%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA088^1 : 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 : n009.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 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA088^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:41:00 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.19/0.28 % (125171)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (125187)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=627441307:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (125185)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3948981417_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (125191)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3718679850:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (125190)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=167671621:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (125190)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (125186)% WARNING: option uhcvi not known.
% 0.19/0.28 % (125186)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=40961293:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (125186)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (125189)dis+10_1_sil=32000:sp=arity:random_seed=4228047829:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (125186)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (125192)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2193466560:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (125198)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2345932045:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (125190) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125171-125190"...
% 0.19/0.28 % (125190)...printing done.
% 0.19/0.28 % (125190)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.28 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.28 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.28 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.28 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_12, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.28 thf(func_def_13, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.28 thf(func_def_14, type, sK2: ('type/realax/real' > $o)).
% 0.19/0.28 thf(func_def_15, type, sK3: 'type/realax/real').
% 0.19/0.29 thf(func_def_16, type, sK4: 'type/realax/real').
% 0.19/0.29 thf(func_def_17, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.19/0.29 thf(func_def_19, type, sK7: 'type/realax/real').
% 0.19/0.29 thf(f1,axiom,(
% 0.19/0.29 ! [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))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.19/0.29 thf(f2,axiom,(
% 0.19/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.19/0.29 thf(f3,axiom,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.19/0.29 thf(f4,conjecture,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_BOUNDS_')).
% 0.19/0.29 thf(f5,negated_conjecture,(
% 0.19/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.29 thf(f6,plain,(
% 0.19/0.29 ! [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))),
% 0.19/0.29 inference(rectify,[],[f1])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 ! [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))),
% 0.19/0.29 inference(fool_elimination,[],[f6])).
% 0.19/0.29 thf(f8,plain,(
% 0.19/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.19/0.29 inference(rectify,[],[f2])).
% 0.19/0.29 thf(f9,plain,(
% 0.19/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))),
% 0.19/0.29 inference(fool_elimination,[],[f8])).
% 0.19/0.29 thf(f10,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 0.19/0.29 inference(rectify,[],[f3])).
% 0.19/0.29 thf(f11,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => ($true = (('const/realax/real_le' @ X3 @ X4)))) => ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))))),
% 0.19/0.29 inference(fool_elimination,[],[f10])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.19/0.29 inference(rectify,[],[f5])).
% 0.19/0.29 thf(f13,plain,(
% 0.19/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => (((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true)))),
% 0.19/0.29 inference(fool_elimination,[],[f12])).
% 0.19/0.29 thf(f14,plain,(
% 0.19/0.29 ! [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)))),
% 0.19/0.29 inference(ennf_transformation,[],[f7])).
% 0.19/0.29 thf(f15,plain,(
% 0.19/0.29 ! [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))),
% 0.19/0.29 inference(flattening,[],[f14])).
% 0.19/0.29 thf(f16,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.19/0.29 inference(ennf_transformation,[],[f11])).
% 0.19/0.29 thf(f17,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.29 inference(flattening,[],[f16])).
% 0.19/0.29 thf(f18,plain,(
% 0.19/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true)) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.19/0.29 inference(ennf_transformation,[],[f13])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & ! [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true)) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.19/0.29 inference(flattening,[],[f18])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ X5))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.29 inference(rectify,[],[f17])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 (($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) | ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))) & ! [X3 : 'type/realax/real'] : ((($true = (('const/realax/real_le' @ X3 @ sK4))) & ($true = (('const/realax/real_le' @ sK3 @ X3)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ( ! [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)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f15])).
% 0.19/0.29 thf(f24,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f9])).
% 0.19/0.29 thf(f25,plain,(
% 0.19/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f26,plain,(
% 0.19/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f27,plain,(
% 0.19/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f28,plain,(
% 0.19/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f29,plain,(
% 0.19/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f30,plain,(
% 0.19/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.19/0.29 inference(cnf_transformation,[],[f22])).
% 0.19/0.29 thf(f32,plain,(
% 0.19/0.29 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X3)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f22])).
% 0.19/0.29 thf(f33,plain,(
% 0.19/0.29 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ X3 @ sK4)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f22])).
% 0.19/0.29 thf(f34,plain,(
% 0.19/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) | ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))),
% 0.19/0.29 inference(cnf_transformation,[],[f22])).
% 0.19/0.29 thf(f36,definition,(
% 0.19/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.29 thf(f37,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f24])).
% 0.19/0.29 thf(f43,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 0.19/0.29 inference(sigma_proxy_clausification,[],[f37])).
% 0.19/0.29 thf(f44,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ($true = (('const/sets/EMPTY' @ X0 = X1)))) )),
% 0.19/0.29 inference(not_proxy_clausification,[],[f43])).
% 0.19/0.29 thf(f45,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f44])).
% 0.19/0.29 thf(f46,plain,(
% 0.19/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f45])).
% 0.19/0.29 thf(f48,definition,(
% 0.19/0.29 spl6_1 <=> ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.19/0.29 thf(f50,plain,(
% 0.19/0.29 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | spl6_1),
% 0.19/0.29 inference(avatar_component_clause,[],[f48])).
% 0.19/0.29 thf(f52,definition,(
% 0.19/0.29 spl6_2 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.19/0.29 thf(f54,plain,(
% 0.19/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) | spl6_2),
% 0.19/0.29 inference(avatar_component_clause,[],[f52])).
% 0.19/0.29 thf(f55,plain,(
% 0.19/0.29 ~spl6_1 | ~spl6_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f34,f52,f48])).
% 0.19/0.29 thf(f87,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ X0))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f32,f36])).
% 0.19/0.29 thf(f89,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X0)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f87])).
% 0.19/0.29 thf(f136,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f32,f25])).
% 0.19/0.29 thf(f137,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f136])).
% 0.19/0.29 thf(f144,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2)))) )),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f137,f31])).
% 0.19/0.29 thf(f149,definition,(
% 0.19/0.29 spl6_7 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.19/0.29 thf(f150,plain,(
% 0.19/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2)))) ) | ~spl6_7),
% 0.19/0.29 inference(avatar_component_clause,[],[f149])).
% 0.19/0.29 thf(f152,definition,(
% 0.19/0.29 spl6_8 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.19/0.29 thf(f153,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))) ) | ~spl6_8),
% 0.19/0.29 inference(avatar_component_clause,[],[f152])).
% 0.19/0.29 thf(f154,plain,(
% 0.19/0.29 spl6_7 | spl6_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f144,f152,f149])).
% 0.19/0.29 thf(f192,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f28,f89])).
% 0.19/0.29 thf(f209,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f192])).
% 0.19/0.29 thf(f215,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f209,f31])).
% 0.19/0.29 thf(f218,definition,(
% 0.19/0.29 spl6_10 <=> ! [X1 : 'type/realax/real'] : ($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.19/0.29 thf(f219,plain,(
% 0.19/0.29 ( ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2))))) ) | ~spl6_10),
% 0.19/0.29 inference(avatar_component_clause,[],[f218])).
% 0.19/0.29 thf(f221,definition,(
% 0.19/0.29 spl6_11 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.19/0.29 thf(f222,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl6_11),
% 0.19/0.29 inference(avatar_component_clause,[],[f221])).
% 0.19/0.29 thf(f230,plain,(
% 0.19/0.29 spl6_11 | spl6_10),
% 0.19/0.29 inference(avatar_split_clause,[],[f215,f218,f221])).
% 0.19/0.29 thf(f249,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f32,f29])).
% 0.19/0.29 thf(f250,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f249])).
% 0.19/0.29 thf(f260,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))))) )),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f250,f31])).
% 0.19/0.29 thf(f267,definition,(
% 0.19/0.29 spl6_13 <=> ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 0.19/0.29 thf(f268,plain,(
% 0.19/0.29 ( ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ sK2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))))) ) | ~spl6_13),
% 0.19/0.29 inference(avatar_component_clause,[],[f267])).
% 0.19/0.29 thf(f269,plain,(
% 0.19/0.29 spl6_13 | spl6_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f260,f152,f267])).
% 0.19/0.29 thf(f275,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_8),
% 0.19/0.29 inference(constrained_superposition,[],[f30,f153])).
% 0.19/0.29 thf(f276,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_8),
% 0.19/0.29 inference(constrained_superposition,[],[f26,f153])).
% 0.19/0.29 thf(f282,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_8),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f276])).
% 0.19/0.29 thf(f283,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_8),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f275])).
% 0.19/0.29 thf(f284,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl6_8),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f283,f31])).
% 0.19/0.29 thf(f285,plain,(
% 0.19/0.29 spl6_13 | ~spl6_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f284,f152,f267])).
% 0.19/0.29 thf(f287,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f27,f89])).
% 0.19/0.29 thf(f308,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f287])).
% 0.19/0.29 thf(f357,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ sK4))) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) ) | spl6_2),
% 0.19/0.29 inference(constrained_superposition,[],[f54,f23])).
% 0.19/0.29 thf(f360,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/realax/real_le' @ X0 @ sK4)))) ) | spl6_2),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f357])).
% 0.19/0.29 thf(f388,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(constrained_superposition,[],[f360,f150])).
% 0.19/0.29 thf(f400,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f388])).
% 0.19/0.29 thf(f403,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f400,f33])).
% 0.19/0.29 thf(f418,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(constrained_superposition,[],[f403,f36])).
% 0.19/0.29 thf(f435,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_8),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f282,f31])).
% 0.19/0.29 thf(f441,definition,(
% 0.19/0.29 spl6_16 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition])).
% 0.19/0.29 thf(f442,plain,(
% 0.19/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl6_16),
% 0.19/0.29 inference(avatar_component_clause,[],[f441])).
% 0.19/0.29 thf(f444,plain,(
% 0.19/0.29 spl6_7 | ~spl6_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f435,f152,f149])).
% 0.19/0.29 thf(f448,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f418])).
% 0.19/0.29 thf(f496,plain,(
% 0.19/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | (~spl6_11 | ~spl6_13)),
% 0.19/0.29 inference(constrained_superposition,[],[f268,f222])).
% 0.19/0.29 thf(f499,plain,(
% 0.19/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | (~spl6_11 | ~spl6_13)),
% 0.19/0.29 inference(duplicate_literal_removal,[],[f496])).
% 0.19/0.29 thf(f500,plain,(
% 0.19/0.29 ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | (~spl6_11 | ~spl6_13)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f499])).
% 0.19/0.29 thf(f551,plain,(
% 0.19/0.29 ($true = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(constrained_superposition,[],[f46,f448])).
% 0.19/0.29 thf(f568,plain,(
% 0.19/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f551])).
% 0.19/0.29 thf(f577,plain,(
% 0.19/0.29 $false | (spl6_2 | ~spl6_7)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f568,f31])).
% 0.19/0.29 thf(f578,plain,(
% 0.19/0.29 spl6_2 | ~spl6_7),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f577])).
% 0.19/0.29 thf(f587,plain,(
% 0.19/0.29 $false | (spl6_1 | ~spl6_11 | ~spl6_13)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f500,f50])).
% 0.19/0.29 thf(f588,plain,(
% 0.19/0.29 spl6_1 | ~spl6_11 | ~spl6_13),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f587])).
% 0.19/0.29 thf(f612,plain,(
% 0.19/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2))))) )),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f308,f31])).
% 0.19/0.29 thf(f615,plain,(
% 0.19/0.29 spl6_11 | spl6_16),
% 0.19/0.29 inference(avatar_split_clause,[],[f612,f441,f221])).
% 0.19/0.29 thf(f632,plain,(
% 0.19/0.29 ($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ ('const/sets/inf' @ sK2) @ sK2) @ sK2))) | (~spl6_7 | ~spl6_10)),
% 0.19/0.29 inference(constrained_superposition,[],[f219,f150])).
% 0.19/0.29 thf(f641,plain,(
% 0.19/0.29 ($true != (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ ('const/sets/inf' @ sK2) @ sK2) @ sK2))) | (~spl6_7 | ~spl6_10)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f632])).
% 0.19/0.29 thf(f642,plain,(
% 0.19/0.29 $false | (~spl6_7 | ~spl6_10 | ~spl6_16)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f641,f442])).
% 0.19/0.29 thf(f643,plain,(
% 0.19/0.29 ~spl6_7 | ~spl6_10 | ~spl6_16),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f642])).
% 0.19/0.29 cnf(s1, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f55])).
% 0.19/0.29 cnf(s5, plain, spl6_7 | spl6_8, inference(sat_conversion,[],[f154])).
% 0.19/0.29 cnf(s13, plain, spl6_10 | spl6_11, inference(sat_conversion,[],[f230])).
% 0.19/0.29 cnf(s15, plain, spl6_8 | spl6_13, inference(sat_conversion,[],[f269])).
% 0.19/0.29 cnf(s22, plain, ~spl6_8 | spl6_13, inference(sat_conversion,[],[f285])).
% 0.19/0.29 cnf(s29, plain, spl6_7 | ~spl6_8, inference(sat_conversion,[],[f444])).
% 0.19/0.29 cnf(s34, plain, spl6_2 | ~spl6_7, inference(sat_conversion,[],[f578])).
% 0.19/0.29 cnf(s38, plain, spl6_1 | ~spl6_11 | ~spl6_13, inference(sat_conversion,[],[f588])).
% 0.19/0.29 cnf(s48, plain, spl6_11 | spl6_16, inference(sat_conversion,[],[f615])).
% 0.19/0.29 cnf(s49, plain, ~spl6_7 | ~spl6_10 | ~spl6_16, inference(sat_conversion,[],[f643])).
% 0.19/0.29 cnf(s50, plain, spl6_7, inference(rat,[],[s5,s29])).
% 0.19/0.29 cnf(s51, plain, spl6_2, inference(rat,[],[s34,s50])).
% 0.19/0.29 cnf(s52, plain, spl6_11, inference(rat,[],[s49,s13,s48,s50])).
% 0.19/0.29 cnf(s53, plain, spl6_13, inference(rat,[],[s15,s22])).
% 0.19/0.29 cnf(s54, plain, ~spl6_1, inference(rat,[],[s1,s51])).
% 0.19/0.29 cnf(s55, plain, $false, inference(rat,[],[s38,s54,s53,s52])).
% 0.19/0.29 thf(f644,plain,(
% 0.19/0.29 $false),
% 0.19/0.29 inference(avatar_sat_refutation,[],[s55])).
% 0.19/0.29 % SZS output end Proof for theBenchmark
% 0.19/0.29 % (125190)------------------------------
% 0.19/0.29 % (125190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (125190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (125190)CaDiCaL version: 2.1.3
% 0.19/0.29 % (125190)Termination reason: Refutation
% 0.19/0.29 % (125190)Time elapsed: 0.032 s
% 0.19/0.29 % (125190)Peak memory usage: 13 MB
% 0.19/0.29 % (125190)Instructions burned: 59 (million)
% 0.19/0.29 % (125171)Success in time 0.074 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------