%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA081^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 07:46:01 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA081^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n004.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 17:40:38 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.08/0.25 % (1618587)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (1618598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3740980817:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.08/0.25 % (1618593)% WARNING: option uhcvi not known.
% 0.08/0.25 % (1618593)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4219769863:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.08/0.25 % (1618595)dis+10_1_sil=32000:sp=arity:random_seed=333558700:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.25 % (1618594)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1716045858:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.08/0.25 % (1618596)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2173822823:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.25 % (1618597)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3577012060:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.08/0.25 % (1618593)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (1618598) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1618587-1618598"...
% 0.08/0.25 % (1618593)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (1618596)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (1618598)...printing done.
% 0.08/0.25 % (1618598)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.08/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.08/0.25 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.08/0.25 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.25 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.08/0.25 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.08/0.25 thf(func_def_8, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.25 thf(func_def_9, type, vIMP: ($o > $o > $o)).
% 0.08/0.25 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.25 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.25 thf(func_def_12, type, sK0: ('type/realax/real' > $o)).
% 0.08/0.25 thf(func_def_13, type, sK1: 'type/realax/real').
% 0.08/0.25 thf(func_def_14, type, sK2: 'type/realax/real').
% 0.08/0.25 thf(func_def_16, type, sK4: 'type/realax/real').
% 0.08/0.25 thf(f1,axiom,(
% 0.08/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.08/0.25 thf(f2,axiom,(
% 0.08/0.25 ! [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' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_')).
% 0.08/0.25 thf(f3,conjecture,(
% 0.08/0.25 ! [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_le' @ X1 @ ('const/sets/inf' @ X0))) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_FINITE_')).
% 0.08/0.25 thf(f4,negated_conjecture,(
% 0.08/0.25 ~ ! [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_le' @ X1 @ ('const/sets/inf' @ X0))) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.25 thf(f5,plain,(
% 0.08/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.08/0.25 inference(rectify,[],[f1])).
% 0.08/0.25 thf(f6,plain,(
% 0.08/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ X1 @ X2)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) => ((('const/realax/real_le' @ X0 @ X2)) = $true))),
% 0.08/0.25 inference(fool_elimination,[],[f5])).
% 0.08/0.25 thf(f7,plain,(
% 0.08/0.25 ! [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' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.08/0.25 inference(rectify,[],[f2])).
% 0.08/0.25 thf(f8,plain,(
% 0.08/0.25 ! [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)))),
% 0.08/0.25 inference(fool_elimination,[],[f7])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 ~ ! [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_le' @ X1 @ ('const/sets/inf' @ X0))) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 0.08/0.25 inference(rectify,[],[f4])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 ~ ! [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_le' @ X1 @ ('const/sets/inf' @ X0))) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0)))))))),
% 0.08/0.25 inference(fool_elimination,[],[f9])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 0.08/0.25 inference(ennf_transformation,[],[f6])).
% 0.08/0.25 thf(f12,plain,(
% 0.08/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true))),
% 0.08/0.25 inference(flattening,[],[f11])).
% 0.08/0.25 thf(f13,plain,(
% 0.08/0.25 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $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)))),
% 0.08/0.25 inference(ennf_transformation,[],[f8])).
% 0.08/0.25 thf(f14,plain,(
% 0.08/0.25 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $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))),
% 0.08/0.25 inference(flattening,[],[f13])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0)))))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)))),
% 0.08/0.25 inference(ennf_transformation,[],[f10])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.08/0.25 inference(flattening,[],[f15])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.08/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.08/0.25 thf(f18,plain,(
% 0.08/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f12])).
% 0.08/0.25 thf(f19,plain,(
% 0.08/0.25 ( ! [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)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f14])).
% 0.08/0.25 thf(f20,plain,(
% 0.08/0.25 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f14])).
% 0.08/0.25 thf(f21,plain,(
% 0.08/0.25 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.08/0.25 inference(cnf_transformation,[],[f17])).
% 0.08/0.25 thf(f22,plain,(
% 0.08/0.25 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.08/0.25 inference(cnf_transformation,[],[f17])).
% 0.08/0.25 thf(f23,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))))))),
% 0.08/0.25 inference(cnf_transformation,[],[f17])).
% 0.08/0.25 thf(f25,definition,(
% 0.08/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.25 thf(f26,plain,(
% 0.08/0.25 ($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))))))),
% 0.08/0.25 inference(xor_proxy_clausification,[],[f23])).
% 0.08/0.25 thf(f27,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))))) = $false)),
% 0.08/0.25 inference(xor_proxy_clausification,[],[f23])).
% 0.08/0.25 thf(f28,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))) @ sK2)))),
% 0.08/0.25 inference(sigma_proxy_clausification,[],[f27])).
% 0.08/0.25 thf(f29,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) => ('const/realax/real_le' @ sK1 @ sK2))))),
% 0.08/0.25 inference(beta-eta_normalization,[],[f28])).
% 0.08/0.25 thf(f30,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | ($false = (('const/realax/real_le' @ sK1 @ sK2)))),
% 0.08/0.25 inference(imp_proxy_clausification,[],[f29])).
% 0.08/0.25 thf(f31,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.08/0.25 inference(imp_proxy_clausification,[],[f29])).
% 0.08/0.25 thf(f32,plain,(
% 0.08/0.25 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))) @ X1)))) )),
% 0.08/0.25 inference(pi_proxy_clausification,[],[f26])).
% 0.08/0.25 thf(f33,plain,(
% 0.08/0.25 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0) => ('const/realax/real_le' @ sK1 @ X1))))) )),
% 0.08/0.25 inference(beta-eta_normalization,[],[f32])).
% 0.08/0.25 thf(f34,plain,(
% 0.08/0.25 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) | ($true = (('const/realax/real_le' @ sK1 @ X1)))) )),
% 0.08/0.25 inference(imp_proxy_clausification,[],[f33])).
% 0.08/0.25 thf(f36,definition,(
% 0.08/0.25 spl3_1 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.08/0.25 thf(f38,plain,(
% 0.08/0.25 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0))) | ~spl3_1),
% 0.08/0.25 inference(avatar_component_clause,[],[f36])).
% 0.08/0.25 thf(f40,definition,(
% 0.08/0.25 spl3_2 <=> ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.08/0.25 thf(f42,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | ~spl3_2),
% 0.08/0.25 inference(avatar_component_clause,[],[f40])).
% 0.08/0.25 thf(f43,plain,(
% 0.08/0.25 spl3_1 | spl3_2),
% 0.08/0.25 inference(avatar_split_clause,[],[f31,f40,f36])).
% 0.08/0.25 thf(f45,definition,(
% 0.08/0.25 spl3_3 <=> ($false = (('const/realax/real_le' @ sK1 @ sK2)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.08/0.25 thf(f47,plain,(
% 0.08/0.25 ($false = (('const/realax/real_le' @ sK1 @ sK2))) | ~spl3_3),
% 0.08/0.25 inference(avatar_component_clause,[],[f45])).
% 0.08/0.25 thf(f48,plain,(
% 0.08/0.25 spl3_3 | spl3_2),
% 0.08/0.25 inference(avatar_split_clause,[],[f30,f40,f45])).
% 0.08/0.25 thf(f50,definition,(
% 0.08/0.25 spl3_4 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) | ($true = (('const/realax/real_le' @ sK1 @ X1))))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.08/0.25 thf(f51,plain,(
% 0.08/0.25 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) | ($true = (('const/realax/real_le' @ sK1 @ X1)))) ) | ~spl3_4),
% 0.08/0.25 inference(avatar_component_clause,[],[f50])).
% 0.08/0.25 thf(f53,definition,(
% 0.08/0.25 spl3_5 <=> ($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.08/0.25 thf(f55,plain,(
% 0.08/0.25 ($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | ~spl3_5),
% 0.08/0.25 inference(avatar_component_clause,[],[f53])).
% 0.08/0.25 thf(f56,plain,(
% 0.08/0.25 spl3_4 | spl3_5),
% 0.08/0.25 inference(avatar_split_clause,[],[f34,f53,f50])).
% 0.08/0.25 thf(f113,plain,(
% 0.08/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f18,f25])).
% 0.08/0.25 thf(f114,plain,(
% 0.08/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f113])).
% 0.08/0.25 thf(f116,plain,(
% 0.08/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f114,f25])).
% 0.08/0.25 thf(f117,plain,(
% 0.08/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f116])).
% 0.08/0.25 thf(f150,plain,(
% 0.08/0.25 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.08/0.25 inference(constrained_superposition,[],[f19,f21])).
% 0.08/0.25 thf(f153,plain,(
% 0.08/0.25 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f150])).
% 0.08/0.25 thf(f155,definition,(
% 0.08/0.25 spl3_10 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.08/0.25 thf(f157,plain,(
% 0.08/0.25 ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0))) | ~spl3_10),
% 0.08/0.25 inference(avatar_component_clause,[],[f155])).
% 0.08/0.25 thf(f159,definition,(
% 0.08/0.25 spl3_11 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK0)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition])).
% 0.08/0.25 thf(f161,plain,(
% 0.08/0.25 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl3_11),
% 0.08/0.25 inference(avatar_component_clause,[],[f159])).
% 0.08/0.25 thf(f162,plain,(
% 0.08/0.25 spl3_10 | spl3_11),
% 0.08/0.25 inference(avatar_split_clause,[],[f153,f159,f155])).
% 0.08/0.25 thf(f164,plain,(
% 0.08/0.25 ($true = $false) | ($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | (~spl3_4 | ~spl3_10)),
% 0.08/0.25 inference(constrained_superposition,[],[f51,f157])).
% 0.08/0.25 thf(f165,plain,(
% 0.08/0.25 ($true = (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) | (~spl3_4 | ~spl3_10)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f164])).
% 0.08/0.25 thf(f167,plain,(
% 0.08/0.25 spl3_5 | ~spl3_4 | ~spl3_10),
% 0.08/0.25 inference(avatar_split_clause,[],[f165,f155,f50,f53])).
% 0.08/0.25 thf(f169,plain,(
% 0.08/0.25 (sK0 != sK0) | ~spl3_11),
% 0.08/0.25 inference(constrained_superposition,[],[f22,f161])).
% 0.08/0.25 thf(f170,plain,(
% 0.08/0.25 $false | ~spl3_11),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f169])).
% 0.08/0.25 thf(f171,plain,(
% 0.08/0.25 ~spl3_11),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f170])).
% 0.08/0.25 thf(f176,plain,(
% 0.08/0.25 ($true = $false) | (~spl3_2 | ~spl3_5)),
% 0.08/0.25 inference(constrained_superposition,[],[f55,f42])).
% 0.08/0.25 thf(f188,plain,(
% 0.08/0.25 $false | (~spl3_2 | ~spl3_5)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f176])).
% 0.08/0.25 thf(f189,plain,(
% 0.08/0.25 ~spl3_2 | ~spl3_5),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f188])).
% 0.08/0.25 thf(f192,plain,(
% 0.08/0.25 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ X0 @ sK2))) | ($false = (('const/realax/real_le' @ sK1 @ X0)))) ) | ~spl3_3),
% 0.08/0.25 inference(constrained_superposition,[],[f117,f47])).
% 0.08/0.25 thf(f195,plain,(
% 0.08/0.25 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK2))) | ($false = (('const/realax/real_le' @ sK1 @ X0)))) ) | ~spl3_3),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f192])).
% 0.08/0.25 thf(f374,plain,(
% 0.08/0.25 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0)))) )),
% 0.08/0.25 inference(constrained_superposition,[],[f20,f21])).
% 0.08/0.25 thf(f377,plain,(
% 0.08/0.25 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0)))) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f374])).
% 0.08/0.25 thf(f379,definition,(
% 0.08/0.25 spl3_14 <=> ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0))))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition])).
% 0.08/0.25 thf(f380,plain,(
% 0.08/0.25 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0)))) ) | ~spl3_14),
% 0.08/0.25 inference(avatar_component_clause,[],[f379])).
% 0.08/0.25 thf(f381,plain,(
% 0.08/0.25 spl3_11 | spl3_14),
% 0.08/0.25 inference(avatar_split_clause,[],[f377,f379,f159])).
% 0.08/0.25 thf(f382,plain,(
% 0.08/0.25 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | (~spl3_1 | ~spl3_14)),
% 0.08/0.25 inference(constrained_superposition,[],[f380,f38])).
% 0.08/0.25 thf(f387,plain,(
% 0.08/0.25 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | (~spl3_1 | ~spl3_14)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f382])).
% 0.08/0.25 thf(f400,plain,(
% 0.08/0.25 ($true = $false) | ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | (~spl3_1 | ~spl3_3 | ~spl3_14)),
% 0.08/0.25 inference(constrained_superposition,[],[f195,f387])).
% 0.08/0.25 thf(f404,plain,(
% 0.08/0.25 ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) = $false) | (~spl3_1 | ~spl3_3 | ~spl3_14)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f400])).
% 0.08/0.25 thf(f418,plain,(
% 0.08/0.25 spl3_2 | ~spl3_1 | ~spl3_3 | ~spl3_14),
% 0.08/0.25 inference(avatar_split_clause,[],[f404,f379,f45,f36,f40])).
% 0.08/0.25 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f43])).
% 0.08/0.25 cnf(s2, plain, spl3_2 | spl3_3, inference(sat_conversion,[],[f48])).
% 0.08/0.26 cnf(s3, plain, spl3_4 | spl3_5, inference(sat_conversion,[],[f56])).
% 0.08/0.26 cnf(s8, plain, spl3_10 | spl3_11, inference(sat_conversion,[],[f162])).
% 0.08/0.26 cnf(s9, plain, ~spl3_4 | spl3_5 | ~spl3_10, inference(sat_conversion,[],[f167])).
% 0.08/0.26 cnf(s11, plain, ~spl3_11, inference(sat_conversion,[],[f171])).
% 0.08/0.26 cnf(s13, plain, ~spl3_2 | ~spl3_5, inference(sat_conversion,[],[f189])).
% 0.08/0.26 cnf(s18, plain, spl3_11 | spl3_14, inference(sat_conversion,[],[f381])).
% 0.08/0.26 cnf(s21, plain, ~spl3_1 | spl3_2 | ~spl3_3 | ~spl3_14, inference(sat_conversion,[],[f418])).
% 0.08/0.26 cnf(s23, plain, spl3_14, inference(rat,[],[s18,s11])).
% 0.08/0.26 cnf(s24, plain, spl3_10, inference(rat,[],[s8,s11])).
% 0.08/0.26 cnf(s25, plain, spl3_5, inference(rat,[],[s3,s9,s24])).
% 0.08/0.26 cnf(s26, plain, ~spl3_2, inference(rat,[],[s13,s25])).
% 0.08/0.26 cnf(s27, plain, spl3_3, inference(rat,[],[s2,s26])).
% 0.08/0.26 cnf(s28, plain, spl3_1, inference(rat,[],[s1,s26])).
% 0.08/0.26 cnf(s30, plain, $false, inference(rat,[],[s21,s23,s26,s28,s27])).
% 0.08/0.26 thf(f419,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s30])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (1618598)------------------------------
% 0.08/0.26 % (1618598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (1618598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (1618598)CaDiCaL version: 2.1.3
% 0.08/0.26 % (1618598)Termination reason: Refutation
% 0.08/0.26 % (1618598)Time elapsed: 0.009 s
% 0.08/0.26 % (1618598)Peak memory usage: 12 MB
% 0.08/0.26 % (1618598)Instructions burned: 28 (million)
% 0.08/0.26 % (1618587)Success in time 0.026 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------