%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA074^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 07:45:51 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA074^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 17:39:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (1133176)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1133186)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3875230055:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (1133187)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (1133187)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (1133183)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3544520552:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1133182)lrs+10_16_si=on:nwc=1.5:random_seed=3717083333:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1133181)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1134559083:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1133185)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4124281707:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (1133184)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2877362589:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (1133187)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=792002645:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (1133183)Instruction limit reached!
% 0.22/0.30 % (1133183)------------------------------
% 0.22/0.30 % (1133183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1133183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1133183)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1133183)Termination reason: Instruction limit
% 0.22/0.30 % (1133183)Termination phase: Saturation
% 0.22/0.30 % (1133183)Time elapsed: 0.003 s
% 0.22/0.30 % (1133183)Peak memory usage: 12 MB
% 0.22/0.30 % (1133183)Instructions burned: 5 (million)
% 0.22/0.30 % (1133181) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1133176-1133181"...
% 0.22/0.30 % (1133182) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1133176-1133182"...
% 0.22/0.30 % (1133184) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1133176-1133184"...
% 0.22/0.30 % (1133181)...printing done.
% 0.22/0.30 % (1133185) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1133176-1133185"...
% 0.22/0.30 % (1133182)...printing done.
% 0.22/0.30 % (1133181)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.30 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.30 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.22/0.30 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.22/0.30 thf(func_def_7, type, sK0: 'type/realax/real').
% 0.22/0.30 thf(func_def_8, type, sK1: ('type/realax/real' > $o)).
% 0.22/0.30 thf(func_def_9, type, sK2: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.30 thf(func_def_10, type, sK3: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.30 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : (((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))) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ! [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))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.22/0.30 thf(f2,conjecture,(
% 0.22/0.30 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ '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))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_')).
% 0.22/0.30 thf(f3,negated_conjecture,(
% 0.22/0.30 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ '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))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f2])).
% 0.22/0.30 thf(f4,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : (((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))) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ X4)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))))),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true))) => (! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X5 @ X4)))) => ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)))) & ! [X3 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) => ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))))))),
% 0.22/0.30 inference(fool_elimination,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0))) => ('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))),
% 0.22/0.30 inference(rectify,[],[f3])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $true) => ($true = (('const/realax/real_le' @ X2 @ X0))))) => ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))))),
% 0.22/0.30 inference(fool_elimination,[],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : ((! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X5 @ X4)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)))) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))))) | (('const/sets/EMPTY' @ 'type/realax/real' = 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))))),
% 0.22/0.30 inference(ennf_transformation,[],[f5])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | (! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X5 @ X4)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)))) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))))))),
% 0.22/0.30 inference(flattening,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) != $true) | ($true = (('const/realax/real_le' @ X2 @ X0))))))),
% 0.22/0.30 inference(ennf_transformation,[],[f7])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) != $true) | ($true = (('const/realax/real_le' @ X2 @ X0)))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ($true != (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))))),
% 0.22/0.30 inference(flattening,[],[f10])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X2 @ sK0)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) != $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | (! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($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)))))))),
% 0.22/0.30 inference(rectify,[],[f9])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X1 @ X0) @ X1))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0)))) | (! [X3 : 'type/realax/real'] : ((((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X3 @ X0) @ X0)) = $true) & ($true != (('const/realax/real_le' @ (sK3 @ X3 @ X0) @ 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)))))))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK3 @ X3 @ X0),skolemize(X4,sK3 @ X3 @ X0)],[f13])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) != $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f12])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.22/0.30 inference(cnf_transformation,[],[f12])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ( ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X2 @ sK0)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f12])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK3 @ X3 @ X0) @ X3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f14])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X3 @ X0) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f14])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f14])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK3 @ X3 @ X0) @ X3))) | ($true != (('const/realax/real_le' @ (sK2 @ X1 @ X0) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f14])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X3 @ X0) @ X0)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f14])).
% 0.22/0.30 thf(f53,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 0.22/0.30 inference(constrained_superposition,[],[f17,f20])).
% 0.22/0.30 thf(f57,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f53])).
% 0.22/0.30 thf(f61,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f57,f16])).
% 0.22/0.30 thf(f64,definition,(
% 0.22/0.30 spl5_5 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1)))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1)))) ) | ~spl5_5),
% 0.22/0.30 inference(avatar_component_clause,[],[f64])).
% 0.22/0.30 thf(f67,definition,(
% 0.22/0.30 spl5_6 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.22/0.30 thf(f68,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl5_6),
% 0.22/0.30 inference(avatar_component_clause,[],[f67])).
% 0.22/0.30 thf(f69,plain,(
% 0.22/0.30 spl5_5 | spl5_6),
% 0.22/0.30 inference(avatar_split_clause,[],[f61,f67,f64])).
% 0.22/0.30 thf(f71,definition,(
% 0.22/0.30 spl5_7 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ sK0)))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.22/0.30 thf(f72,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ sK0)))) ) | ~spl5_7),
% 0.22/0.30 inference(avatar_component_clause,[],[f71])).
% 0.22/0.30 thf(f74,definition,(
% 0.22/0.30 spl5_8 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.22/0.30 thf(f75,plain,(
% 0.22/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1)))) ) | ~spl5_8),
% 0.22/0.30 inference(avatar_component_clause,[],[f74])).
% 0.22/0.30 thf(f77,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_7),
% 0.22/0.30 inference(constrained_superposition,[],[f23,f72])).
% 0.22/0.30 thf(f78,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true)) ) | ~spl5_7),
% 0.22/0.30 inference(constrained_superposition,[],[f21,f72])).
% 0.22/0.30 thf(f79,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_7),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.30 thf(f80,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))))) ) | ~spl5_7),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f78])).
% 0.22/0.30 thf(f81,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl5_7),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f79,f16])).
% 0.22/0.30 thf(f82,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))))) ) | ~spl5_7),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f80,f16])).
% 0.22/0.30 thf(f83,plain,(
% 0.22/0.30 spl5_8 | ~spl5_7),
% 0.22/0.30 inference(avatar_split_clause,[],[f81,f71,f74])).
% 0.22/0.30 thf(f84,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ sK0))) | ($true != $true)) ) | ~spl5_5),
% 0.22/0.30 inference(constrained_superposition,[],[f17,f65])).
% 0.22/0.30 thf(f87,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ sK0)))) ) | ~spl5_5),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.30 thf(f90,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ ('const/sets/sup' @ sK1))) = $true) | ($true != $true)) ) | (~spl5_5 | ~spl5_7)),
% 0.22/0.30 inference(constrained_superposition,[],[f82,f65])).
% 0.22/0.30 thf(f92,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ ('const/sets/sup' @ sK1))) = $true)) ) | (~spl5_5 | ~spl5_7)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f90])).
% 0.22/0.30 thf(f99,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true != $true)) ) | ~spl5_8),
% 0.22/0.30 inference(constrained_superposition,[],[f17,f75])).
% 0.22/0.30 thf(f101,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK3 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl5_8),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f99])).
% 0.22/0.30 thf(f104,plain,(
% 0.22/0.30 spl5_6 | ~spl5_8),
% 0.22/0.30 inference(avatar_split_clause,[],[f101,f74,f67])).
% 0.22/0.30 thf(f105,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ($true != $true) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true)) ) | ~spl5_6),
% 0.22/0.30 inference(constrained_superposition,[],[f19,f68])).
% 0.22/0.30 thf(f106,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ($true != (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ X0))) | ($true != $true)) ) | ~spl5_6),
% 0.22/0.30 inference(constrained_superposition,[],[f22,f68])).
% 0.22/0.30 thf(f107,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ($true != $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl5_6),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f105])).
% 0.22/0.30 thf(f108,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl5_6),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f107])).
% 0.22/0.30 thf(f109,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_6),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f106])).
% 0.22/0.30 thf(f110,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_6),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f109])).
% 0.22/0.30 thf(f111,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_6),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f110,f15])).
% 0.22/0.30 thf(f112,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK2 @ X0 @ sK1) @ X0)))) ) | ~spl5_6),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f111,f16])).
% 0.22/0.30 thf(f114,plain,(
% 0.22/0.30 ($true != $true) | (~spl5_5 | ~spl5_6 | ~spl5_7)),
% 0.22/0.30 inference(constrained_superposition,[],[f112,f92])).
% 0.22/0.30 thf(f115,plain,(
% 0.22/0.30 $false | (~spl5_5 | ~spl5_6 | ~spl5_7)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f114])).
% 0.22/0.30 thf(f116,plain,(
% 0.22/0.30 ~spl5_5 | ~spl5_6 | ~spl5_7),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f115])).
% 0.22/0.30 thf(f119,plain,(
% 0.22/0.30 spl5_7 | ~spl5_5),
% 0.22/0.30 inference(avatar_split_clause,[],[f87,f64,f71])).
% 0.22/0.30 thf(f121,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)) = $true)) ) | ~spl5_6),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f108,f16])).
% 0.22/0.30 thf(f126,plain,(
% 0.22/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl5_6),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f121,f15])).
% 0.22/0.30 thf(f127,plain,(
% 0.22/0.30 spl5_5 | ~spl5_6),
% 0.22/0.30 inference(avatar_split_clause,[],[f126,f67,f64])).
% 0.22/0.30 cnf(s4, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f69])).
% 0.22/0.30 cnf(s6, plain, ~spl5_7 | spl5_8, inference(sat_conversion,[],[f83])).
% 0.22/0.30 cnf(s7, plain, spl5_6 | ~spl5_8, inference(sat_conversion,[],[f104])).
% 0.22/0.30 cnf(s8, plain, ~spl5_5 | ~spl5_6 | ~spl5_7, inference(sat_conversion,[],[f116])).
% 0.22/0.30 cnf(s10, plain, ~spl5_5 | spl5_7, inference(sat_conversion,[],[f119])).
% 0.22/0.30 cnf(s12, plain, spl5_5 | ~spl5_6, inference(sat_conversion,[],[f127])).
% 0.22/0.30 cnf(s13, plain, spl5_5, inference(rat,[],[s4,s12])).
% 0.22/0.30 cnf(s14, plain, spl5_7, inference(rat,[],[s10,s13])).
% 0.22/0.30 cnf(s15, plain, ~spl5_6, inference(rat,[],[s8,s14,s13])).
% 0.22/0.30 cnf(s16, plain, spl5_8, inference(rat,[],[s6,s14])).
% 0.22/0.30 cnf(s17, plain, $false, inference(rat,[],[s7,s16,s15])).
% 0.22/0.30 thf(f128,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(avatar_sat_refutation,[],[s17])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (1133181)------------------------------
% 0.22/0.30 % (1133181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1133181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1133181)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1133181)Termination reason: Refutation
% 0.22/0.30 % (1133181)Time elapsed: 0.008 s
% 0.22/0.30 % (1133181)Peak memory usage: 13 MB
% 0.22/0.30 % (1133181)Instructions burned: 12 (million)
% 0.22/0.30 % (1133176)Success in time 0.048 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------