%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV084^5 : 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 : n016.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 08:38:58 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV084^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n016.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 15:14:17 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.19/0.28 % (468703)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (468712)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1521014369:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (468712)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (468712) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-468703-468712"...
% 0.19/0.28 % (468709)% WARNING: option uhcvi not known.
% 0.19/0.28 % (468712)...printing done.
% 0.19/0.28 % (468712)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, cP: $o).
% 0.19/0.28 thf(func_def_2, type, vOR: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_3, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.28 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.28 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.28 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.28 thf(f1,conjecture,(
% 0.19/0.28 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : (~cP | cP)) @ (^[X1 : $i] : (~cP & cP))))),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120J_pme)).
% 0.19/0.28 thf(f2,negated_conjecture,(
% 0.19/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : (~cP | cP)) @ (^[X1 : $i] : (~cP & cP))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 thf(f3,plain,(
% 0.19/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X4 : ($i > $o)] : (X0 @ X4 @ X4) & ~(X0 @ (^[X5 : $i] : (~cP | cP)) @ (^[X6 : $i] : (~cP & cP))))),
% 0.19/0.28 inference(rectify,[],[f2])).
% 0.19/0.28 thf(f4,plain,(
% 0.19/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (((X0 @ X1 @ X3)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true) & ~ (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true))),
% 0.19/0.28 inference(fool_elimination,[],[f3])).
% 0.19/0.28 thf(f5,plain,(
% 0.19/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (((X0 @ X1 @ X3)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true) & (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) != $true))),
% 0.19/0.28 inference(flattening,[],[f4])).
% 0.19/0.28 thf(f6,plain,(
% 0.19/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & ((((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true))) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true))),
% 0.19/0.28 inference(ennf_transformation,[],[f5])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & (((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true))),
% 0.19/0.28 inference(flattening,[],[f6])).
% 0.19/0.28 thf(f8,plain,(
% 0.19/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0)],[f7])).
% 0.19/0.28 thf(f9,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP))))) = $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f8])).
% 0.19/0.28 thf(f14,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f9])).
% 0.19/0.28 thf(f15,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f14])).
% 0.19/0.28 thf(f16,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f10])).
% 0.19/0.28 thf(f17,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f16])).
% 0.19/0.28 thf(f18,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f11])).
% 0.19/0.28 thf(f19,plain,(
% 0.19/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))) )),
% 0.19/0.28 inference(boolean_simplification,[],[f18])).
% 0.19/0.28 thf(f27,plain,(
% 0.19/0.28 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(primitive_instantiation,[],[f15])).
% 0.19/0.28 thf(f56,plain,(
% 0.19/0.28 ($true = (((sK0 @ =) = (sK1 @ =)))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(beta-eta_normalization,[],[f27])).
% 0.19/0.28 thf(f57,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK0 @ =))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f56])).
% 0.19/0.28 thf(f58,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK0 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f57])).
% 0.19/0.28 thf(f59,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK0 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f58])).
% 0.19/0.28 thf(f60,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f59])).
% 0.19/0.28 thf(f62,definition,(
% 0.19/0.28 spl4_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.28 thf(f63,plain,(
% 0.19/0.28 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl4_1),
% 0.19/0.28 inference(avatar_component_clause,[],[f62])).
% 0.19/0.28 thf(f64,plain,(
% 0.19/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl4_1),
% 0.19/0.28 inference(avatar_component_clause,[],[f62])).
% 0.19/0.28 thf(f66,definition,(
% 0.19/0.28 spl4_2 <=> (((sK1 @ =)) = ((sK0 @ =)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.28 thf(f68,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK0 @ =))) | ~spl4_2),
% 0.19/0.28 inference(avatar_component_clause,[],[f66])).
% 0.19/0.28 thf(f69,plain,(
% 0.19/0.28 spl4_1 | spl4_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f60,f66,f62])).
% 0.19/0.28 thf(f70,plain,(
% 0.19/0.28 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(primitive_instantiation,[],[f17])).
% 0.19/0.28 thf(f99,plain,(
% 0.19/0.28 ($true = (((sK1 @ =) = (sK2 @ =)))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(beta-eta_normalization,[],[f70])).
% 0.19/0.28 thf(f100,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK2 @ =))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f99])).
% 0.19/0.28 thf(f101,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f100])).
% 0.19/0.28 thf(f102,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f101])).
% 0.19/0.28 thf(f103,plain,(
% 0.19/0.28 (((sK1 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f102])).
% 0.19/0.28 thf(f104,plain,(
% 0.19/0.28 (((sK0 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl4_2),
% 0.19/0.28 inference(forward_demodulation,[],[f103,f68])).
% 0.19/0.28 thf(f106,definition,(
% 0.19/0.28 spl4_3 <=> (((sK0 @ =)) = ((sK2 @ =)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.19/0.28 thf(f108,plain,(
% 0.19/0.28 (((sK0 @ =)) = ((sK2 @ =))) | ~spl4_3),
% 0.19/0.28 inference(avatar_component_clause,[],[f106])).
% 0.19/0.28 thf(f109,plain,(
% 0.19/0.28 spl4_1 | spl4_3 | ~spl4_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f104,f66,f106,f62])).
% 0.19/0.28 thf(f110,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl4_1),
% 0.19/0.28 inference(argument_congruence,[],[f64])).
% 0.19/0.28 thf(f111,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ($false = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl4_1),
% 0.19/0.28 inference(iff_proxy_clausification,[],[f110])).
% 0.19/0.28 thf(f114,plain,(
% 0.19/0.28 ($true = $false) | ($true = $false) | ~spl4_1),
% 0.19/0.28 inference(beta-eta_normalization,[],[f111])).
% 0.19/0.28 thf(f115,plain,(
% 0.19/0.28 ($true = $false) | ~spl4_1),
% 0.19/0.28 inference(duplicate_literal_removal,[],[f114])).
% 0.19/0.28 thf(f116,plain,(
% 0.19/0.28 $false | ~spl4_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f115])).
% 0.19/0.28 thf(f117,plain,(
% 0.19/0.28 ~spl4_1),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f116])).
% 0.19/0.28 thf(f118,plain,(
% 0.19/0.28 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(primitive_instantiation,[],[f19])).
% 0.19/0.28 thf(f154,plain,(
% 0.19/0.28 ($true != (((sK0 @ =) = (sK2 @ =)))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(beta-eta_normalization,[],[f118])).
% 0.19/0.28 thf(f155,plain,(
% 0.19/0.28 (((sK0 @ =)) != ((sK2 @ =))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f154])).
% 0.19/0.28 thf(f156,plain,(
% 0.19/0.28 (((sK0 @ =)) != ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f155])).
% 0.19/0.28 thf(f157,plain,(
% 0.19/0.28 (((sK0 @ =)) != ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(equality_proxy_clausification,[],[f156])).
% 0.19/0.28 thf(f158,plain,(
% 0.19/0.28 (((sK0 @ =)) != ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f157])).
% 0.19/0.28 thf(f173,plain,(
% 0.19/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl4_3),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f158,f108])).
% 0.19/0.28 thf(f174,plain,(
% 0.19/0.28 $false | (spl4_1 | ~spl4_3)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f173,f63])).
% 0.19/0.28 thf(f175,plain,(
% 0.19/0.28 spl4_1 | ~spl4_3),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f174])).
% 0.19/0.28 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f69])).
% 0.19/0.28 cnf(s2, plain, spl4_1 | ~spl4_2 | spl4_3, inference(sat_conversion,[],[f109])).
% 0.19/0.28 cnf(s3, plain, ~spl4_1, inference(sat_conversion,[],[f117])).
% 0.19/0.28 cnf(s7, plain, spl4_1 | ~spl4_3, inference(sat_conversion,[],[f175])).
% 0.19/0.28 cnf(s8, plain, ~spl4_3, inference(rat,[],[s7,s3])).
% 0.19/0.28 cnf(s9, plain, ~spl4_2, inference(rat,[],[s2,s8,s3])).
% 0.19/0.28 cnf(s10, plain, $false, inference(rat,[],[s1,s9,s3])).
% 0.19/0.28 thf(f176,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(avatar_sat_refutation,[],[s10])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (468712)------------------------------
% 0.19/0.28 % (468712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (468712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (468712)CaDiCaL version: 2.1.3
% 0.19/0.28 % (468712)Termination reason: Refutation
% 0.19/0.28 % (468712)Time elapsed: 0.004 s
% 0.19/0.28 % (468712)Peak memory usage: 12 MB
% 0.19/0.28 % (468712)Instructions burned: 12 (million)
% 0.19/0.28 % (468703)Success in time 0.037 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------