%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:50:34 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.16 % Computer : n005.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Sep 29 17:26:16 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 Running first-order model finding
% 0.07/0.19 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
% 0.07/0.24 % (1956389)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (1956397)dis+10_1_sil=32000:sp=arity:random_seed=785498810:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.24 % (1956395)% WARNING: option uhcvi not known.
% 0.07/0.24 % (1956395)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=230958957:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.24 % (1956398)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3770517300:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.24 % (1956394)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2736714504_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.24 % (1956396)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1144430313:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.24 % (1956395)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (1956398)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (1956395)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.24 % Exception at run slice level
% 0.07/0.24 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.24 % (1956397) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1956389-1956397"...
% 0.07/0.24 % (1956397)...printing done.
% 0.07/0.24 % (1956397)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% 0.07/0.24 thf(type_def_5, type, mworld: $tType).
% 0.07/0.24 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.24 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.07/0.24 thf(func_def_1, type, mactual: mworld).
% 0.07/0.24 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.07/0.24 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.07/0.24 thf(func_def_11, type, p: (mworld > $o)).
% 0.07/0.24 thf(func_def_12, type, q: (mworld > $o)).
% 0.07/0.24 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.24 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.24 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.07/0.24 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.24 thf(func_def_17, type, vAND: ($o > $o > $o)).
% 0.07/0.24 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.07/0.24 thf(func_def_19, type, vOR: ($o > $o > $o)).
% 0.07/0.24 thf(func_def_20, type, vIMP: ($o > $o > $o)).
% 0.07/0.24 thf(func_def_21, type, vIFF: ($o > $o > $o)).
% 0.07/0.24 thf(func_def_22, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.24 thf(func_def_23, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.24 thf(func_def_26, type, sK0: mworld).
% 0.07/0.24 thf(func_def_27, type, sK1: mworld).
% 0.07/0.24 thf(func_def_28, type, sK2: mworld).
% 0.07/0.24 thf(f1,axiom,(
% 0.07/0.24 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.07/0.24 thf(f5,axiom,(
% 0.07/0.24 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.07/0.24 thf(f6,axiom,(
% 0.07/0.24 (mequiv = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def)).
% 0.07/0.24 thf(f7,axiom,(
% 0.07/0.24 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.07/0.24 thf(f9,axiom,(
% 0.07/0.24 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.07/0.24 thf(f10,axiom,(
% 0.07/0.24 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X0 @ X1) & (mrel @ X0 @ X2)) => (mrel @ X2 @ X1))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean)).
% 0.07/0.24 thf(f11,conjecture,(
% 0.07/0.24 (mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 0.07/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.07/0.24 thf(f12,negated_conjecture,(
% 0.07/0.24 ~(mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 0.07/0.24 inference(negated_conjecture,[status(cth)],[f11])).
% 0.07/0.24 thf(f13,plain,(
% 0.07/0.24 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.07/0.24 inference(fool_elimination,[],[f1])).
% 0.07/0.24 thf(f20,plain,(
% 0.07/0.24 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.07/0.24 inference(rectify,[],[f5])).
% 0.07/0.24 thf(f21,plain,(
% 0.07/0.24 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.07/0.24 inference(fool_elimination,[],[f20])).
% 0.07/0.24 thf(f22,plain,(
% 0.07/0.24 (mequiv = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 0.07/0.24 inference(rectify,[],[f6])).
% 0.07/0.24 thf(f23,plain,(
% 0.07/0.24 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.07/0.24 inference(fool_elimination,[],[f22])).
% 0.07/0.24 thf(f24,plain,(
% 0.07/0.24 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.07/0.24 inference(rectify,[],[f7])).
% 0.07/0.24 thf(f25,plain,(
% 0.07/0.24 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.07/0.24 inference(fool_elimination,[],[f24])).
% 0.07/0.24 thf(f28,plain,(
% 0.07/0.24 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.07/0.24 inference(rectify,[],[f9])).
% 0.07/0.24 thf(f29,plain,(
% 0.07/0.24 ! [X0 : mworld] : (((mrel @ X0 @ X0)) = $true)),
% 0.07/0.24 inference(fool_elimination,[],[f28])).
% 0.07/0.24 thf(f30,plain,(
% 0.07/0.24 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X0 @ X1) & (mrel @ X0 @ X2)) => (mrel @ X2 @ X1))),
% 0.07/0.24 inference(rectify,[],[f10])).
% 0.07/0.24 thf(f31,plain,(
% 0.07/0.24 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((((mrel @ X0 @ X1)) = $true) & (((mrel @ X0 @ X2)) = $true)) => (((mrel @ X2 @ X1)) = $true))),
% 0.07/0.24 inference(fool_elimination,[],[f30])).
% 0.07/0.24 thf(f32,plain,(
% 0.07/0.24 ~(mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 0.07/0.24 inference(rectify,[],[f12])).
% 0.07/0.24 thf(f33,plain,(
% 0.07/0.24 ~ (((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))) = $true)),
% 0.07/0.24 inference(fool_elimination,[],[f32])).
% 0.07/0.24 thf(f34,plain,(
% 0.07/0.24 (((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))) != $true)),
% 0.07/0.24 inference(flattening,[],[f33])).
% 0.07/0.24 thf(f35,plain,(
% 0.07/0.24 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X2 @ X1)) = $true) | ((((mrel @ X0 @ X1)) != $true) | (((mrel @ X0 @ X2)) != $true)))),
% 0.07/0.24 inference(ennf_transformation,[],[f31])).
% 0.07/0.24 thf(f36,plain,(
% 0.07/0.24 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X2 @ X1)) = $true) | (((mrel @ X0 @ X1)) != $true) | (((mrel @ X0 @ X2)) != $true))),
% 0.07/0.24 inference(flattening,[],[f35])).
% 0.07/0.24 thf(f37,plain,(
% 0.07/0.24 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.07/0.24 inference(cnf_transformation,[],[f13])).
% 0.07/0.24 thf(f41,plain,(
% 0.07/0.24 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.07/0.24 inference(cnf_transformation,[],[f21])).
% 0.07/0.24 thf(f42,plain,(
% 0.07/0.24 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.07/0.24 inference(cnf_transformation,[],[f23])).
% 0.07/0.24 thf(f43,plain,(
% 0.07/0.24 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.07/0.24 inference(cnf_transformation,[],[f25])).
% 0.07/0.24 thf(f45,plain,(
% 0.07/0.24 ( ! [X0 : mworld] : ((((mrel @ X0 @ X0)) = $true)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f29])).
% 0.07/0.24 thf(f46,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X2)) != $true) | (((mrel @ X0 @ X1)) != $true) | (((mrel @ X2 @ X1)) = $true)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f36])).
% 0.07/0.24 thf(f47,plain,(
% 0.07/0.24 (((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))) != $true)),
% 0.07/0.24 inference(cnf_transformation,[],[f34])).
% 0.07/0.24 thf(f49,definition,(
% 0.07/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.24 thf(f50,plain,(
% 0.07/0.24 ($true != (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ p @ q)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q)))))))),
% 0.07/0.24 inference(definition_unfolding,[],[f47,f37,f41,f43,f42,f43,f42,f43,f43])).
% 0.07/0.24 thf(f51,plain,(
% 0.07/0.24 ($true != (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))))))))))),
% 0.07/0.24 inference(beta-eta_normalization,[],[f50])).
% 0.07/0.24 thf(f52,plain,(
% 0.07/0.24 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))))))))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f51])).
% 0.07/0.24 thf(f53,plain,(
% 0.07/0.24 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0)))))))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f51])).
% 0.07/0.24 thf(f54,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0)))) @ X1)))) )),
% 0.07/0.24 inference(pi_proxy_clausification,[],[f53])).
% 0.07/0.24 thf(f55,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => ((p @ X1) = (q @ X1)))))) )),
% 0.07/0.24 inference(beta-eta_normalization,[],[f54])).
% 0.07/0.24 thf(f56,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((p @ X1) = (q @ X1))))) )),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f55])).
% 0.07/0.24 thf(f57,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | (((p @ X1)) = ((q @ X1)))) )),
% 0.07/0.24 inference(iff_proxy_clausification,[],[f56])).
% 0.07/0.24 thf(f58,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((p @ X1))) | ($false = ((q @ X1)))) )),
% 0.07/0.24 inference(iff_proxy_clausification,[],[f57])).
% 0.07/0.24 thf(f59,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((p @ X1))) | ($true = ((q @ X1)))) )),
% 0.07/0.24 inference(iff_proxy_clausification,[],[f57])).
% 0.07/0.24 thf(f60,plain,(
% 0.07/0.24 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))))) @ sK0)))),
% 0.07/0.24 inference(sigma_proxy_clausification,[],[f52])).
% 0.07/0.24 thf(f61,plain,(
% 0.07/0.24 ($false = (((mrel @ mactual @ sK0) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0)))) = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))))),
% 0.07/0.24 inference(beta-eta_normalization,[],[f60])).
% 0.07/0.24 thf(f62,plain,(
% 0.07/0.24 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0)))) = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0)))))))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f61])).
% 0.07/0.24 thf(f63,plain,(
% 0.07/0.24 ($true = ((mrel @ mactual @ sK0)))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f61])).
% 0.07/0.24 thf(f64,plain,(
% 0.07/0.24 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0))))) != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))),
% 0.07/0.24 inference(iff_proxy_clausification,[],[f62])).
% 0.07/0.24 thf(f65,plain,(
% 0.07/0.24 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))),
% 0.07/0.24 inference(xor_proxy_clausification,[],[f64])).
% 0.07/0.24 thf(f66,plain,(
% 0.07/0.24 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))),
% 0.07/0.24 inference(xor_proxy_clausification,[],[f64])).
% 0.07/0.24 thf(f67,plain,(
% 0.07/0.24 ($false = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0))) @ sK1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))),
% 0.07/0.24 inference(sigma_proxy_clausification,[],[f66])).
% 0.07/0.24 thf(f68,plain,(
% 0.07/0.24 ($false = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0))) @ sK1))) | ($false = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))) @ sK2)))),
% 0.07/0.24 inference(sigma_proxy_clausification,[],[f67])).
% 0.07/0.24 thf(f69,plain,(
% 0.07/0.24 ($false = (((mrel @ sK0 @ sK1) => (p @ sK1)))) | ($false = (((mrel @ sK0 @ sK2) => (q @ sK2))))),
% 0.07/0.24 inference(beta-eta_normalization,[],[f68])).
% 0.07/0.24 thf(f70,plain,(
% 0.07/0.24 ($false = ((p @ sK1))) | ($false = (((mrel @ sK0 @ sK2) => (q @ sK2))))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f69])).
% 0.07/0.24 thf(f71,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ sK1))) | ($false = (((mrel @ sK0 @ sK2) => (q @ sK2))))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f69])).
% 0.07/0.24 thf(f72,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ sK1))) | ($false = ((q @ sK2)))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f71])).
% 0.07/0.24 thf(f73,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ sK1))) | ($true = ((mrel @ sK0 @ sK2)))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f71])).
% 0.07/0.24 thf(f74,plain,(
% 0.07/0.24 ($false = ((p @ sK1))) | ($false = ((q @ sK2)))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f70])).
% 0.07/0.24 thf(f75,plain,(
% 0.07/0.24 ($false = ((p @ sK1))) | ($true = ((mrel @ sK0 @ sK2)))),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f70])).
% 0.07/0.24 thf(f76,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0))) @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))))))) )),
% 0.07/0.24 inference(pi_proxy_clausification,[],[f65])).
% 0.07/0.24 thf(f77,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (p @ Y0))) @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (q @ Y0))) @ X2)))) )),
% 0.07/0.24 inference(pi_proxy_clausification,[],[f76])).
% 0.07/0.24 thf(f78,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK0 @ X1) => (p @ X1)))) | ($true = (((mrel @ sK0 @ X2) => (q @ X2))))) )),
% 0.07/0.24 inference(beta-eta_normalization,[],[f77])).
% 0.07/0.24 thf(f79,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK0 @ X1))) | ($true = (((mrel @ sK0 @ X2) => (q @ X2)))) | ($true = ((p @ X1)))) )),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f78])).
% 0.07/0.24 thf(f80,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK0 @ X1))) | ($false = ((mrel @ sK0 @ X2))) | ($true = ((p @ X1))) | ($true = ((q @ X2)))) )),
% 0.07/0.24 inference(imp_proxy_clausification,[],[f79])).
% 0.07/0.24 thf(f82,definition,(
% 0.07/0.24 spl3_1 <=> ($true = ((mrel @ sK0 @ sK2)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.07/0.24 thf(f84,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ sK2))) | ~spl3_1),
% 0.07/0.24 inference(avatar_component_clause,[],[f82])).
% 0.07/0.24 thf(f86,definition,(
% 0.07/0.24 spl3_2 <=> ($true = ((mrel @ sK0 @ sK1)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.07/0.24 thf(f88,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ sK1))) | ~spl3_2),
% 0.07/0.24 inference(avatar_component_clause,[],[f86])).
% 0.07/0.24 thf(f89,plain,(
% 0.07/0.24 spl3_1 | spl3_2),
% 0.07/0.24 inference(avatar_split_clause,[],[f73,f86,f82])).
% 0.07/0.24 thf(f91,definition,(
% 0.07/0.24 spl3_3 <=> ($false = ((q @ sK2)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.07/0.24 thf(f93,plain,(
% 0.07/0.24 ($false = ((q @ sK2))) | ~spl3_3),
% 0.07/0.24 inference(avatar_component_clause,[],[f91])).
% 0.07/0.24 thf(f94,plain,(
% 0.07/0.24 spl3_3 | spl3_2),
% 0.07/0.24 inference(avatar_split_clause,[],[f72,f86,f91])).
% 0.07/0.24 thf(f96,definition,(
% 0.07/0.24 spl3_4 <=> ($false = ((p @ sK1)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.07/0.24 thf(f98,plain,(
% 0.07/0.24 ($false = ((p @ sK1))) | ~spl3_4),
% 0.07/0.24 inference(avatar_component_clause,[],[f96])).
% 0.07/0.24 thf(f99,plain,(
% 0.07/0.24 spl3_1 | spl3_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f75,f96,f82])).
% 0.07/0.24 thf(f100,plain,(
% 0.07/0.24 spl3_3 | spl3_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f74,f96,f91])).
% 0.07/0.24 thf(f102,definition,(
% 0.07/0.24 spl3_5 <=> ! [X2 : mworld] : (($false = ((mrel @ sK0 @ X2))) | ($true = ((q @ X2))))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.07/0.24 thf(f103,plain,(
% 0.07/0.24 ( ! [X2 : mworld] : (($false = ((mrel @ sK0 @ X2))) | ($true = ((q @ X2)))) ) | ~spl3_5),
% 0.07/0.24 inference(avatar_component_clause,[],[f102])).
% 0.07/0.24 thf(f105,definition,(
% 0.07/0.24 spl3_6 <=> ! [X1 : mworld] : (($false = ((mrel @ sK0 @ X1))) | ($true = ((p @ X1))))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition])).
% 0.07/0.24 thf(f106,plain,(
% 0.07/0.24 ( ! [X1 : mworld] : (($false = ((mrel @ sK0 @ X1))) | ($true = ((p @ X1)))) ) | ~spl3_6),
% 0.07/0.24 inference(avatar_component_clause,[],[f105])).
% 0.07/0.24 thf(f107,plain,(
% 0.07/0.24 spl3_5 | spl3_6),
% 0.07/0.24 inference(avatar_split_clause,[],[f80,f105,f102])).
% 0.07/0.24 thf(f120,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((q @ sK1))) | (~spl3_2 | ~spl3_5)),
% 0.07/0.24 inference(constrained_superposition,[],[f88,f103])).
% 0.07/0.24 thf(f123,plain,(
% 0.07/0.24 ($true = ((q @ sK1))) | (~spl3_2 | ~spl3_5)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f120])).
% 0.07/0.24 thf(f127,plain,(
% 0.07/0.24 ( ! [X0 : mworld] : (($true != $true) | ($true != ((mrel @ mactual @ X0))) | ($true = ((mrel @ sK0 @ X0)))) )),
% 0.07/0.24 inference(constrained_superposition,[],[f46,f63])).
% 0.07/0.24 thf(f131,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != $true) | (((mrel @ X0 @ X2)) != $true) | (((mrel @ X1 @ X2)) = $true) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.07/0.24 inference(constrained_superposition,[],[f46,f49])).
% 0.07/0.24 thf(f132,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X2)) != $true) | (((mrel @ X1 @ X2)) = $true) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f131])).
% 0.07/0.24 thf(f134,plain,(
% 0.07/0.24 ( ! [X0 : mworld] : (($true != ((mrel @ mactual @ X0))) | ($true = ((mrel @ sK0 @ X0)))) )),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f127])).
% 0.07/0.24 thf(f139,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != $true) | (((mrel @ X2 @ X1)) = $true) | (((mrel @ X0 @ X2)) = $false) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.07/0.24 inference(constrained_superposition,[],[f132,f49])).
% 0.07/0.24 thf(f140,plain,(
% 0.07/0.24 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X2 @ X1)) = $true) | (((mrel @ X0 @ X2)) = $false) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f139])).
% 0.07/0.24 thf(f236,plain,(
% 0.07/0.24 ( ! [X0 : mworld,X1 : mworld] : (($true = $false) | ($false = ((p @ X0))) | ($true = ((q @ X0))) | ($false = ((mrel @ X1 @ mactual))) | ($false = ((mrel @ X1 @ X0)))) )),
% 0.07/0.24 inference(constrained_superposition,[],[f59,f140])).
% 0.07/0.24 thf(f237,plain,(
% 0.07/0.24 ( ! [X0 : mworld,X1 : mworld] : (($true = $false) | ($true = ((p @ X0))) | ($false = ((q @ X0))) | ($false = ((mrel @ X1 @ mactual))) | ($false = ((mrel @ X1 @ X0)))) )),
% 0.07/0.24 inference(constrained_superposition,[],[f58,f140])).
% 0.07/0.24 thf(f267,plain,(
% 0.07/0.24 ( ! [X0 : mworld,X1 : mworld] : (($false = ((mrel @ X1 @ mactual))) | ($false = ((mrel @ X1 @ X0))) | ($false = ((q @ X0))) | ($true = ((p @ X0)))) )),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f237])).
% 0.07/0.24 thf(f268,plain,(
% 0.07/0.24 ( ! [X0 : mworld,X1 : mworld] : (($false = ((mrel @ X1 @ mactual))) | ($false = ((mrel @ X1 @ X0))) | ($true = ((q @ X0))) | ($false = ((p @ X0)))) )),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f236])).
% 0.07/0.24 thf(f291,plain,(
% 0.07/0.24 ($true != $true) | ($true = ((mrel @ sK0 @ mactual)))),
% 0.07/0.24 inference(constrained_superposition,[],[f134,f45])).
% 0.07/0.24 thf(f305,plain,(
% 0.07/0.24 ($true = ((mrel @ sK0 @ mactual)))),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f291])).
% 0.07/0.24 thf(f493,plain,(
% 0.07/0.24 ($true = $false) | ($false = ((mrel @ sK0 @ mactual))) | ($false = ((q @ sK1))) | ($true = ((p @ sK1))) | ~spl3_2),
% 0.07/0.24 inference(constrained_superposition,[],[f267,f88])).
% 0.07/0.24 thf(f526,plain,(
% 0.07/0.24 ($false = ((mrel @ sK0 @ mactual))) | ($false = ((q @ sK1))) | ($true = ((p @ sK1))) | ~spl3_2),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f493])).
% 0.07/0.24 thf(f541,plain,(
% 0.07/0.24 ($true = $false) | ($false = ((q @ sK1))) | ($true = ((p @ sK1))) | ~spl3_2),
% 0.07/0.24 inference(forward_demodulation,[],[f526,f305])).
% 0.07/0.24 thf(f542,plain,(
% 0.07/0.24 ($false = ((q @ sK1))) | ($true = ((p @ sK1))) | ~spl3_2),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f541])).
% 0.07/0.24 thf(f545,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((p @ sK1))) | (~spl3_2 | ~spl3_5)),
% 0.07/0.24 inference(forward_demodulation,[],[f542,f123])).
% 0.07/0.24 thf(f546,plain,(
% 0.07/0.24 ($true = ((p @ sK1))) | (~spl3_2 | ~spl3_5)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f545])).
% 0.07/0.24 thf(f550,plain,(
% 0.07/0.24 ($true = $false) | (~spl3_2 | ~spl3_4 | ~spl3_5)),
% 0.07/0.24 inference(forward_demodulation,[],[f546,f98])).
% 0.07/0.24 thf(f551,plain,(
% 0.07/0.24 $false | (~spl3_2 | ~spl3_4 | ~spl3_5)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f550])).
% 0.07/0.24 thf(f552,plain,(
% 0.07/0.24 ~spl3_2 | ~spl3_4 | ~spl3_5),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f551])).
% 0.07/0.24 thf(f616,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((p @ sK1))) | (~spl3_2 | ~spl3_6)),
% 0.07/0.24 inference(constrained_superposition,[],[f106,f88])).
% 0.07/0.24 thf(f633,plain,(
% 0.07/0.24 ($true = ((p @ sK1))) | (~spl3_2 | ~spl3_6)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f616])).
% 0.07/0.24 thf(f642,plain,(
% 0.07/0.24 ($true = $false) | (~spl3_2 | ~spl3_4 | ~spl3_6)),
% 0.07/0.24 inference(forward_demodulation,[],[f633,f98])).
% 0.07/0.24 thf(f643,plain,(
% 0.07/0.24 $false | (~spl3_2 | ~spl3_4 | ~spl3_6)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f642])).
% 0.07/0.24 thf(f644,plain,(
% 0.07/0.24 ~spl3_2 | ~spl3_4 | ~spl3_6),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f643])).
% 0.07/0.24 thf(f760,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((p @ sK2))) | (~spl3_1 | ~spl3_6)),
% 0.07/0.24 inference(constrained_superposition,[],[f106,f84])).
% 0.07/0.24 thf(f766,plain,(
% 0.07/0.24 ($true = $false) | ($false = ((mrel @ sK0 @ mactual))) | ($true = ((q @ sK2))) | ($false = ((p @ sK2))) | ~spl3_1),
% 0.07/0.24 inference(constrained_superposition,[],[f268,f84])).
% 0.07/0.24 thf(f767,plain,(
% 0.07/0.24 ($false = ((mrel @ sK0 @ mactual))) | ($true = ((q @ sK2))) | ($false = ((p @ sK2))) | ~spl3_1),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f766])).
% 0.07/0.24 thf(f773,plain,(
% 0.07/0.24 ($true = ((p @ sK2))) | (~spl3_1 | ~spl3_6)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f760])).
% 0.07/0.24 thf(f778,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((q @ sK2))) | ($false = ((p @ sK2))) | ~spl3_1),
% 0.07/0.24 inference(forward_demodulation,[],[f767,f305])).
% 0.07/0.24 thf(f779,plain,(
% 0.07/0.24 ($true = ((q @ sK2))) | ($false = ((p @ sK2))) | ~spl3_1),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f778])).
% 0.07/0.24 thf(f782,plain,(
% 0.07/0.24 ($true = $false) | ($false = ((p @ sK2))) | (~spl3_1 | ~spl3_3)),
% 0.07/0.24 inference(forward_demodulation,[],[f779,f93])).
% 0.07/0.24 thf(f783,plain,(
% 0.07/0.24 ($false = ((p @ sK2))) | (~spl3_1 | ~spl3_3)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f782])).
% 0.07/0.24 thf(f1060,plain,(
% 0.07/0.24 ($true = $false) | (~spl3_1 | ~spl3_3 | ~spl3_6)),
% 0.07/0.24 inference(constrained_superposition,[],[f783,f773])).
% 0.07/0.24 thf(f1066,plain,(
% 0.07/0.24 $false | (~spl3_1 | ~spl3_3 | ~spl3_6)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f1060])).
% 0.07/0.24 thf(f1067,plain,(
% 0.07/0.24 ~spl3_1 | ~spl3_3 | ~spl3_6),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f1066])).
% 0.07/0.24 thf(f1093,plain,(
% 0.07/0.24 ($true = $false) | ($true = ((q @ sK2))) | (~spl3_1 | ~spl3_5)),
% 0.07/0.24 inference(constrained_superposition,[],[f103,f84])).
% 0.07/0.24 thf(f1115,plain,(
% 0.07/0.24 ($true = ((q @ sK2))) | (~spl3_1 | ~spl3_5)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f1093])).
% 0.07/0.24 thf(f1126,plain,(
% 0.07/0.24 ($true = $false) | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 0.07/0.24 inference(forward_demodulation,[],[f1115,f93])).
% 0.07/0.24 thf(f1127,plain,(
% 0.07/0.24 $false | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f1126])).
% 0.07/0.24 thf(f1128,plain,(
% 0.07/0.24 ~spl3_1 | ~spl3_3 | ~spl3_5),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f1127])).
% 0.07/0.24 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f89])).
% 0.07/0.24 cnf(s2, plain, spl3_2 | spl3_3, inference(sat_conversion,[],[f94])).
% 0.07/0.24 cnf(s3, plain, spl3_1 | spl3_4, inference(sat_conversion,[],[f99])).
% 0.07/0.24 cnf(s4, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f100])).
% 0.07/0.24 cnf(s5, plain, spl3_5 | spl3_6, inference(sat_conversion,[],[f107])).
% 0.07/0.24 cnf(s12, plain, ~spl3_2 | ~spl3_4 | ~spl3_5, inference(sat_conversion,[],[f552])).
% 0.07/0.24 cnf(s31, plain, ~spl3_2 | ~spl3_4 | ~spl3_6, inference(sat_conversion,[],[f644])).
% 0.07/0.24 cnf(s39, plain, ~spl3_1 | ~spl3_3 | ~spl3_6, inference(sat_conversion,[],[f1067])).
% 0.07/0.24 cnf(s41, plain, ~spl3_1 | ~spl3_3 | ~spl3_5, inference(sat_conversion,[],[f1128])).
% 0.07/0.24 cnf(s42, plain, ~spl3_2 | ~spl3_4, inference(rat,[],[s5,s12,s31])).
% 0.07/0.24 cnf(s43, plain, spl3_1, inference(rat,[],[s42,s1,s3])).
% 0.07/0.24 cnf(s44, plain, ~spl3_3, inference(rat,[],[s5,s39,s41,s43])).
% 0.07/0.24 cnf(s45, plain, spl3_4, inference(rat,[],[s4,s44])).
% 0.07/0.24 cnf(s46, plain, spl3_2, inference(rat,[],[s2,s44])).
% 0.07/0.24 cnf(s47, plain, $false, inference(rat,[],[s42,s45,s46])).
% 0.07/0.24 thf(f1129,plain,(
% 0.07/0.24 $false),
% 0.07/0.24 inference(avatar_sat_refutation,[],[s47])).
% 0.07/0.24 % SZS output end Proof for theBenchmark
% 0.07/0.24 % (1956397)------------------------------
% 0.07/0.24 % (1956397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (1956397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (1956397)CaDiCaL version: 2.1.3
% 0.07/0.24 % (1956397)Termination reason: Refutation
% 0.07/0.24 % (1956397)Time elapsed: 0.019 s
% 0.07/0.24 % (1956397)Peak memory usage: 12 MB
% 0.07/0.24 % (1956397)Instructions burned: 71 (million)
% 0.07/0.24 % (1956389)Success in time 0.045 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------