%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA091^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA091^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:41:39 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (3486312)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3486321)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1585540079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3486321)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (3486317)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3591971875_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3486319)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1842332839:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3486318)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3486320)dis+10_1_sil=32000:sp=arity:random_seed=3957502304:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3486318)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=210746687:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3486318)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (3486322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1370785773:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3486318)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (3486321) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3486312-3486321"...
% 0.20/0.29 % (3486323)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1200646513:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (3486321)...printing done.
% 0.20/0.29 % (3486321)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.29 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_12, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_13, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_14, type, sK2: ('type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_15, type, sK3: 'type/realax/real').
% 0.20/0.29 thf(func_def_16, type, sK4: 'type/realax/real').
% 0.20/0.29 thf(func_def_17, type, sK5: 'type/realax/real').
% 0.20/0.29 thf(func_def_18, type, sK6: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_20, type, sK8: 'type/realax/real').
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [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))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [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))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.20/0.29 thf(f4,conjecture,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_')).
% 0.20/0.29 thf(f5,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [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))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [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))),
% 0.20/0.29 inference(fool_elimination,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))),
% 0.20/0.29 inference(fool_elimination,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ! [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))))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ! [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'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ($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))))))),
% 0.20/0.29 inference(fool_elimination,[],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 0.20/0.29 inference(rectify,[],[f5])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X4)) = $true)) & ((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f12])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ! [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)))),
% 0.20/0.29 inference(ennf_transformation,[],[f7])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [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))),
% 0.20/0.29 inference(flattening,[],[f14])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [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))) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($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)))),
% 0.20/0.29 inference(ennf_transformation,[],[f11])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [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))) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($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))),
% 0.20/0.29 inference(flattening,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) != $true) & (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) & ((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f13])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) != $true) & ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) & ((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true))),
% 0.20/0.29 inference(flattening,[],[f18])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [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))),
% 0.20/0.29 inference(rectify,[],[f17])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ! [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)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) & ! [X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ X4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2)))) & ($true = (('const/realax/real_le' @ sK5 @ sK4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f19])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ( ! [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)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f15])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f9])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ( ! [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)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ( ! [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)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK5 @ sK4)))),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ( ! [X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X4)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f34,plain,(
% 0.20/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4)))),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f38,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = $false) | ($true = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.20/0.29 inference(iff_proxy_clausification,[],[f24])).
% 0.20/0.29 thf(f39,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ($true = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.20/0.29 inference(pi_proxy_clausification,[],[f38])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ((('const/sets/EMPTY' @ X0 = X1)) = $false)) )),
% 0.20/0.29 inference(not_proxy_clausification,[],[f39])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ('const/sets/EMPTY' @ X0 != X1)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f40])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X1)) = $false) | ('const/sets/EMPTY' @ X0 != X1)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f41])).
% 0.20/0.29 thf(f60,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ sK4))) | ($true != (('const/realax/real_le' @ X0 @ sK5)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f23,f32])).
% 0.20/0.29 thf(f77,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ sK5))) | ($true = (('const/realax/real_le' @ X0 @ sK4)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f60])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($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)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f33,f25])).
% 0.20/0.29 thf(f107,plain,(
% 0.20/0.29 ( ! [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))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f106])).
% 0.20/0.29 thf(f112,definition,(
% 0.20/0.29 spl7_1 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.20/0.29 thf(f113,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) | spl7_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f112])).
% 0.20/0.29 thf(f114,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl7_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f112])).
% 0.20/0.29 thf(f116,definition,(
% 0.20/0.29 spl7_2 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.20/0.29 thf(f117,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2)))) ) | ~spl7_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f116])).
% 0.20/0.29 thf(f119,definition,(
% 0.20/0.29 spl7_3 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))) ) | ~spl7_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f119])).
% 0.20/0.29 thf(f121,plain,(
% 0.20/0.29 spl7_1 | spl7_2 | spl7_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f107,f119,f116,f112])).
% 0.20/0.29 thf(f278,plain,(
% 0.20/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2))) | ~spl7_2),
% 0.20/0.29 inference(constrained_superposition,[],[f77,f117])).
% 0.20/0.29 thf(f285,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2))) | ~spl7_2),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f278])).
% 0.20/0.29 thf(f295,plain,(
% 0.20/0.29 ($true != (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2))) | ~spl7_2),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f285,f34])).
% 0.20/0.29 thf(f310,plain,(
% 0.20/0.29 $false | ~spl7_2),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f295,f31])).
% 0.20/0.29 thf(f311,plain,(
% 0.20/0.29 ~spl7_2),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f310])).
% 0.20/0.29 thf(f471,plain,(
% 0.20/0.29 ($true = $false) | ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.20/0.29 inference(constrained_superposition,[],[f42,f31])).
% 0.20/0.29 thf(f494,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f471])).
% 0.20/0.29 thf(f507,plain,(
% 0.20/0.29 $false | ~spl7_1),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f494,f114])).
% 0.20/0.29 thf(f508,plain,(
% 0.20/0.29 ~spl7_1),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f507])).
% 0.20/0.29 thf(f550,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl7_3),
% 0.20/0.29 inference(constrained_superposition,[],[f26,f120])).
% 0.20/0.29 thf(f551,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl7_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f550])).
% 0.20/0.29 thf(f554,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f551,f113])).
% 0.20/0.29 thf(f556,plain,(
% 0.20/0.29 spl7_2 | spl7_1 | ~spl7_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f554,f119,f112,f116])).
% 0.20/0.29 cnf(s1, plain, spl7_1 | spl7_2 | spl7_3, inference(sat_conversion,[],[f121])).
% 0.20/0.29 cnf(s5, plain, ~spl7_2, inference(sat_conversion,[],[f311])).
% 0.20/0.29 cnf(s7, plain, ~spl7_1, inference(sat_conversion,[],[f508])).
% 0.20/0.29 cnf(s13, plain, spl7_1 | spl7_2 | ~spl7_3, inference(sat_conversion,[],[f556])).
% 0.20/0.29 cnf(s14, plain, ~spl7_3, inference(rat,[],[s13,s7,s5])).
% 0.20/0.29 cnf(s16, plain, $false, inference(rat,[],[s1,s14,s5,s7])).
% 0.20/0.29 thf(f557,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s16])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3486321)------------------------------
% 0.20/0.29 % (3486321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3486321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3486321)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3486321)Termination reason: Refutation
% 0.20/0.29 % (3486321)Time elapsed: 0.018 s
% 0.20/0.29 % (3486321)Peak memory usage: 13 MB
% 0.20/0.29 % (3486321)Instructions burned: 64 (million)
% 0.20/0.29 % (3486312)Success in time 0.045 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------