%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA076^1 : 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 : n011.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 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA076^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:40:43 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.27 % (416860)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (416869)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1810882032:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (416869)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (416866)% WARNING: option uhcvi not known.
% 0.19/0.27 % (416868)dis+10_1_sil=32000:sp=arity:random_seed=1747486158:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (416865)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=182361973_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (416866)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2002025497:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (416867)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4269467895:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (416871)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2182675813:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (416870)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1491692574:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (416866)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (416866)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (416869) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-416860-416869"...
% 0.19/0.27 % (416869)...printing done.
% 0.19/0.27 % (416869)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.27 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.27 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(func_def_12, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_13, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_14, type, sK2: ('type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_15, type, sK3: 'type/realax/real').
% 0.19/0.27 thf(func_def_16, type, sK4: 'type/realax/real').
% 0.19/0.27 thf(func_def_17, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.19/0.27 thf(func_def_19, type, sK7: 'type/realax/real').
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 ! [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))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.19/0.27 thf(f3,axiom,(
% 0.19/0.27 ! [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' @ X2 @ X1)) & (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' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.19/0.27 thf(f4,conjecture,(
% 0.19/0.27 ! [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/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_')).
% 0.19/0.27 thf(f5,negated_conjecture,(
% 0.19/0.27 ~ ! [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/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 ! [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))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 ! [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))),
% 0.19/0.27 inference(fool_elimination,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))),
% 0.19/0.27 inference(fool_elimination,[],[f8])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ! [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' @ X2 @ X1)) & (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' @ X4 @ X3)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))),
% 0.19/0.27 inference(rectify,[],[f3])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 ! [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' @ X2 @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => ($true = (('const/realax/real_le' @ X4 @ X3)))) => ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)))) & ! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))))),
% 0.19/0.27 inference(fool_elimination,[],[f10])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ~ ! [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/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 0.19/0.27 inference(rectify,[],[f5])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ~ ! [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/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f12])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ! [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)))),
% 0.19/0.27 inference(ennf_transformation,[],[f7])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [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))),
% 0.19/0.27 inference(flattening,[],[f14])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ X3))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.19/0.27 inference(ennf_transformation,[],[f11])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ X3))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.27 inference(flattening,[],[f16])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ 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)))),
% 0.19/0.27 inference(ennf_transformation,[],[f13])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ 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))),
% 0.19/0.27 inference(flattening,[],[f18])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X5 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.27 inference(rectify,[],[f17])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 (($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2))))) & ! [X3 : 'type/realax/real'] : ((($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)),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ( ! [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)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f15])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ($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)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ( ! [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' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ( ! [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' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f21])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X3)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ X3 @ sK4)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2))))),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f36,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 0.19/0.27 inference(iff_proxy_clausification,[],[f24])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 0.19/0.27 inference(sigma_proxy_clausification,[],[f37])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ($true = (('const/sets/EMPTY' @ X0 = X1)))) )),
% 0.19/0.27 inference(not_proxy_clausification,[],[f43])).
% 0.19/0.27 thf(f45,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f44])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f45])).
% 0.19/0.27 thf(f48,definition,(
% 0.19/0.27 spl6_1 <=> ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.19/0.27 thf(f50,plain,(
% 0.19/0.27 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | spl6_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f48])).
% 0.19/0.27 thf(f52,definition,(
% 0.19/0.27 spl6_2 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | spl6_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f52])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 ~spl6_1 | ~spl6_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f34,f52,f48])).
% 0.19/0.27 thf(f86,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ sK4))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f33,f36])).
% 0.19/0.27 thf(f90,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ sK4)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f86])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)))) | ($true != (('const/realax/real_le' @ sK3 @ X0)))) ) | spl6_1),
% 0.19/0.27 inference(constrained_superposition,[],[f50,f23])).
% 0.19/0.27 thf(f102,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)))) | ($true != (('const/realax/real_le' @ sK3 @ X0)))) ) | spl6_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f101])).
% 0.19/0.27 thf(f156,definition,(
% 0.19/0.27 spl6_9 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.19/0.27 thf(f157,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f156])).
% 0.19/0.27 thf(f188,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ sK3 @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(constrained_superposition,[],[f102,f25])).
% 0.19/0.27 thf(f189,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ sK3 @ X0))) | ($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(constrained_superposition,[],[f102,f26])).
% 0.19/0.27 thf(f192,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ sK3 @ X0))) | ($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f189])).
% 0.19/0.27 thf(f193,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ sK3 @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f188])).
% 0.19/0.27 thf(f195,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f192,f32])).
% 0.19/0.27 thf(f196,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | spl6_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f193,f32])).
% 0.19/0.27 thf(f197,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | spl6_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f195,f31])).
% 0.19/0.27 thf(f198,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | spl6_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f196,f31])).
% 0.19/0.27 thf(f200,definition,(
% 0.19/0.27 spl6_10 <=> ! [X0 : 'type/realax/real'] : ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.19/0.27 thf(f201,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_10),
% 0.19/0.27 inference(avatar_component_clause,[],[f200])).
% 0.19/0.27 thf(f203,definition,(
% 0.19/0.27 spl6_11 <=> ! [X1 : 'type/realax/real'] : ($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.19/0.27 thf(f204,plain,(
% 0.19/0.27 ( ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))) ) | ~spl6_11),
% 0.19/0.27 inference(avatar_component_clause,[],[f203])).
% 0.19/0.27 thf(f205,plain,(
% 0.19/0.27 spl6_10 | spl6_11 | spl6_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f197,f48,f203,f200])).
% 0.19/0.27 thf(f207,definition,(
% 0.19/0.27 spl6_12 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.19/0.27 thf(f208,plain,(
% 0.19/0.27 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl6_12),
% 0.19/0.27 inference(avatar_component_clause,[],[f207])).
% 0.19/0.27 thf(f209,plain,(
% 0.19/0.27 spl6_10 | spl6_12 | spl6_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f198,f48,f207,f200])).
% 0.19/0.27 thf(f216,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f28,f90])).
% 0.19/0.27 thf(f235,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f216])).
% 0.19/0.27 thf(f241,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f235,f31])).
% 0.19/0.27 thf(f247,definition,(
% 0.19/0.27 spl6_14 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 0.19/0.27 thf(f248,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl6_14),
% 0.19/0.27 inference(avatar_component_clause,[],[f247])).
% 0.19/0.27 thf(f253,plain,(
% 0.19/0.27 spl6_14 | spl6_11),
% 0.19/0.27 inference(avatar_split_clause,[],[f241,f203,f247])).
% 0.19/0.27 thf(f267,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f29,f90])).
% 0.19/0.27 thf(f278,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f267])).
% 0.19/0.27 thf(f288,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f278,f31])).
% 0.19/0.27 thf(f290,definition,(
% 0.19/0.27 spl6_15 <=> ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition])).
% 0.19/0.27 thf(f291,plain,(
% 0.19/0.27 ( ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ sK2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1)))) ) | ~spl6_15),
% 0.19/0.27 inference(avatar_component_clause,[],[f290])).
% 0.19/0.27 thf(f297,plain,(
% 0.19/0.27 spl6_9 | spl6_15),
% 0.19/0.27 inference(avatar_split_clause,[],[f288,f290,f156])).
% 0.19/0.27 thf(f300,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f27,f90])).
% 0.19/0.27 thf(f323,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f300])).
% 0.19/0.27 thf(f329,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f323,f31])).
% 0.19/0.27 thf(f335,plain,(
% 0.19/0.27 spl6_14 | spl6_12),
% 0.19/0.27 inference(avatar_split_clause,[],[f329,f207,f247])).
% 0.19/0.27 thf(f360,plain,(
% 0.19/0.27 ($true != $true) | (~spl6_9 | ~spl6_11)),
% 0.19/0.27 inference(constrained_superposition,[],[f204,f157])).
% 0.19/0.27 thf(f363,plain,(
% 0.19/0.27 $false | (~spl6_9 | ~spl6_11)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f360])).
% 0.19/0.27 thf(f364,plain,(
% 0.19/0.27 ~spl6_9 | ~spl6_11),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f363])).
% 0.19/0.27 thf(f380,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_12),
% 0.19/0.27 inference(constrained_superposition,[],[f33,f208])).
% 0.19/0.27 thf(f383,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_12),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f380])).
% 0.19/0.27 thf(f430,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))) ) | ~spl6_14),
% 0.19/0.27 inference(constrained_superposition,[],[f30,f248])).
% 0.19/0.27 thf(f435,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_14),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f430])).
% 0.19/0.27 thf(f436,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_14),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f435])).
% 0.19/0.27 thf(f437,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | (spl6_2 | ~spl6_14)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f436,f54])).
% 0.19/0.27 thf(f438,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | (spl6_2 | ~spl6_14)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f437,f31])).
% 0.19/0.27 thf(f439,plain,(
% 0.19/0.27 spl6_11 | spl6_2 | ~spl6_14),
% 0.19/0.27 inference(avatar_split_clause,[],[f438,f247,f52,f203])).
% 0.19/0.27 thf(f443,plain,(
% 0.19/0.27 spl6_9 | ~spl6_12),
% 0.19/0.27 inference(avatar_split_clause,[],[f383,f207,f156])).
% 0.19/0.27 thf(f460,plain,(
% 0.19/0.27 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | (~spl6_14 | ~spl6_15)),
% 0.19/0.27 inference(constrained_superposition,[],[f291,f248])).
% 0.19/0.27 thf(f463,plain,(
% 0.19/0.27 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | (~spl6_14 | ~spl6_15)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f460])).
% 0.19/0.27 thf(f464,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | (~spl6_14 | ~spl6_15)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f463])).
% 0.19/0.27 thf(f470,plain,(
% 0.19/0.27 $false | (spl6_2 | ~spl6_14 | ~spl6_15)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f464,f54])).
% 0.19/0.27 thf(f471,plain,(
% 0.19/0.27 spl6_2 | ~spl6_14 | ~spl6_15),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f470])).
% 0.19/0.27 thf(f490,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_10),
% 0.19/0.27 inference(constrained_superposition,[],[f201,f36])).
% 0.19/0.27 thf(f491,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_10),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f490])).
% 0.19/0.27 thf(f656,plain,(
% 0.19/0.27 ($true = $false) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl6_10),
% 0.19/0.27 inference(constrained_superposition,[],[f46,f491])).
% 0.19/0.27 thf(f675,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl6_10),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f656])).
% 0.19/0.27 thf(f686,plain,(
% 0.19/0.27 $false | ~spl6_10),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f675,f31])).
% 0.19/0.27 thf(f687,plain,(
% 0.19/0.27 ~spl6_10),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f686])).
% 0.19/0.28 cnf(s1, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f55])).
% 0.19/0.28 cnf(s9, plain, spl6_1 | spl6_10 | spl6_11, inference(sat_conversion,[],[f205])).
% 0.19/0.28 cnf(s10, plain, spl6_1 | spl6_10 | spl6_12, inference(sat_conversion,[],[f209])).
% 0.19/0.28 cnf(s16, plain, spl6_11 | spl6_14, inference(sat_conversion,[],[f253])).
% 0.19/0.28 cnf(s22, plain, spl6_9 | spl6_15, inference(sat_conversion,[],[f297])).
% 0.19/0.28 cnf(s28, plain, spl6_12 | spl6_14, inference(sat_conversion,[],[f335])).
% 0.19/0.28 cnf(s29, plain, ~spl6_9 | ~spl6_11, inference(sat_conversion,[],[f364])).
% 0.19/0.28 cnf(s30, plain, spl6_2 | spl6_11 | ~spl6_14, inference(sat_conversion,[],[f439])).
% 0.19/0.28 cnf(s31, plain, spl6_9 | ~spl6_12, inference(sat_conversion,[],[f443])).
% 0.19/0.28 cnf(s37, plain, spl6_2 | ~spl6_14 | ~spl6_15, inference(sat_conversion,[],[f471])).
% 0.19/0.28 cnf(s42, plain, ~spl6_10, inference(sat_conversion,[],[f687])).
% 0.19/0.28 cnf(s43, plain, spl6_1 | spl6_12, inference(rat,[],[s10,s42])).
% 0.19/0.28 cnf(s44, plain, spl6_1 | spl6_11, inference(rat,[],[s9,s42])).
% 0.19/0.28 cnf(s45, plain, spl6_1, inference(rat,[],[s29,s31,s44,s43])).
% 0.19/0.28 cnf(s46, plain, ~spl6_2, inference(rat,[],[s1,s45])).
% 0.19/0.28 cnf(s47, plain, spl6_11, inference(rat,[],[s30,s16,s46])).
% 0.19/0.28 cnf(s48, plain, ~spl6_9, inference(rat,[],[s29,s47])).
% 0.19/0.28 cnf(s50, plain, ~spl6_12, inference(rat,[],[s31,s48])).
% 0.19/0.28 cnf(s51, plain, spl6_15, inference(rat,[],[s22,s48])).
% 0.19/0.28 cnf(s53, plain, spl6_14, inference(rat,[],[s28,s50])).
% 0.19/0.28 cnf(s55, plain, $false, inference(rat,[],[s37,s46,s51,s53])).
% 0.19/0.28 thf(f688,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(avatar_sat_refutation,[],[s55])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (416869)------------------------------
% 0.19/0.28 % (416869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (416869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (416869)CaDiCaL version: 2.1.3
% 0.19/0.28 % (416869)Termination reason: Refutation
% 0.19/0.28 % (416869)Time elapsed: 0.017 s
% 0.19/0.28 % (416869)Peak memory usage: 13 MB
% 0.19/0.28 % (416869)Instructions burned: 58 (million)
% 0.19/0.28 % (416860)Success in time 0.042 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------