%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA071^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 07:46:00 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA071^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n004.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 17:40:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (1617529)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1617544)dis+10_1_sil=32000:sp=arity:random_seed=259175169:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1617542)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1617544) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1617529-1617544"...
% 0.20/0.29 % (1617544)...printing done.
% 0.20/0.29 % (1617544)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.29 thf(func_def_4, type, 'const/realax/real_lt': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_9, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_10, type, vAND: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_13, type, sK0: ('type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_14, type, sK1: 'type/realax/real').
% 0.20/0.29 thf(func_def_15, type, sK2: 'type/realax/real').
% 0.20/0.29 thf(func_def_17, type, sK4: 'type/realax/real').
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_lt' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_LTE_TRANS_')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_FINITE_')).
% 0.20/0.29 thf(f3,conjecture,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LT_SUP_FINITE_')).
% 0.20/0.29 thf(f4,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_lt' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ X1 @ X2)) = $true) & ((('const/realax/real_lt' @ X0 @ X1)) = $true)) => ((('const/realax/real_lt' @ X0 @ X2)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => (! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)) = $true)))),
% 0.20/0.29 inference(fool_elimination,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => ((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ X1 @ Y0)))))))),
% 0.20/0.29 inference(fool_elimination,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X2)) = $true) | (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X1)) != $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f6])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(flattening,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)) = $true)) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f8])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 0.20/0.29 inference(flattening,[],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ X1 @ Y0)))))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f10])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0))) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ X1 @ Y0)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.20/0.29 inference(flattening,[],[f15])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X2)) = $true) | ((('const/realax/real_lt' @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o)] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.20/0.29 inference(cnf_transformation,[],[f17])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.20/0.29 inference(cnf_transformation,[],[f17])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0))))))),
% 0.20/0.29 inference(cnf_transformation,[],[f17])).
% 0.20/0.29 thf(f25,definition,(
% 0.20/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ($true = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0))))))),
% 0.20/0.29 inference(xor_proxy_clausification,[],[f23])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0))))) = $false)),
% 0.20/0.29 inference(xor_proxy_clausification,[],[f23])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0))) @ X1)))) )),
% 0.20/0.29 inference(pi_proxy_clausification,[],[f27])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0) & ('const/realax/real_lt' @ sK1 @ X1))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f28])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ($false = (('const/realax/real_lt' @ sK1 @ X1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)))) )),
% 0.20/0.29 inference(and_proxy_clausification,[],[f29])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ sK1 @ Y0))) @ sK2)))),
% 0.20/0.29 inference(sigma_proxy_clausification,[],[f26])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) & ('const/realax/real_lt' @ sK1 @ sK2))))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f31])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ($true = (('const/realax/real_lt' @ sK1 @ sK2)))),
% 0.20/0.29 inference(and_proxy_clausification,[],[f32])).
% 0.20/0.29 thf(f34,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.20/0.29 inference(and_proxy_clausification,[],[f32])).
% 0.20/0.29 thf(f36,definition,(
% 0.20/0.29 spl3_1 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_lt' @ sK1 @ X1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) | ($false = (('const/realax/real_lt' @ sK1 @ X1)))) ) | ~spl3_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f36])).
% 0.20/0.29 thf(f39,definition,(
% 0.20/0.29 spl3_2 <=> ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) != $false) | spl3_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f39])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ~spl3_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f39])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 spl3_1 | spl3_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f30,f39,f36])).
% 0.20/0.29 thf(f44,definition,(
% 0.20/0.29 spl3_3 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.20/0.29 thf(f46,plain,(
% 0.20/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0))) | ~spl3_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f44])).
% 0.20/0.29 thf(f48,definition,(
% 0.20/0.29 spl3_4 <=> ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | ~spl3_4),
% 0.20/0.29 inference(avatar_component_clause,[],[f48])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 spl3_3 | spl3_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f34,f48,f44])).
% 0.20/0.29 thf(f53,definition,(
% 0.20/0.29 spl3_5 <=> ($true = (('const/realax/real_lt' @ sK1 @ sK2)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.20/0.29 thf(f55,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ sK2))) | ~spl3_5),
% 0.20/0.29 inference(avatar_component_clause,[],[f53])).
% 0.20/0.29 thf(f56,plain,(
% 0.20/0.29 spl3_5 | spl3_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f33,f48,f53])).
% 0.20/0.29 thf(f89,plain,(
% 0.20/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_lt' @ X2 @ X1))) | ($true != (('const/realax/real_lt' @ X2 @ X0))) | ($false = (('const/realax/real_le' @ X0 @ X1)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f18,f25])).
% 0.20/0.29 thf(f90,plain,(
% 0.20/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_lt' @ X2 @ X0))) | ($true = (('const/realax/real_lt' @ X2 @ X1))) | ($false = (('const/realax/real_le' @ X0 @ X1)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f89])).
% 0.20/0.29 thf(f92,plain,(
% 0.20/0.29 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ sK0) @ sK0)))),
% 0.20/0.29 inference(constrained_superposition,[],[f19,f21])).
% 0.20/0.29 thf(f95,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ sK0) @ sK0)))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f92])).
% 0.20/0.29 thf(f96,plain,(
% 0.20/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ sK0) @ sK0)))),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f95,f22])).
% 0.20/0.29 thf(f107,plain,(
% 0.20/0.29 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.20/0.29 inference(forward_demodulation,[],[f50,f41])).
% 0.20/0.29 thf(f108,plain,(
% 0.20/0.29 $false | (~spl3_2 | ~spl3_4)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f107])).
% 0.20/0.29 thf(f109,plain,(
% 0.20/0.29 ~spl3_2 | ~spl3_4),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f108])).
% 0.20/0.29 thf(f114,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_lt' @ sK1 @ X0))) | ($false = (('const/realax/real_le' @ sK2 @ X0)))) ) | ~spl3_5),
% 0.20/0.29 inference(constrained_superposition,[],[f90,f55])).
% 0.20/0.29 thf(f115,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ sK2 @ X0))) | ($true = (('const/realax/real_lt' @ sK1 @ X0)))) ) | ~spl3_5),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f114])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl3_3),
% 0.20/0.29 inference(constrained_superposition,[],[f20,f46])).
% 0.20/0.29 thf(f121,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl3_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f120])).
% 0.20/0.29 thf(f122,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl3_3),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f121,f22])).
% 0.20/0.29 thf(f123,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0)))) | ~spl3_3),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f122,f21])).
% 0.20/0.29 thf(f135,plain,(
% 0.20/0.29 ($true = $false) | ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | (~spl3_3 | ~spl3_5)),
% 0.20/0.29 inference(constrained_superposition,[],[f123,f115])).
% 0.20/0.29 thf(f136,plain,(
% 0.20/0.29 ($true = (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)))) | (~spl3_3 | ~spl3_5)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f135])).
% 0.20/0.29 thf(f145,plain,(
% 0.20/0.29 spl3_4 | ~spl3_3 | ~spl3_5),
% 0.20/0.29 inference(avatar_split_clause,[],[f136,f53,f44,f48])).
% 0.20/0.29 thf(f150,plain,(
% 0.20/0.29 ($true = $false) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ~spl3_1),
% 0.20/0.29 inference(constrained_superposition,[],[f37,f96])).
% 0.20/0.29 thf(f164,plain,(
% 0.20/0.29 ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0))) = $false) | ~spl3_1),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.20/0.29 thf(f169,plain,(
% 0.20/0.29 $false | (~spl3_1 | spl3_2)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f164,f40])).
% 0.20/0.29 thf(f170,plain,(
% 0.20/0.29 ~spl3_1 | spl3_2),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f169])).
% 0.20/0.29 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f42])).
% 0.20/0.29 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f51])).
% 0.20/0.29 cnf(s3, plain, spl3_4 | spl3_5, inference(sat_conversion,[],[f56])).
% 0.20/0.29 cnf(s7, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f109])).
% 0.20/0.29 cnf(s10, plain, ~spl3_3 | spl3_4 | ~spl3_5, inference(sat_conversion,[],[f145])).
% 0.20/0.29 cnf(s13, plain, ~spl3_1 | spl3_2, inference(sat_conversion,[],[f170])).
% 0.20/0.29 cnf(s14, plain, spl3_4, inference(rat,[],[s10,s2,s3])).
% 0.20/0.29 cnf(s15, plain, ~spl3_2, inference(rat,[],[s7,s14])).
% 0.20/0.29 cnf(s16, plain, ~spl3_1, inference(rat,[],[s13,s15])).
% 0.20/0.29 cnf(s17, plain, $false, inference(rat,[],[s1,s15,s16])).
% 0.20/0.29 thf(f173,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s17])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (1617544)------------------------------
% 0.20/0.29 % (1617544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1617544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1617544)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1617544)Termination reason: Refutation
% 0.20/0.29 % (1617544)Time elapsed: 0.004 s
% 0.20/0.29 % (1617544)Peak memory usage: 12 MB
% 0.20/0.29 % (1617544)Instructions burned: 12 (million)
% 0.20/0.29 % (1617529)Success in time 0.037 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------