0 = ((cP @ X0 @ X1))) | (X1 = c0))) = (((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0))) & ((^[X0 : iS] : (? [X1 : iS] : (c0 = ((cP @ X0 @ X1))) | (X0 = c0))) = (((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0))))),
% 0.07/0.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_T_LR_LEM2_pme)).
% 0.07/0.17 thf(f2,negated_conjecture,(
% 0.07/0.17 ~((! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0)) => (((^[X1 : iS] : (? [X0 : iS] : (c0 = ((cP @ X0 @ X1))) | (X1 = c0))) = (((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0))) & ((^[X0 : iS] : (? [X1 : iS] : (c0 = ((cP @ X0 @ X1))) | (X0 = c0))) = (((^[X0 : iS, X1 : iS] : ((X0 = X1))) @ c0)))))),
% 0.07/0.17 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.17 thf(f3,plain,(
% 0.07/0.17 ~((! [X0 : (iS > $o)] : ((! [X1 : iS,X2 : iS] : (((X0 @ X2) & (X0 @ X1)) => (X0 @ (cP @ X1 @ X2))) & (X0 @ c0)) => ! [X3 : iS] : (X0 @ X3)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))) => (((^[X10 : iS] : (? [X11 : iS] : (c0 = ((cP @ X11 @ X10))) | (c0 = X10))) = (((^[X12 : iS, X13 : iS] : ((X12 = X13))) @ c0))) & ((^[X14 : iS] : (? [X15 : iS] : (c0 = ((cP @ X14 @ X15))) | (c0 = X14))) = (((^[X16 : iS, X17 : iS] : ((X16 = X17))) @ c0)))))),
% 0.07/0.17 inference(rectify,[],[f2])).
% 0.07/0.17 thf(f4,plain,(
% 0.07/0.17 ~((! [X0 : (iS > $o)] : ((! [X1 : iS,X2 : iS] : (((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ (cP @ X1 @ X2))) = $true)) & (((X0 @ c0)) = $true)) => ! [X3 : iS] : (((X0 @ X3)) = $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))) => (((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) = (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) & ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) = (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))))),
% 0.07/0.17 inference(fool_elimination,[],[f3])).
% 0.07/0.17 thf(f5,plain,(
% 0.07/0.17 (((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))) & (! [X0 : (iS > $o)] : (! [X3 : iS] : (((X0 @ X3)) = $true) | (? [X1 : iS,X2 : iS] : ((((X0 @ (cP @ X1 @ X2))) != $true) & ((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true))) | (((X0 @ c0)) != $true))) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9))))),
% 0.07/0.17 inference(ennf_transformation,[],[f4])).
% 0.07/0.17 thf(f6,plain,(
% 0.07/0.17 (((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))) & ! [X0 : (iS > $o)] : (! [X3 : iS] : (((X0 @ X3)) = $true) | ? [X1 : iS,X2 : iS] : ((((X0 @ (cP @ X1 @ X2))) != $true) & (((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) | (((X0 @ c0)) != $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))),
% 0.07/0.17 inference(flattening,[],[f5])).
% 0.07/0.17 thf(f7,plain,(
% 0.07/0.17 (((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))) & ! [X0 : (iS > $o)] : (! [X1 : iS] : (((X0 @ X1)) = $true) | ? [X2 : iS,X3 : iS] : (($true != ((X0 @ (cP @ X2 @ X3)))) & (((X0 @ X3)) = $true) & (((X0 @ X2)) = $true)) | (((X0 @ c0)) != $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))),
% 0.07/0.17 inference(rectify,[],[f6])).
% 0.07/0.17 thf(f8,plain,(
% 0.07/0.17 (((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))) & ! [X0 : (iS > $o)] : (! [X1 : iS] : (((X0 @ X1)) = $true) | (($true != ((X0 @ (cP @ (sK0 @ X0) @ (sK1 @ X0))))) & ($true = ((X0 @ (sK1 @ X0)))) & ($true = ((X0 @ (sK0 @ X0))))) | (((X0 @ c0)) != $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))),
% 0.07/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X0),skolemize(X3,sK1 @ X0)],[f7])).
% 0.07/0.17 thf(f9,plain,(
% 0.07/0.17 ( ! [X8 : iS,X9 : iS] : ((c0 != ((cP @ X8 @ X9)))) )),
% 0.07/0.17 inference(cnf_transformation,[],[f8])).
% 0.07/0.17 thf(f15,plain,(
% 0.07/0.17 ((((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | ((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) != (((^[Y0 : iS]: ((^[Y1 : iS]: (Y0 = Y1)))) @ c0)))),
% 0.07/0.17 inference(cnf_transformation,[],[f8])).
% 0.07/0.17 thf(f18,plain,(
% 0.07/0.17 (((= @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | (((= @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))))),
% 0.07/0.17 inference(beta-eta_normalization,[],[f15])).
% 0.07/0.17 thf(f20,definition,(
% 0.07/0.17 spl2_1 <=> (((= @ c0)) = (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))))),
% 0.07/0.17 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.07/0.17 thf(f22,plain,(
% 0.07/0.17 (((= @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1))))))) | spl2_1),
% 0.07/0.17 inference(avatar_component_clause,[],[f20])).
% 0.07/0.17 thf(f24,definition,(
% 0.07/0.17 spl2_2 <=> (((= @ c0)) = (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))))),
% 0.07/0.17 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.07/0.17 thf(f26,plain,(
% 0.07/0.17 (((= @ c0)) != (^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0))))))) | spl2_2),
% 0.07/0.17 inference(avatar_component_clause,[],[f24])).
% 0.07/0.17 thf(f27,plain,(
% 0.07/0.17 ~spl2_1 | ~spl2_2),
% 0.07/0.17 inference(avatar_split_clause,[],[f18,f24,f20])).
% 0.07/0.17 thf(f28,plain,(
% 0.07/0.17 (((c0 = sK3)) != (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK3))) | spl2_1),
% 0.07/0.17 inference(negative_extensionality,[],[f22])).
% 0.07/0.17 thf(f29,plain,(
% 0.07/0.17 ($true = ((c0 = sK3))) | ($true = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK3))) | spl2_1),
% 0.07/0.17 inference(xor_proxy_clausification,[],[f28])).
% 0.07/0.17 thf(f30,plain,(
% 0.07/0.17 ($false = ((c0 = sK3))) | ($false = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK3))) | spl2_1),
% 0.07/0.17 inference(xor_proxy_clausification,[],[f28])).
% 0.07/0.17 thf(f31,plain,(
% 0.07/0.17 (c0 != sK3) | ($false = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK3))) | spl2_1),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f30])).
% 0.07/0.17 thf(f32,plain,(
% 0.07/0.17 (c0 != sK3) | ($false = (((c0 = sK3) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0))))))) | spl2_1),
% 0.07/0.17 inference(beta-eta_normalization,[],[f31])).
% 0.07/0.17 thf(f34,plain,(
% 0.07/0.17 (c0 != sK3) | ($false = ((c0 = sK3))) | spl2_1),
% 0.07/0.17 inference(or_proxy_clausification,[],[f32])).
% 0.07/0.17 thf(f35,plain,(
% 0.07/0.17 (c0 != sK3) | (c0 != sK3) | spl2_1),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f34])).
% 0.07/0.17 thf(f36,plain,(
% 0.07/0.17 (c0 != sK3) | spl2_1),
% 0.07/0.17 inference(duplicate_literal_removal,[],[f35])).
% 0.07/0.17 thf(f40,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y0 @ Y1)))))) @ sK3))) | spl2_1),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f29])).
% 0.07/0.17 thf(f41,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = (((c0 = sK3) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0))))))) | spl2_1),
% 0.07/0.17 inference(beta-eta_normalization,[],[f40])).
% 0.07/0.17 thf(f42,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = ((?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0)))))) | ($true = ((c0 = sK3))) | spl2_1),
% 0.07/0.17 inference(or_proxy_clausification,[],[f41])).
% 0.07/0.17 thf(f43,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = (((^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0))) @ sK4))) | ($true = ((c0 = sK3))) | spl2_1),
% 0.07/0.17 inference(sigma_proxy_clausification,[],[f42])).
% 0.07/0.17 thf(f44,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = (((^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0))) @ sK4))) | (c0 = sK3) | spl2_1),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f43])).
% 0.07/0.17 thf(f45,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = (((^[Y0 : iS]: (c0 = (cP @ sK3 @ Y0))) @ sK4))) | spl2_1),
% 0.07/0.17 inference(duplicate_literal_removal,[],[f44])).
% 0.07/0.17 thf(f46,plain,(
% 0.07/0.17 (c0 = sK3) | ($true = ((c0 = (cP @ sK3 @ sK4)))) | spl2_1),
% 0.07/0.17 inference(beta-eta_normalization,[],[f45])).
% 0.07/0.17 thf(f47,plain,(
% 0.07/0.17 (c0 = sK3) | (c0 = ((cP @ sK3 @ sK4))) | spl2_1),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f46])).
% 0.07/0.17 thf(f48,plain,(
% 0.07/0.17 (c0 = sK3) | spl2_1),
% 0.07/0.17 inference(forward_subsumption_resolution,[],[f47,f9])).
% 0.07/0.17 thf(f49,plain,(
% 0.07/0.17 $false | spl2_1),
% 0.07/0.17 inference(global_subsumption,[],[f48,f36])).
% 0.07/0.17 thf(f50,plain,(
% 0.07/0.17 spl2_1),
% 0.07/0.17 inference(avatar_contradiction_clause,[],[f49])).
% 0.07/0.17 thf(f51,plain,(
% 0.07/0.17 (((c0 = sK5)) != (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK5))) | spl2_2),
% 0.07/0.17 inference(negative_extensionality,[],[f26])).
% 0.07/0.17 thf(f52,plain,(
% 0.07/0.17 ($true = ((c0 = sK5))) | ($true = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK5))) | spl2_2),
% 0.07/0.17 inference(xor_proxy_clausification,[],[f51])).
% 0.07/0.17 thf(f53,plain,(
% 0.07/0.17 ($false = ((c0 = sK5))) | ($false = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK5))) | spl2_2),
% 0.07/0.17 inference(xor_proxy_clausification,[],[f51])).
% 0.07/0.17 thf(f54,plain,(
% 0.07/0.17 (c0 != sK5) | ($false = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK5))) | spl2_2),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f53])).
% 0.07/0.17 thf(f55,plain,(
% 0.07/0.17 (c0 != sK5) | ($false = (((c0 = sK5) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5))))))) | spl2_2),
% 0.07/0.17 inference(beta-eta_normalization,[],[f54])).
% 0.07/0.17 thf(f57,plain,(
% 0.07/0.17 (c0 != sK5) | ($false = ((c0 = sK5))) | spl2_2),
% 0.07/0.17 inference(or_proxy_clausification,[],[f55])).
% 0.07/0.17 thf(f58,plain,(
% 0.07/0.17 (c0 != sK5) | (c0 != sK5) | spl2_2),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f57])).
% 0.07/0.17 thf(f59,plain,(
% 0.07/0.17 (c0 != sK5) | spl2_2),
% 0.07/0.17 inference(duplicate_literal_removal,[],[f58])).
% 0.07/0.17 thf(f63,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = (((^[Y0 : iS]: ((c0 = Y0) | (?? @ iS @ (^[Y1 : iS]: (c0 = (cP @ Y1 @ Y0)))))) @ sK5))) | spl2_2),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f52])).
% 0.07/0.17 thf(f64,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = (((c0 = sK5) | (?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5))))))) | spl2_2),
% 0.07/0.17 inference(beta-eta_normalization,[],[f63])).
% 0.07/0.17 thf(f65,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = ((?? @ iS @ (^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5)))))) | ($true = ((c0 = sK5))) | spl2_2),
% 0.07/0.17 inference(or_proxy_clausification,[],[f64])).
% 0.07/0.17 thf(f66,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = (((^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5))) @ sK6))) | ($true = ((c0 = sK5))) | spl2_2),
% 0.07/0.17 inference(sigma_proxy_clausification,[],[f65])).
% 0.07/0.17 thf(f67,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = (((^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5))) @ sK6))) | (c0 = sK5) | spl2_2),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f66])).
% 0.07/0.17 thf(f68,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = (((^[Y0 : iS]: (c0 = (cP @ Y0 @ sK5))) @ sK6))) | spl2_2),
% 0.07/0.17 inference(duplicate_literal_removal,[],[f67])).
% 0.07/0.17 thf(f69,plain,(
% 0.07/0.17 (c0 = sK5) | ($true = ((c0 = (cP @ sK6 @ sK5)))) | spl2_2),
% 0.07/0.17 inference(beta-eta_normalization,[],[f68])).
% 0.07/0.17 thf(f70,plain,(
% 0.07/0.17 (c0 = sK5) | (c0 = ((cP @ sK6 @ sK5))) | spl2_2),
% 0.07/0.17 inference(equality_proxy_clausification,[],[f69])).
% 0.07/0.17 thf(f71,plain,(
% 0.07/0.17 (c0 = sK5) | spl2_2),
% 0.07/0.17 inference(forward_subsumption_resolution,[],[f70,f9])).
% 0.07/0.17 thf(f72,plain,(
% 0.07/0.17 $false | spl2_2),
% 0.07/0.17 inference(global_subsumption,[],[f71,f59])).
% 0.07/0.17 thf(f73,plain,(
% 0.07/0.17 spl2_2),
% 0.07/0.17 inference(avatar_contradiction_clause,[],[f72])).
% 0.07/0.17 cnf(s12, plain, ~spl2_1 | ~spl2_2, inference(sat_conversion,[],[f27])).
% 0.07/0.17 cnf(s18, plain, spl2_1, inference(sat_conversion,[],[f50])).
% 0.07/0.17 cnf(s24, plain, spl2_2, inference(sat_conversion,[],[f73])).
% 0.07/0.17 cnf(s25, plain, $false, inference(rat,[],[s12,s24,s18])).
% 0.07/0.17 thf(f74,plain,(
% 0.07/0.17 $false),
% 0.07/0.17 inference(avatar_sat_refutation,[],[s25])).
% 0.07/0.17 % SZS output end Proof for theBenchmark
% 0.07/0.17 % (239837)------------------------------
% 0.07/0.17 % (239837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.17 % (239837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.17 % (239837)CaDiCaL version: 2.1.3
% 0.07/0.17 % (239837)Termination reason: Refutation
% 0.07/0.17 % (239837)Time elapsed: 0.003 s
% 0.07/0.17 % (239837)Peak memory usage: 12 MB
% 0.07/0.17 % (239837)Instructions burned: 7 (million)
% 0.07/0.17 % (239830)Success in time 0.027 s
% 0.07/0.17 % Vampire exiting
%------------------------------------------------------------------------------