%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA080^1 : 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 07:46:01 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA080^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n006.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:40:20 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 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
% 0.21/0.30 % (1071453)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (1071464)% WARNING: option uhcvi not known.
% 0.21/0.30 % (1071464)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1843761391:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (1071464)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (1071464)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.30 % (1071462)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=255875510_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (1071465)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3801928814:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (1071466)dis+10_1_sil=32000:sp=arity:random_seed=896846895:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.30 % (1071467)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4293382659:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.30 % (1071468)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3414677207:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.30 % (1071469)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1596485416:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.30 % (1071467)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (1071483)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1528948233:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (1071464) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1071453-1071464"...
% 0.21/0.30 % (1071464)...printing done.
% 0.21/0.30 % (1071464)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.30 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.30 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.30 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.21/0.30 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_11, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.30 thf(func_def_12, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.30 thf(func_def_13, type, sK2: ('type/realax/real' > $o)).
% 0.21/0.30 thf(func_def_14, type, sK3: 'type/realax/real').
% 0.21/0.30 thf(func_def_15, type, sK4: 'type/realax/real').
% 0.21/0.30 thf(func_def_16, type, sK5: 'type/realax/real').
% 0.21/0.30 thf(func_def_18, type, sK7: 'type/realax/real').
% 0.21/0.30 thf(f1,axiom,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.21/0.30 thf(f2,axiom,(
% 0.21/0.30 ! [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)))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.21/0.30 thf(f3,conjecture,(
% 0.21/0.30 ! [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)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_EQ_')).
% 0.21/0.30 thf(f4,negated_conjecture,(
% 0.21/0.30 ~ ! [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)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.30 thf(f5,plain,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 inference(rectify,[],[f1])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 inference(fool_elimination,[],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ! [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)))))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ! [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)))))))),
% 0.21/0.30 inference(fool_elimination,[],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ~ ! [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)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X1))))),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ~ ! [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/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))))),
% 0.21/0.30 inference(fool_elimination,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ! [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)))),
% 0.21/0.30 inference(ennf_transformation,[],[f6])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 inference(flattening,[],[f11])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ! [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)))),
% 0.21/0.30 inference(ennf_transformation,[],[f8])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 inference(flattening,[],[f13])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))) & (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.21/0.30 inference(ennf_transformation,[],[f10])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ Y0 @ X1)))))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.21/0.30 inference(flattening,[],[f15])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ! [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))),
% 0.21/0.30 inference(rectify,[],[f14])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ! [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))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f17])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3)))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f16])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f12])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.21/0.30 inference(cnf_transformation,[],[f19])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ X3 @ sK4)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f19])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3))))))),
% 0.21/0.30 inference(cnf_transformation,[],[f19])).
% 0.21/0.30 thf(f31,definition,(
% 0.21/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.30 thf(f32,plain,(
% 0.21/0.30 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3))))))),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f29])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3))))) = $false)),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f29])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3))) @ sK5)))),
% 0.21/0.30 inference(sigma_proxy_clausification,[],[f33])).
% 0.21/0.30 thf(f35,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2) => ('const/realax/real_le' @ sK5 @ sK3))))),
% 0.21/0.30 inference(beta-eta_normalization,[],[f34])).
% 0.21/0.30 thf(f36,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | ($false = (('const/realax/real_le' @ sK5 @ sK3)))),
% 0.21/0.30 inference(imp_proxy_clausification,[],[f35])).
% 0.21/0.30 thf(f37,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.21/0.30 inference(imp_proxy_clausification,[],[f35])).
% 0.21/0.30 thf(f38,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ Y0 @ sK3))) @ X1)))) )),
% 0.21/0.30 inference(pi_proxy_clausification,[],[f32])).
% 0.21/0.30 thf(f39,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) => ('const/realax/real_le' @ X1 @ sK3))))) )),
% 0.21/0.30 inference(beta-eta_normalization,[],[f38])).
% 0.21/0.30 thf(f40,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ sK3)))) )),
% 0.21/0.30 inference(imp_proxy_clausification,[],[f39])).
% 0.21/0.30 thf(f42,definition,(
% 0.21/0.30 spl6_1 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.21/0.30 thf(f44,plain,(
% 0.21/0.30 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2))) | ~spl6_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f42])).
% 0.21/0.30 thf(f46,definition,(
% 0.21/0.30 spl6_2 <=> ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.21/0.30 thf(f48,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) = $false) | ~spl6_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f46])).
% 0.21/0.30 thf(f49,plain,(
% 0.21/0.30 spl6_1 | spl6_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f37,f46,f42])).
% 0.21/0.30 thf(f51,definition,(
% 0.21/0.30 spl6_3 <=> ($false = (('const/realax/real_le' @ sK5 @ sK3)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.21/0.30 thf(f53,plain,(
% 0.21/0.30 ($false = (('const/realax/real_le' @ sK5 @ sK3))) | ~spl6_3),
% 0.21/0.30 inference(avatar_component_clause,[],[f51])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 spl6_3 | spl6_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f36,f46,f51])).
% 0.21/0.30 thf(f56,definition,(
% 0.21/0.30 spl6_4 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ sK3))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.21/0.30 thf(f57,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(avatar_component_clause,[],[f56])).
% 0.21/0.30 thf(f59,definition,(
% 0.21/0.30 spl6_5 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.21/0.30 thf(f61,plain,(
% 0.21/0.30 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ~spl6_5),
% 0.21/0.30 inference(avatar_component_clause,[],[f59])).
% 0.21/0.30 thf(f62,plain,(
% 0.21/0.30 spl6_4 | spl6_5),
% 0.21/0.30 inference(avatar_split_clause,[],[f40,f59,f56])).
% 0.21/0.30 thf(f100,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/sup' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f22,f31])).
% 0.21/0.30 thf(f101,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/sup' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f100])).
% 0.21/0.30 thf(f102,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f21,f31])).
% 0.21/0.30 thf(f103,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f102])).
% 0.21/0.30 thf(f104,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1) @ X2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f26,f31])).
% 0.21/0.30 thf(f105,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1) @ X2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f104])).
% 0.21/0.30 thf(f106,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f24,f31])).
% 0.21/0.30 thf(f107,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1) @ X1))) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f106])).
% 0.21/0.30 thf(f120,plain,(
% 0.21/0.30 ( ! [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) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(constrained_superposition,[],[f23,f57])).
% 0.21/0.30 thf(f135,plain,(
% 0.21/0.30 ( ! [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) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f120])).
% 0.21/0.30 thf(f141,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($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) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f135,f27])).
% 0.21/0.30 thf(f144,definition,(
% 0.21/0.30 spl6_10 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.21/0.30 thf(f145,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl6_10),
% 0.21/0.30 inference(avatar_component_clause,[],[f144])).
% 0.21/0.30 thf(f151,definition,(
% 0.21/0.30 spl6_12 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.21/0.30 thf(f152,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl6_12),
% 0.21/0.30 inference(avatar_component_clause,[],[f151])).
% 0.21/0.30 thf(f158,definition,(
% 0.21/0.30 spl6_14 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 0.21/0.30 thf(f159,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_14),
% 0.21/0.30 inference(avatar_component_clause,[],[f158])).
% 0.21/0.30 thf(f162,definition,(
% 0.21/0.30 spl6_15 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition])).
% 0.21/0.30 thf(f163,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | ~spl6_15),
% 0.21/0.30 inference(avatar_component_clause,[],[f162])).
% 0.21/0.30 thf(f165,plain,(
% 0.21/0.30 spl6_12 | spl6_10 | ~spl6_4),
% 0.21/0.30 inference(avatar_split_clause,[],[f141,f56,f144,f151])).
% 0.21/0.30 thf(f191,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | (~spl6_4 | ~spl6_10)),
% 0.21/0.30 inference(constrained_superposition,[],[f57,f145])).
% 0.21/0.30 thf(f192,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_10),
% 0.21/0.30 inference(constrained_superposition,[],[f28,f145])).
% 0.21/0.30 thf(f195,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_10),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f192])).
% 0.21/0.30 thf(f196,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | (~spl6_4 | ~spl6_10)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f191])).
% 0.21/0.30 thf(f200,plain,(
% 0.21/0.30 spl6_14 | ~spl6_10),
% 0.21/0.30 inference(avatar_split_clause,[],[f195,f144,f158])).
% 0.21/0.30 thf(f201,plain,(
% 0.21/0.30 spl6_15 | ~spl6_4 | ~spl6_10),
% 0.21/0.30 inference(avatar_split_clause,[],[f196,f144,f56,f162])).
% 0.21/0.30 thf(f293,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X2 @ X1) @ X2))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f101,f31])).
% 0.21/0.30 thf(f306,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($false = (('const/realax/real_le' @ (sK1 @ X2 @ X1) @ X2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f293])).
% 0.21/0.30 thf(f310,definition,(
% 0.21/0.30 spl6_18 <=> ! [X1 : 'type/realax/real'] : ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_18])],[avatar_definition])).
% 0.21/0.30 thf(f311,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))) ) | ~spl6_18),
% 0.21/0.30 inference(avatar_component_clause,[],[f310])).
% 0.21/0.30 thf(f363,plain,(
% 0.21/0.30 ($true = $false) | (~spl6_15 | ~spl6_18)),
% 0.21/0.30 inference(constrained_superposition,[],[f311,f163])).
% 0.21/0.30 thf(f372,plain,(
% 0.21/0.30 ($true = $false) | (~spl6_14 | ~spl6_18)),
% 0.21/0.30 inference(constrained_superposition,[],[f159,f311])).
% 0.21/0.30 thf(f373,plain,(
% 0.21/0.30 $false | (~spl6_14 | ~spl6_18)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f372])).
% 0.21/0.30 thf(f374,plain,(
% 0.21/0.30 ~spl6_14 | ~spl6_18),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f373])).
% 0.21/0.30 thf(f380,plain,(
% 0.21/0.30 $false | (~spl6_15 | ~spl6_18)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f363])).
% 0.21/0.30 thf(f381,plain,(
% 0.21/0.30 ~spl6_15 | ~spl6_18),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f380])).
% 0.21/0.30 thf(f413,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(constrained_superposition,[],[f107,f57])).
% 0.21/0.30 thf(f442,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f413])).
% 0.21/0.30 thf(f446,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = (('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) @ sK3)))) ) | ~spl6_4),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f442,f27])).
% 0.21/0.30 thf(f449,plain,(
% 0.21/0.30 spl6_12 | spl6_18 | ~spl6_4),
% 0.21/0.30 inference(avatar_split_clause,[],[f446,f56,f310,f151])).
% 0.21/0.30 thf(f612,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))) ) | ~spl6_12),
% 0.21/0.30 inference(constrained_superposition,[],[f105,f152])).
% 0.21/0.30 thf(f620,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl6_12),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f612])).
% 0.21/0.30 thf(f621,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl6_12),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f620])).
% 0.21/0.30 thf(f622,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl6_12),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f621,f27])).
% 0.21/0.30 thf(f623,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | (~spl6_2 | ~spl6_12)),
% 0.21/0.30 inference(forward_demodulation,[],[f622,f48])).
% 0.21/0.30 thf(f624,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | (~spl6_2 | ~spl6_12)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f623])).
% 0.21/0.30 thf(f625,plain,(
% 0.21/0.30 spl6_18 | ~spl6_2 | ~spl6_12),
% 0.21/0.30 inference(avatar_split_clause,[],[f624,f151,f46,f310])).
% 0.21/0.30 thf(f626,plain,(
% 0.21/0.30 ($true = $false) | (~spl6_2 | ~spl6_5)),
% 0.21/0.30 inference(forward_demodulation,[],[f61,f48])).
% 0.21/0.30 thf(f627,plain,(
% 0.21/0.30 $false | (~spl6_2 | ~spl6_5)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f626])).
% 0.21/0.30 thf(f628,plain,(
% 0.21/0.30 ~spl6_2 | ~spl6_5),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f627])).
% 0.21/0.30 thf(f630,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ sK3))) | ($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))))) ) | ~spl6_5),
% 0.21/0.30 inference(constrained_superposition,[],[f20,f61])).
% 0.21/0.30 thf(f631,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ sK3)))) ) | ~spl6_5),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f630])).
% 0.21/0.30 thf(f674,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(constrained_superposition,[],[f631,f103])).
% 0.21/0.30 thf(f679,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f674])).
% 0.21/0.30 thf(f731,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))) ) | ~spl6_12),
% 0.21/0.30 inference(constrained_superposition,[],[f25,f152])).
% 0.21/0.30 thf(f736,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_12),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f731])).
% 0.21/0.30 thf(f737,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_12),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f736])).
% 0.21/0.30 thf(f981,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ sK3))) | ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(constrained_superposition,[],[f631,f306])).
% 0.21/0.30 thf(f985,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK3))) | ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f981])).
% 0.21/0.30 thf(f1019,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK3))) | ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f985,f27])).
% 0.21/0.30 thf(f1026,plain,(
% 0.21/0.30 spl6_18 | spl6_4 | ~spl6_5),
% 0.21/0.30 inference(avatar_split_clause,[],[f1019,f59,f56,f310])).
% 0.21/0.30 thf(f1054,plain,(
% 0.21/0.30 ($true = $false) | ($true = (('const/realax/real_le' @ sK5 @ sK3))) | (~spl6_1 | ~spl6_4)),
% 0.21/0.30 inference(constrained_superposition,[],[f57,f44])).
% 0.21/0.30 thf(f1093,plain,(
% 0.21/0.30 ($true = (('const/realax/real_le' @ sK5 @ sK3))) | (~spl6_1 | ~spl6_4)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f1054])).
% 0.21/0.30 thf(f1100,plain,(
% 0.21/0.30 ($true = $false) | (~spl6_1 | ~spl6_3 | ~spl6_4)),
% 0.21/0.30 inference(forward_demodulation,[],[f1093,f53])).
% 0.21/0.30 thf(f1101,plain,(
% 0.21/0.30 $false | (~spl6_1 | ~spl6_3 | ~spl6_4)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f1100])).
% 0.21/0.30 thf(f1102,plain,(
% 0.21/0.30 ~spl6_1 | ~spl6_3 | ~spl6_4),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f1101])).
% 0.21/0.30 thf(f1116,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_5),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f679,f27])).
% 0.21/0.30 thf(f1127,plain,(
% 0.21/0.30 spl6_10 | spl6_4 | ~spl6_5),
% 0.21/0.30 inference(avatar_split_clause,[],[f1116,f59,f56,f144])).
% 0.21/0.30 thf(f1196,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl6_12),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f737,f27])).
% 0.21/0.30 thf(f1223,plain,(
% 0.21/0.30 spl6_10 | spl6_5 | ~spl6_12),
% 0.21/0.30 inference(avatar_split_clause,[],[f1196,f151,f59,f144])).
% 0.21/0.30 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f49])).
% 0.21/0.30 cnf(s2, plain, spl6_2 | spl6_3, inference(sat_conversion,[],[f54])).
% 0.21/0.30 cnf(s3, plain, spl6_4 | spl6_5, inference(sat_conversion,[],[f62])).
% 0.21/0.30 cnf(s11, plain, ~spl6_4 | spl6_10 | spl6_12, inference(sat_conversion,[],[f165])).
% 0.21/0.30 cnf(s17, plain, ~spl6_10 | spl6_14, inference(sat_conversion,[],[f200])).
% 0.21/0.30 cnf(s18, plain, ~spl6_4 | ~spl6_10 | spl6_15, inference(sat_conversion,[],[f201])).
% 0.21/0.30 cnf(s44, plain, ~spl6_14 | ~spl6_18, inference(sat_conversion,[],[f374])).
% 0.21/0.30 cnf(s47, plain, ~spl6_15 | ~spl6_18, inference(sat_conversion,[],[f381])).
% 0.21/0.30 cnf(s56, plain, ~spl6_4 | spl6_12 | spl6_18, inference(sat_conversion,[],[f449])).
% 0.21/0.30 cnf(s59, plain, ~spl6_2 | ~spl6_12 | spl6_18, inference(sat_conversion,[],[f625])).
% 0.21/0.30 cnf(s60, plain, ~spl6_2 | ~spl6_5, inference(sat_conversion,[],[f628])).
% 0.21/0.30 cnf(s65, plain, spl6_4 | ~spl6_5 | spl6_18, inference(sat_conversion,[],[f1026])).
% 0.21/0.30 cnf(s73, plain, ~spl6_1 | ~spl6_3 | ~spl6_4, inference(sat_conversion,[],[f1102])).
% 0.21/0.30 cnf(s83, plain, spl6_4 | ~spl6_5 | spl6_10, inference(sat_conversion,[],[f1127])).
% 0.21/0.30 cnf(s115, plain, spl6_5 | spl6_10 | ~spl6_12, inference(sat_conversion,[],[f1223])).
% 0.21/0.30 cnf(s117, plain, spl6_10 | spl6_5, inference(rat,[],[s115,s11,s3])).
% 0.21/0.30 cnf(s118, plain, ~spl6_2, inference(rat,[],[s56,s59,s47,s18,s117,s3,s60])).
% 0.21/0.30 cnf(s119, plain, spl6_3, inference(rat,[],[s2,s118])).
% 0.21/0.30 cnf(s120, plain, spl6_1, inference(rat,[],[s1,s118])).
% 0.21/0.30 cnf(s121, plain, ~spl6_4, inference(rat,[],[s73,s119,s120])).
% 0.21/0.30 cnf(s122, plain, spl6_5, inference(rat,[],[s3,s121])).
% 0.21/0.30 cnf(s123, plain, spl6_10, inference(rat,[],[s83,s121,s122])).
% 0.21/0.30 cnf(s124, plain, spl6_18, inference(rat,[],[s65,s121,s122])).
% 0.21/0.30 cnf(s125, plain, spl6_14, inference(rat,[],[s17,s123])).
% 0.21/0.30 cnf(s127, plain, $false, inference(rat,[],[s44,s124,s125])).
% 0.21/0.30 thf(f1225,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s127])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (1071464)------------------------------
% 0.21/0.30 % (1071464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1071464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1071464)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1071464)Termination reason: Refutation
% 0.21/0.30 % (1071464)Time elapsed: 0.032 s
% 0.21/0.30 % (1071464)Peak memory usage: 13 MB
% 0.21/0.30 % (1071464)Instructions burned: 118 (million)
% 0.21/0.30 % (1071453)Success in time 0.055 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------