%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA083^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 07:45:52 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA083^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:41:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.27 % (3485435)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (3485445)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1853706334:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (3485445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3485435-3485445"...
% 0.19/0.27 % (3485440)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2246098081:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (3485442)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=182731184:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (3485443)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1361109544:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (3485445)...printing done.
% 0.19/0.27 % (3485445)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.27 thf(func_def_4, type, 'const/realax/real_lt': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_9, type, sK0: ('type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_10, type, sK1: 'type/realax/real').
% 0.19/0.27 thf(func_def_11, type, sK2: 'type/realax/real').
% 0.19/0.27 thf(func_def_13, type, sK4: 'type/realax/real').
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_LTE_TRANS_')).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_')).
% 0.19/0.27 thf(f3,conjecture,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LT_INF_FINITE_')).
% 0.19/0.27 thf(f4,negated_conjecture,(
% 0.19/0.27 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)))))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => (((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true) <=> ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_lt' @ X1 @ X2)) = $true))))),
% 0.19/0.27 inference(fool_elimination,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ! [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' @ ('const/sets/inf' @ X0) @ X1)) = $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) & ('const/realax/real_le' @ X2 @ X0)) => ('const/realax/real_lt' @ X1 @ X0))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : ((($true = (('const/realax/real_le' @ X2 @ X0))) & ((('const/realax/real_lt' @ X1 @ X2)) = $true)) => ($true = (('const/realax/real_lt' @ X1 @ X0))))),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_lt' @ X1 @ X0))) | (($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_lt' @ X1 @ X2)) != $true)))),
% 0.19/0.27 inference(ennf_transformation,[],[f10])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_lt' @ X1 @ X2)) != $true) | ($true = (('const/realax/real_lt' @ X1 @ X0))))),
% 0.19/0.27 inference(flattening,[],[f11])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true) <~> ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/realax/real_lt' @ X1 @ X2)) = $true))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)))),
% 0.19/0.27 inference(ennf_transformation,[],[f6])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true) <~> ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/realax/real_lt' @ X1 @ X2)) = $true))) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.19/0.27 inference(flattening,[],[f13])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) = $true)) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)))),
% 0.19/0.27 inference(ennf_transformation,[],[f8])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) = $true)))),
% 0.19/0.27 inference(flattening,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_lt' @ X2 @ X1)) != $true) | ((('const/realax/real_lt' @ X2 @ X0)) = $true))),
% 0.19/0.27 inference(rectify,[],[f12])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_lt' @ X1 @ X2)) != $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/realax/real_lt' @ X1 @ X2)) = $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true))) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.19/0.27 inference(nnf_transformation,[],[f14])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_lt' @ X1 @ X2)) != $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/realax/real_lt' @ X1 @ X2)) = $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true)) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.19/0.27 inference(flattening,[],[f18])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_lt' @ X1 @ X2)) != $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_lt' @ X1 @ X3)) = $true)) | ((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))) = $true)) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.19/0.27 inference(rectify,[],[f19])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ((((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) = $true) & ($true != (('const/realax/real_lt' @ sK1 @ sK2)))) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) != $true)) & (! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) != $true) | ((('const/realax/real_lt' @ sK1 @ X3)) = $true)) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true)) & ((('const/sets/FINITE' @ 'type/realax/real' @ sK0)) = $true)),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f20])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ( ! [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/inf' @ X0) @ X0)) = $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f16])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f16])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_lt' @ X2 @ X1)) != $true) | ((('const/realax/real_lt' @ X2 @ X0)) = $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f17])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ((('const/sets/FINITE' @ 'type/realax/real' @ sK0)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real'] : (((('const/realax/real_lt' @ sK1 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) != $true) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ($true != (('const/realax/real_lt' @ sK1 @ sK2))) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) != $true) | ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f31,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f33,definition,(
% 0.19/0.27 spl3_1 <=> ($true = (('const/realax/real_lt' @ sK1 @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ($true != (('const/realax/real_lt' @ sK1 @ sK2))) | spl3_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f33])).
% 0.19/0.27 thf(f36,definition,(
% 0.19/0.27 spl3_2 <=> ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) != $true) | spl3_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f36])).
% 0.19/0.27 thf(f38,plain,(
% 0.19/0.27 ~spl3_1 | ~spl3_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f27,f36,f33])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true) | ~spl3_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f36])).
% 0.19/0.27 thf(f41,definition,(
% 0.19/0.27 spl3_3 <=> ! [X3 : 'type/realax/real'] : (((('const/realax/real_lt' @ sK1 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) != $true))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) != $true) | ((('const/realax/real_lt' @ sK1 @ X3)) = $true)) ) | ~spl3_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f41])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 spl3_2 | spl3_3),
% 0.19/0.27 inference(avatar_split_clause,[],[f26,f41,f36])).
% 0.19/0.27 thf(f45,definition,(
% 0.19/0.27 spl3_4 <=> ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) = $true) | ~spl3_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f45])).
% 0.19/0.27 thf(f47,plain,(
% 0.19/0.27 ~spl3_2 | spl3_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f28,f45,f36])).
% 0.19/0.27 thf(f72,plain,(
% 0.19/0.27 ($false = (('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) | ($true != $true) | spl3_2),
% 0.19/0.27 inference(constrained_superposition,[],[f37,f31])).
% 0.19/0.27 thf(f81,plain,(
% 0.19/0.27 ($false = (('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) | spl3_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f72])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)) = $true) | ($true != $true)),
% 0.19/0.27 inference(constrained_superposition,[],[f22,f25])).
% 0.19/0.27 thf(f87,plain,(
% 0.19/0.27 ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f84])).
% 0.19/0.27 thf(f88,plain,(
% 0.19/0.27 ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)) = $true)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f87,f29])).
% 0.19/0.27 thf(f93,plain,(
% 0.19/0.27 ($true != $true) | ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true) | ~spl3_3),
% 0.19/0.27 inference(constrained_superposition,[],[f42,f88])).
% 0.19/0.27 thf(f95,plain,(
% 0.19/0.27 ((('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) = $true) | ~spl3_3),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f93])).
% 0.19/0.27 thf(f97,plain,(
% 0.19/0.27 ($false = $true) | (spl3_2 | ~spl3_3)),
% 0.19/0.27 inference(forward_demodulation,[],[f95,f81])).
% 0.19/0.27 thf(f98,plain,(
% 0.19/0.27 $false | (spl3_2 | ~spl3_3)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f97])).
% 0.19/0.27 thf(f99,plain,(
% 0.19/0.27 spl3_2 | ~spl3_3),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f98])).
% 0.19/0.27 thf(f102,plain,(
% 0.19/0.27 ($true != $true) | ($false = (('const/realax/real_lt' @ sK1 @ sK2))) | spl3_1),
% 0.19/0.27 inference(constrained_superposition,[],[f34,f31])).
% 0.19/0.27 thf(f103,plain,(
% 0.19/0.27 ($false = (('const/realax/real_lt' @ sK1 @ sK2))) | spl3_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f102])).
% 0.19/0.27 thf(f107,plain,(
% 0.19/0.27 ($true != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2)) = $true) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl3_4),
% 0.19/0.27 inference(constrained_superposition,[],[f23,f46])).
% 0.19/0.27 thf(f108,plain,(
% 0.19/0.27 ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2)) = $true) | ((('const/sets/FINITE' @ 'type/realax/real' @ sK0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl3_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f107])).
% 0.19/0.27 thf(f109,plain,(
% 0.19/0.27 ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl3_4),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f108,f25])).
% 0.19/0.27 thf(f110,plain,(
% 0.19/0.27 ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2)) = $true) | ~spl3_4),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f109,f29])).
% 0.19/0.27 thf(f111,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_lt' @ X0 @ sK2))) | ($true != (('const/realax/real_lt' @ X0 @ ('const/sets/inf' @ sK0)))) | ($true != $true)) ) | ~spl3_4),
% 0.19/0.27 inference(constrained_superposition,[],[f24,f110])).
% 0.19/0.27 thf(f112,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_lt' @ X0 @ ('const/sets/inf' @ sK0)))) | ($true = (('const/realax/real_lt' @ X0 @ sK2)))) ) | ~spl3_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f111])).
% 0.19/0.27 thf(f114,plain,(
% 0.19/0.27 ($true != $true) | ($true = (('const/realax/real_lt' @ sK1 @ sK2))) | (~spl3_2 | ~spl3_4)),
% 0.19/0.27 inference(constrained_superposition,[],[f112,f39])).
% 0.19/0.27 thf(f117,plain,(
% 0.19/0.27 ($true = (('const/realax/real_lt' @ sK1 @ sK2))) | (~spl3_2 | ~spl3_4)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f114])).
% 0.19/0.27 thf(f118,plain,(
% 0.19/0.27 ($false = $true) | (spl3_1 | ~spl3_2 | ~spl3_4)),
% 0.19/0.27 inference(forward_demodulation,[],[f117,f103])).
% 0.19/0.27 thf(f119,plain,(
% 0.19/0.27 $false | (spl3_1 | ~spl3_2 | ~spl3_4)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f118])).
% 0.19/0.27 thf(f120,plain,(
% 0.19/0.27 spl3_1 | ~spl3_2 | ~spl3_4),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f119])).
% 0.19/0.27 cnf(s1, plain, ~spl3_1 | ~spl3_2, inference(sat_conversion,[],[f38])).
% 0.19/0.27 cnf(s2, plain, spl3_2 | spl3_3, inference(sat_conversion,[],[f43])).
% 0.19/0.27 cnf(s3, plain, ~spl3_2 | spl3_4, inference(sat_conversion,[],[f47])).
% 0.19/0.27 cnf(s7, plain, spl3_2 | ~spl3_3, inference(sat_conversion,[],[f99])).
% 0.19/0.27 cnf(s8, plain, spl3_1 | ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f120])).
% 0.19/0.27 cnf(s9, plain, spl3_2, inference(rat,[],[s2,s7])).
% 0.19/0.27 cnf(s10, plain, spl3_4, inference(rat,[],[s3,s9])).
% 0.19/0.27 cnf(s11, plain, ~spl3_1, inference(rat,[],[s1,s9])).
% 0.19/0.27 cnf(s12, plain, $false, inference(rat,[],[s8,s9,s11,s10])).
% 0.19/0.27 thf(f121,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s12])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3485445)------------------------------
% 0.19/0.27 % (3485445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3485445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3485445)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3485445)Termination reason: Refutation
% 0.19/0.27 % (3485445)Time elapsed: 0.004 s
% 0.19/0.27 % (3485445)Peak memory usage: 13 MB
% 0.19/0.27 % (3485445)Instructions burned: 10 (million)
% 0.19/0.27 % (3485435)Success in time 0.042 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------