%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA084^1 : 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 : n006.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 07:46:02 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA084^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:40:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (1073004)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1073013)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1416788940:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (1073012)% WARNING: option uhcvi not known.
% 0.09/0.25 % (1073012)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2961237704:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (1073011)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1147498880_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (1073014)dis+10_1_sil=32000:sp=arity:random_seed=1096645357:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (1073015)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2350239956:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (1073013) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1073004-1073013"...
% 0.09/0.25 % (1073012)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (1073012)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (1073015)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (1073013)...printing done.
% 0.09/0.25 % (1073017)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1531773991:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (1073013)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.09/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.09/0.25 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.09/0.25 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.25 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.09/0.25 thf(func_def_4, type, 'const/realax/real_lt': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.09/0.25 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.09/0.25 thf(func_def_9, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.25 thf(func_def_10, type, vAND: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.25 thf(func_def_13, type, sK0: ('type/realax/real' > $o)).
% 0.09/0.25 thf(func_def_14, type, sK1: 'type/realax/real').
% 0.09/0.25 thf(func_def_15, type, sK2: 'type/realax/real').
% 0.09/0.25 thf(func_def_16, type, sK3: 'type/realax/real').
% 0.09/0.25 thf(func_def_18, type, sK5: (('type/realax/real' > $o) > 'type/realax/real')).
% 0.09/0.25 thf(f1,axiom,(
% 0.09/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_LET_TRANS_')).
% 0.09/0.25 thf(f2,axiom,(
% 0.09/0.25 ! [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)))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_')).
% 0.09/0.25 thf(f3,conjecture,(
% 0.09/0.25 ! [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_lt' @ ('const/sets/inf' @ X0) @ X1)) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X2 @ X1) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LT_FINITE_')).
% 0.09/0.25 thf(f4,negated_conjecture,(
% 0.09/0.25 ~ ! [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_lt' @ ('const/sets/inf' @ X0) @ X1)) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X2 @ X1) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.09/0.25 inference(rectify,[],[f1])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_lt' @ X1 @ X2)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) => ((('const/realax/real_lt' @ X0 @ X2)) = $true))),
% 0.09/0.25 inference(fool_elimination,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ! [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)))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ! [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)))),
% 0.09/0.25 inference(fool_elimination,[],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 ~ ! [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_lt' @ ('const/sets/inf' @ X0) @ X1)) = ? [X2 : 'type/realax/real'] : (('const/realax/real_lt' @ X2 @ X1) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 0.09/0.25 inference(rectify,[],[f4])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ~ ! [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_lt' @ ('const/sets/inf' @ X0) @ X1)) = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ Y0 @ X1)))))))),
% 0.09/0.25 inference(fool_elimination,[],[f9])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X2)) = $true) | (((('const/realax/real_lt' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f6])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X2)) = $true) | ((('const/realax/real_lt' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true))),
% 0.09/0.25 inference(flattening,[],[f11])).
% 0.09/0.25 thf(f13,plain,(
% 0.09/0.25 ! [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)))),
% 0.09/0.25 inference(ennf_transformation,[],[f8])).
% 0.09/0.25 thf(f14,plain,(
% 0.09/0.25 ! [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))),
% 0.09/0.25 inference(flattening,[],[f13])).
% 0.09/0.25 thf(f15,plain,(
% 0.09/0.25 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ ('const/sets/inf' @ X0) @ X1)) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ Y0 @ X1)))))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f10])).
% 0.09/0.25 thf(f16,plain,(
% 0.09/0.25 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ ('const/sets/inf' @ X0) @ X1)) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) & ('const/realax/real_lt' @ Y0 @ X1)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.09/0.25 inference(flattening,[],[f15])).
% 0.09/0.25 thf(f17,plain,(
% 0.09/0.25 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.09/0.25 thf(f18,plain,(
% 0.09/0.25 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_lt' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X2)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f12])).
% 0.09/0.25 thf(f19,plain,(
% 0.09/0.25 ( ! [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)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f14])).
% 0.09/0.25 thf(f20,plain,(
% 0.09/0.25 ( ! [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/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f14])).
% 0.09/0.25 thf(f21,plain,(
% 0.09/0.25 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK0)))),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 thf(f22,plain,(
% 0.09/0.25 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) != ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f17])).
% 0.09/0.25 thf(f25,definition,(
% 0.09/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.25 thf(f26,plain,(
% 0.09/0.25 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ($true = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1))))))),
% 0.09/0.25 inference(xor_proxy_clausification,[],[f23])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1))))) = $false)),
% 0.09/0.25 inference(xor_proxy_clausification,[],[f23])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1))) @ X1)))) )),
% 0.09/0.25 inference(pi_proxy_clausification,[],[f27])).
% 0.09/0.25 thf(f29,plain,(
% 0.09/0.25 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0) & ('const/realax/real_lt' @ X1 @ sK1))))) )),
% 0.09/0.26 inference(beta-eta_normalization,[],[f28])).
% 0.09/0.26 thf(f30,plain,(
% 0.09/0.26 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ($false = (('const/realax/real_lt' @ X1 @ sK1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)))) )),
% 0.09/0.26 inference(and_proxy_clausification,[],[f29])).
% 0.09/0.26 thf(f31,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) & ('const/realax/real_lt' @ Y0 @ sK1))) @ sK2)))),
% 0.09/0.26 inference(sigma_proxy_clausification,[],[f26])).
% 0.09/0.26 thf(f32,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) & ('const/realax/real_lt' @ sK2 @ sK1))))),
% 0.09/0.26 inference(beta-eta_normalization,[],[f31])).
% 0.09/0.26 thf(f33,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ($true = (('const/realax/real_lt' @ sK2 @ sK1)))),
% 0.09/0.26 inference(and_proxy_clausification,[],[f32])).
% 0.09/0.26 thf(f34,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.09/0.26 inference(and_proxy_clausification,[],[f32])).
% 0.09/0.26 thf(f50,definition,(
% 0.09/0.26 spl4_3 <=> ($true = (('const/realax/real_lt' @ sK2 @ sK1)))),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.09/0.26 thf(f52,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ sK2 @ sK1))) | ~spl4_3),
% 0.09/0.26 inference(avatar_component_clause,[],[f50])).
% 0.09/0.26 thf(f54,definition,(
% 0.09/0.26 spl4_4 <=> ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)))),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.09/0.26 thf(f55,plain,(
% 0.09/0.26 ($true != (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | spl4_4),
% 0.09/0.26 inference(avatar_component_clause,[],[f54])).
% 0.09/0.26 thf(f56,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | ~spl4_4),
% 0.09/0.26 inference(avatar_component_clause,[],[f54])).
% 0.09/0.26 thf(f57,plain,(
% 0.09/0.26 spl4_3 | spl4_4),
% 0.09/0.26 inference(avatar_split_clause,[],[f33,f54,f50])).
% 0.09/0.26 thf(f59,definition,(
% 0.09/0.26 spl4_5 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.09/0.26 thf(f61,plain,(
% 0.09/0.26 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0))) | ~spl4_5),
% 0.09/0.26 inference(avatar_component_clause,[],[f59])).
% 0.09/0.26 thf(f62,plain,(
% 0.09/0.26 spl4_5 | spl4_4),
% 0.09/0.26 inference(avatar_split_clause,[],[f34,f54,f59])).
% 0.09/0.26 thf(f149,definition,(
% 0.09/0.26 spl4_10 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_lt' @ X1 @ sK1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))))),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.09/0.26 thf(f150,plain,(
% 0.09/0.26 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) | ($false = (('const/realax/real_lt' @ X1 @ sK1)))) ) | ~spl4_10),
% 0.09/0.26 inference(avatar_component_clause,[],[f149])).
% 0.09/0.26 thf(f152,definition,(
% 0.09/0.26 spl4_11 <=> ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.09/0.26 thf(f153,plain,(
% 0.09/0.26 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) != $false) | spl4_11),
% 0.09/0.26 inference(avatar_component_clause,[],[f152])).
% 0.09/0.26 thf(f154,plain,(
% 0.09/0.26 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ~spl4_11),
% 0.09/0.26 inference(avatar_component_clause,[],[f152])).
% 0.09/0.26 thf(f155,plain,(
% 0.09/0.26 spl4_10 | spl4_11),
% 0.09/0.26 inference(avatar_split_clause,[],[f30,f152,f149])).
% 0.09/0.26 thf(f201,plain,(
% 0.09/0.26 ($true = $false) | (~spl4_4 | ~spl4_11)),
% 0.09/0.26 inference(forward_demodulation,[],[f56,f154])).
% 0.09/0.26 thf(f202,plain,(
% 0.09/0.26 $false | (~spl4_4 | ~spl4_11)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f201])).
% 0.09/0.26 thf(f203,plain,(
% 0.09/0.26 ~spl4_4 | ~spl4_11),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f202])).
% 0.09/0.26 thf(f214,plain,(
% 0.09/0.26 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_lt' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.09/0.26 inference(constrained_superposition,[],[f18,f25])).
% 0.09/0.26 thf(f215,plain,(
% 0.09/0.26 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X1 @ X2)) != $true) | ((('const/realax/real_lt' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f214])).
% 0.09/0.26 thf(f244,plain,(
% 0.09/0.26 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.09/0.26 inference(constrained_superposition,[],[f19,f21])).
% 0.09/0.26 thf(f245,plain,(
% 0.09/0.26 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f244])).
% 0.09/0.26 thf(f247,plain,(
% 0.09/0.26 ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0)))),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f245,f22])).
% 0.09/0.26 thf(f296,plain,(
% 0.09/0.26 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_lt' @ X0 @ sK1))) | ($false = (('const/realax/real_le' @ X0 @ sK2)))) ) | ~spl4_3),
% 0.09/0.26 inference(constrained_superposition,[],[f215,f52])).
% 0.09/0.26 thf(f298,plain,(
% 0.09/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ sK2))) | ($true = (('const/realax/real_lt' @ X0 @ sK1)))) ) | ~spl4_3),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f296])).
% 0.09/0.26 thf(f355,plain,(
% 0.09/0.26 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl4_5),
% 0.09/0.26 inference(constrained_superposition,[],[f20,f61])).
% 0.09/0.26 thf(f356,plain,(
% 0.09/0.26 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl4_5),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f355])).
% 0.09/0.26 thf(f357,plain,(
% 0.09/0.26 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK0))) | ~spl4_5),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f356,f22])).
% 0.09/0.26 thf(f358,plain,(
% 0.09/0.26 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) | ~spl4_5),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f357,f21])).
% 0.09/0.26 thf(f366,plain,(
% 0.09/0.26 ($true = $false) | ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | (~spl4_3 | ~spl4_5)),
% 0.09/0.26 inference(constrained_superposition,[],[f358,f298])).
% 0.09/0.26 thf(f371,plain,(
% 0.09/0.26 ($true = (('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1))) | (~spl4_3 | ~spl4_5)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f366])).
% 0.09/0.26 thf(f374,plain,(
% 0.09/0.26 $false | (~spl4_3 | spl4_4 | ~spl4_5)),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f371,f55])).
% 0.09/0.26 thf(f375,plain,(
% 0.09/0.26 ~spl4_3 | spl4_4 | ~spl4_5),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f374])).
% 0.09/0.26 thf(f388,plain,(
% 0.09/0.26 ($true = $false) | ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ~spl4_10),
% 0.09/0.26 inference(constrained_superposition,[],[f150,f247])).
% 0.09/0.26 thf(f400,plain,(
% 0.09/0.26 ((('const/realax/real_lt' @ ('const/sets/inf' @ sK0) @ sK1)) = $false) | ~spl4_10),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f388])).
% 0.09/0.26 thf(f408,plain,(
% 0.09/0.26 $false | (~spl4_10 | spl4_11)),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f400,f153])).
% 0.09/0.26 thf(f409,plain,(
% 0.09/0.26 ~spl4_10 | spl4_11),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f408])).
% 0.09/0.26 cnf(s23, plain, spl4_3 | spl4_4, inference(sat_conversion,[],[f57])).
% 0.09/0.26 cnf(s27, plain, spl4_4 | spl4_5, inference(sat_conversion,[],[f62])).
% 0.09/0.26 cnf(s64, plain, spl4_10 | spl4_11, inference(sat_conversion,[],[f155])).
% 0.09/0.26 cnf(s88, plain, ~spl4_4 | ~spl4_11, inference(sat_conversion,[],[f203])).
% 0.09/0.26 cnf(s180, plain, ~spl4_3 | spl4_4 | ~spl4_5, inference(sat_conversion,[],[f375])).
% 0.09/0.26 cnf(s196, plain, ~spl4_10 | spl4_11, inference(sat_conversion,[],[f409])).
% 0.09/0.26 cnf(s198, plain, spl4_11, inference(rat,[],[s64,s196])).
% 0.09/0.26 cnf(s201, plain, ~spl4_4, inference(rat,[],[s88,s198])).
% 0.09/0.26 cnf(s202, plain, spl4_5, inference(rat,[],[s27,s201])).
% 0.09/0.26 cnf(s203, plain, spl4_3, inference(rat,[],[s23,s201])).
% 0.09/0.26 cnf(s206, plain, $false, inference(rat,[],[s180,s201,s203,s202])).
% 0.09/0.26 thf(f410,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(avatar_sat_refutation,[],[s206])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (1073013)------------------------------
% 0.09/0.26 % (1073013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (1073013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (1073013)CaDiCaL version: 2.1.3
% 0.09/0.26 % (1073013)Termination reason: Refutation
% 0.09/0.26 % (1073013)Time elapsed: 0.008 s
% 0.09/0.26 % (1073013)Peak memory usage: 13 MB
% 0.09/0.26 % (1073013)Instructions burned: 22 (million)
% 0.09/0.26 % (1073004)Success in time 0.036 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------