%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA079^1 : 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 : n026.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 0.18s 0.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA079^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:43:23 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.18/0.28 % (931703)Will run a generic schedule for satisfiability detection.
% 0.18/0.28 % (931711)dis+10_1_sil=32000:sp=arity:random_seed=623996929:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.28 % (931709)% WARNING: option uhcvi not known.
% 0.18/0.28 % (931708)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3999214548_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.28 % (931709)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=284290670:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.28 % (931710)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2350834730:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.28 % (931709)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % Exception at run slice level
% 0.18/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.28 % (931709)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.28 % (931713)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3206109702:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.28 % (931711) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-931703-931711"...
% 0.18/0.28 % (931712)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3183174081:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.28 % (931714)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2232492543:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.28 % (931712)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % (931711)...printing done.
% 0.18/0.28 % (931711)Refutation found. Thanks to Tanya!
% 0.18/0.28 % SZS status Theorem for theBenchmark
% 0.18/0.28 % SZS output start Proof for theBenchmark
% 0.18/0.28 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.18/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.28 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.28 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.18/0.28 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.18/0.28 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.18/0.28 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.18/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.28 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.18/0.28 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.18/0.28 thf(func_def_12, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.28 thf(func_def_13, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.28 thf(func_def_14, type, sK2: ('type/realax/real' > $o)).
% 0.18/0.28 thf(func_def_15, type, sK3: 'type/realax/real').
% 0.18/0.28 thf(func_def_16, type, sK4: 'type/realax/real').
% 0.18/0.28 thf(func_def_17, type, sK5: 'type/realax/real').
% 0.18/0.28 thf(func_def_18, type, sK6: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.18/0.28 thf(func_def_20, type, sK8: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.18/0.28 thf(func_def_21, type, sK9: (('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.28 thf(func_def_22, type, sK10: 'type/realax/real').
% 0.18/0.28 thf(f1,axiom,(
% 0.18/0.28 ! [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))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.18/0.28 thf(f2,axiom,(
% 0.18/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.18/0.28 thf(f3,axiom,(
% 0.18/0.28 ! [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)))))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.18/0.28 thf(f4,conjecture,(
% 0.18/0.28 ! [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' @ X4 @ X2)) & ('const/realax/real_le' @ X1 @ X3) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_')).
% 0.18/0.28 thf(f5,negated_conjecture,(
% 0.18/0.28 ~ ! [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' @ X4 @ X2)) & ('const/realax/real_le' @ X1 @ X3) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))),
% 0.18/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.18/0.28 thf(f6,plain,(
% 0.18/0.28 ! [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))),
% 0.18/0.28 inference(rectify,[],[f1])).
% 0.18/0.28 thf(f7,plain,(
% 0.18/0.28 ! [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))),
% 0.18/0.28 inference(fool_elimination,[],[f6])).
% 0.18/0.28 thf(f8,plain,(
% 0.18/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.18/0.28 inference(rectify,[],[f2])).
% 0.18/0.28 thf(f9,plain,(
% 0.18/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))),
% 0.18/0.28 inference(fool_elimination,[],[f8])).
% 0.18/0.28 thf(f10,plain,(
% 0.18/0.28 ! [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)))))),
% 0.18/0.28 inference(rectify,[],[f3])).
% 0.18/0.28 thf(f11,plain,(
% 0.18/0.28 ! [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'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ($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)))))))),
% 0.18/0.28 inference(fool_elimination,[],[f10])).
% 0.18/0.28 thf(f12,plain,(
% 0.18/0.28 ~ ! [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' @ X4 @ X2)) & ('const/realax/real_le' @ X1 @ X3) & ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))),
% 0.18/0.28 inference(rectify,[],[f5])).
% 0.18/0.28 thf(f13,plain,(
% 0.18/0.28 ~ ! [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' @ X4 @ X2)) = $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) => ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true))),
% 0.18/0.28 inference(fool_elimination,[],[f12])).
% 0.18/0.28 thf(f14,plain,(
% 0.18/0.28 ! [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)))),
% 0.18/0.28 inference(ennf_transformation,[],[f7])).
% 0.18/0.28 thf(f15,plain,(
% 0.18/0.28 ! [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))),
% 0.18/0.28 inference(flattening,[],[f14])).
% 0.18/0.28 thf(f16,plain,(
% 0.18/0.28 ! [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))) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($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)))),
% 0.18/0.28 inference(ennf_transformation,[],[f11])).
% 0.18/0.28 thf(f17,plain,(
% 0.18/0.28 ! [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))) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($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))),
% 0.18/0.28 inference(flattening,[],[f16])).
% 0.18/0.28 thf(f18,plain,(
% 0.18/0.28 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) != $true) & (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)))),
% 0.18/0.28 inference(ennf_transformation,[],[f13])).
% 0.18/0.28 thf(f19,plain,(
% 0.18/0.28 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) != $true) & ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true))),
% 0.18/0.28 inference(flattening,[],[f18])).
% 0.18/0.28 thf(f20,plain,(
% 0.18/0.28 ! [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))),
% 0.18/0.28 inference(rectify,[],[f17])).
% 0.18/0.28 thf(f21,plain,(
% 0.18/0.28 ! [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))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.18/0.28 thf(f22,plain,(
% 0.18/0.28 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) & ! [X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X4 @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2)))) & ($true = (('const/realax/real_le' @ sK3 @ sK5))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f19])).
% 0.18/0.28 thf(f23,plain,(
% 0.18/0.28 ( ! [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)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f15])).
% 0.18/0.28 thf(f24,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f9])).
% 0.18/0.28 thf(f25,plain,(
% 0.18/0.28 ( ! [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)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f21])).
% 0.18/0.28 thf(f26,plain,(
% 0.18/0.28 ( ! [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)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f21])).
% 0.18/0.28 thf(f31,plain,(
% 0.18/0.28 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2)))),
% 0.18/0.28 inference(cnf_transformation,[],[f22])).
% 0.18/0.28 thf(f32,plain,(
% 0.18/0.28 ($true = (('const/realax/real_le' @ sK3 @ sK5)))),
% 0.18/0.28 inference(cnf_transformation,[],[f22])).
% 0.18/0.28 thf(f33,plain,(
% 0.18/0.28 ( ! [X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2))) | ($true = (('const/realax/real_le' @ X4 @ sK4)))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f22])).
% 0.18/0.28 thf(f34,plain,(
% 0.18/0.28 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2))))),
% 0.18/0.28 inference(cnf_transformation,[],[f22])).
% 0.18/0.28 thf(f36,definition,(
% 0.18/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.28 thf(f38,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = $false) | ($true = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.18/0.28 inference(iff_proxy_clausification,[],[f24])).
% 0.18/0.28 thf(f39,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ($true = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 0.18/0.28 inference(pi_proxy_clausification,[],[f38])).
% 0.18/0.28 thf(f40,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ((('const/sets/EMPTY' @ X0 = X1)) = $false)) )),
% 0.18/0.28 inference(not_proxy_clausification,[],[f39])).
% 0.18/0.28 thf(f41,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($false = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) | ('const/sets/EMPTY' @ X0 != X1)) )),
% 0.18/0.28 inference(equality_proxy_clausification,[],[f40])).
% 0.18/0.28 thf(f42,plain,(
% 0.18/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) | ((('const/sets/IN' @ X0 @ X2 @ X1)) = $false)) )),
% 0.18/0.28 inference(beta-eta_normalization,[],[f41])).
% 0.18/0.28 thf(f62,plain,(
% 0.18/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true) | ($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.18/0.28 inference(constrained_superposition,[],[f23,f36])).
% 0.18/0.28 thf(f63,plain,(
% 0.18/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.18/0.28 thf(f70,plain,(
% 0.18/0.28 ( ! [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)))) )),
% 0.18/0.28 inference(constrained_superposition,[],[f26,f36])).
% 0.18/0.28 thf(f71,plain,(
% 0.18/0.28 ( ! [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)))) )),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f70])).
% 0.18/0.28 thf(f74,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.18/0.28 inference(constrained_superposition,[],[f25,f31])).
% 0.18/0.28 thf(f77,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f74])).
% 0.18/0.28 thf(f79,definition,(
% 0.18/0.28 spl7_1 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.18/0.28 thf(f80,plain,(
% 0.18/0.28 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) | spl7_1),
% 0.18/0.28 inference(avatar_component_clause,[],[f79])).
% 0.18/0.28 thf(f81,plain,(
% 0.18/0.28 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl7_1),
% 0.18/0.28 inference(avatar_component_clause,[],[f79])).
% 0.18/0.28 thf(f83,definition,(
% 0.18/0.28 spl7_2 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.18/0.28 thf(f84,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl7_2),
% 0.18/0.28 inference(avatar_component_clause,[],[f83])).
% 0.18/0.28 thf(f86,definition,(
% 0.18/0.28 spl7_3 <=> ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2))))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.18/0.28 thf(f88,plain,(
% 0.18/0.28 ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ~spl7_3),
% 0.18/0.28 inference(avatar_component_clause,[],[f86])).
% 0.18/0.28 thf(f89,plain,(
% 0.18/0.28 spl7_1 | spl7_2 | spl7_3),
% 0.18/0.28 inference(avatar_split_clause,[],[f77,f86,f83,f79])).
% 0.18/0.28 thf(f149,definition,(
% 0.18/0.28 spl7_6 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.18/0.28 thf(f150,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl7_6),
% 0.18/0.28 inference(avatar_component_clause,[],[f149])).
% 0.18/0.28 thf(f174,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl7_2),
% 0.18/0.28 inference(constrained_superposition,[],[f33,f84])).
% 0.18/0.28 thf(f177,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl7_2),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f174])).
% 0.18/0.28 thf(f180,plain,(
% 0.18/0.28 spl7_6 | ~spl7_2),
% 0.18/0.28 inference(avatar_split_clause,[],[f177,f83,f149])).
% 0.18/0.28 thf(f210,plain,(
% 0.18/0.28 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((sK2 != X0) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $false)) ) | ~spl7_1),
% 0.18/0.28 inference(constrained_superposition,[],[f42,f81])).
% 0.18/0.28 thf(f215,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl7_1),
% 0.18/0.28 inference(equality_resolution,[],[f210])).
% 0.18/0.28 thf(f229,plain,(
% 0.18/0.28 ($true = $false) | ~spl7_1),
% 0.18/0.28 inference(constrained_superposition,[],[f215,f31])).
% 0.18/0.28 thf(f255,plain,(
% 0.18/0.28 $false | ~spl7_1),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f229])).
% 0.18/0.28 thf(f256,plain,(
% 0.18/0.28 ~spl7_1),
% 0.18/0.28 inference(avatar_contradiction_clause,[],[f255])).
% 0.18/0.28 thf(f319,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ X0))) | ($false = (('const/realax/real_le' @ sK5 @ X0)))) )),
% 0.18/0.28 inference(constrained_superposition,[],[f63,f32])).
% 0.18/0.28 thf(f327,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ sK5 @ X0))) | ($true = (('const/realax/real_le' @ sK3 @ X0)))) )),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f319])).
% 0.18/0.28 thf(f336,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) )),
% 0.18/0.28 inference(constrained_superposition,[],[f71,f31])).
% 0.18/0.28 thf(f353,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) )),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f336])).
% 0.18/0.28 thf(f357,plain,(
% 0.18/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK2)))) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | spl7_1),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f353,f80])).
% 0.18/0.28 thf(f359,definition,(
% 0.18/0.28 spl7_14 <=> ! [X1 : 'type/realax/real'] : ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition])).
% 0.18/0.28 thf(f360,plain,(
% 0.18/0.28 ( ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))) ) | ~spl7_14),
% 0.18/0.28 inference(avatar_component_clause,[],[f359])).
% 0.18/0.28 thf(f369,plain,(
% 0.18/0.28 spl7_14 | spl7_3 | spl7_1),
% 0.18/0.28 inference(avatar_split_clause,[],[f357,f79,f86,f359])).
% 0.18/0.28 thf(f450,plain,(
% 0.18/0.28 ($true = $false) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ~spl7_3),
% 0.18/0.28 inference(constrained_superposition,[],[f327,f88])).
% 0.18/0.28 thf(f469,plain,(
% 0.18/0.28 ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ~spl7_3),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f450])).
% 0.18/0.28 thf(f475,plain,(
% 0.18/0.28 $false | ~spl7_3),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f469,f34])).
% 0.18/0.28 thf(f476,plain,(
% 0.18/0.28 ~spl7_3),
% 0.18/0.28 inference(avatar_contradiction_clause,[],[f475])).
% 0.18/0.28 thf(f620,plain,(
% 0.18/0.28 ($true = $false) | (~spl7_6 | ~spl7_14)),
% 0.18/0.28 inference(constrained_superposition,[],[f360,f150])).
% 0.18/0.28 thf(f639,plain,(
% 0.18/0.28 $false | (~spl7_6 | ~spl7_14)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f620])).
% 0.18/0.28 thf(f640,plain,(
% 0.18/0.28 ~spl7_6 | ~spl7_14),
% 0.18/0.28 inference(avatar_contradiction_clause,[],[f639])).
% 0.18/0.28 cnf(s1, plain, spl7_1 | spl7_2 | spl7_3, inference(sat_conversion,[],[f89])).
% 0.18/0.28 cnf(s4, plain, ~spl7_2 | spl7_6, inference(sat_conversion,[],[f180])).
% 0.18/0.28 cnf(s10, plain, ~spl7_1, inference(sat_conversion,[],[f256])).
% 0.18/0.28 cnf(s25, plain, spl7_1 | spl7_3 | spl7_14, inference(sat_conversion,[],[f369])).
% 0.18/0.28 cnf(s31, plain, ~spl7_3, inference(sat_conversion,[],[f476])).
% 0.18/0.28 cnf(s34, plain, ~spl7_6 | ~spl7_14, inference(sat_conversion,[],[f640])).
% 0.18/0.28 cnf(s35, plain, spl7_1 | spl7_14, inference(rat,[],[s25,s31])).
% 0.18/0.28 cnf(s36, plain, spl7_14, inference(rat,[],[s35,s10])).
% 0.18/0.28 cnf(s38, plain, ~spl7_6, inference(rat,[],[s34,s36])).
% 0.18/0.28 cnf(s39, plain, ~spl7_2, inference(rat,[],[s4,s38])).
% 0.18/0.28 cnf(s44, plain, $false, inference(rat,[],[s1,s31,s39,s10])).
% 0.18/0.28 thf(f644,plain,(
% 0.18/0.28 $false),
% 0.18/0.28 inference(avatar_sat_refutation,[],[s44])).
% 0.18/0.28 % SZS output end Proof for theBenchmark
% 0.18/0.28 % (931711)------------------------------
% 0.18/0.28 % (931711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (931711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (931711)CaDiCaL version: 2.1.3
% 0.18/0.28 % (931711)Termination reason: Refutation
% 0.18/0.28 % (931711)Time elapsed: 0.018 s
% 0.18/0.28 % (931711)Peak memory usage: 13 MB
% 0.18/0.28 % (931711)Instructions burned: 57 (million)
% 0.18/0.28 % (931703)Success in time 0.042 s
% 0.18/0.28 % Vampire exiting
%------------------------------------------------------------------------------