%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA086^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 07:45:53 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA086^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n016.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 17:45:35 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running higher-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.36 % (681031)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (681041)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3541044110:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.36 % (681038)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1714485883:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.36 % (681042)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.36 % (681042)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
% 0.25/0.36 % (681038)Instruction limit reached!
% 0.25/0.36 % (681038)------------------------------
% 0.25/0.36 % (681038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (681038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (681038)CaDiCaL version: 2.1.3
% 0.25/0.36 % (681038)Termination reason: Instruction limit
% 0.25/0.36 % (681038)Termination phase: Saturation
% 0.25/0.36 % (681038)Time elapsed: 0.004 s
% 0.25/0.36 % (681038)Peak memory usage: 12 MB
% 0.25/0.36 % (681038)Instructions burned: 3 (million)
% 0.25/0.36 % (681036)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3656880196:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.36 % (681040)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2511027007:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.36 % (681039)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=4206206748: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)
% 0.25/0.36 % (681042)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=433340696:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.36 % (681041) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-681031-681041"...
% 0.25/0.36 % (681037)lrs+10_16_si=on:nwc=1.5:random_seed=1312617140:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.36 % (681041)...printing done.
% 0.25/0.36 % (681041)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% 0.25/0.36 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.25/0.36 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.36 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.25/0.36 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.25/0.36 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.25/0.36 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.25/0.36 thf(func_def_7, type, sK0: 'type/realax/real').
% 0.25/0.36 thf(func_def_8, type, sK1: ('type/realax/real' > $o)).
% 0.25/0.36 thf(func_def_9, type, sK2: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.25/0.36 thf(func_def_10, type, sK3: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.25/0.36 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.25/0.36 thf(f1,axiom,(
% 0.25/0.36 ! [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'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ! [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)))))),
% 0.25/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.25/0.36 thf(f2,conjecture,(
% 0.25/0.36 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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)))),
% 0.25/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_')).
% 0.25/0.36 thf(f3,negated_conjecture,(
% 0.25/0.36 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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)))),
% 0.25/0.36 inference(negated_conjecture,[status(cth)],[f2])).
% 0.25/0.36 thf(f4,plain,(
% 0.25/0.36 ! [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'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X4 @ X5)) => ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))),
% 0.25/0.36 inference(rectify,[],[f1])).
% 0.25/0.36 thf(f5,plain,(
% 0.25/0.36 ! [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)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X4 @ X5)))) => ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) => ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))))),
% 0.25/0.36 inference(fool_elimination,[],[f4])).
% 0.25/0.36 thf(f6,plain,(
% 0.25/0.36 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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)))),
% 0.25/0.36 inference(rectify,[],[f3])).
% 0.25/0.36 thf(f7,plain,(
% 0.25/0.36 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X2)) = $true))) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true))),
% 0.25/0.36 inference(fool_elimination,[],[f6])).
% 0.25/0.36 thf(f8,plain,(
% 0.25/0.36 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true))))),
% 0.25/0.36 inference(ennf_transformation,[],[f7])).
% 0.25/0.36 thf(f9,plain,(
% 0.25/0.36 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('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)))),
% 0.25/0.36 inference(flattening,[],[f8])).
% 0.25/0.36 thf(f10,plain,(
% 0.25/0.36 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)))) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X5)))) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))) | (! [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)))),
% 0.25/0.36 inference(ennf_transformation,[],[f5])).
% 0.25/0.36 thf(f11,plain,(
% 0.25/0.36 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)))) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X5)))) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))) | ! [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))),
% 0.25/0.36 inference(flattening,[],[f10])).
% 0.25/0.36 thf(f12,plain,(
% 0.25/0.36 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ($true != (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ X2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)))))),
% 0.25/0.36 inference(rectify,[],[f9])).
% 0.25/0.36 thf(f13,plain,(
% 0.25/0.36 ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ($true != (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ X2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))))),
% 0.25/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12])).
% 0.25/0.36 thf(f14,plain,(
% 0.25/0.36 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) & ($true != (('const/realax/real_le' @ X2 @ X3)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)))))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X5)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.25/0.36 inference(rectify,[],[f11])).
% 0.25/0.36 thf(f15,plain,(
% 0.25/0.36 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : ((($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0))))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)))))) | ! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.25/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK3 @ X4 @ X0),skolemize(X5,sK3 @ X4 @ X0)],[f14])).
% 0.25/0.36 thf(f16,plain,(
% 0.25/0.36 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) | ($true = (('const/realax/real_le' @ sK0 @ X2)))) )),
% 0.25/0.36 inference(cnf_transformation,[],[f13])).
% 0.25/0.36 thf(f17,plain,(
% 0.25/0.36 ($true != (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))))),
% 0.25/0.36 inference(cnf_transformation,[],[f13])).
% 0.25/0.36 thf(f18,plain,(
% 0.25/0.36 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.25/0.36 inference(cnf_transformation,[],[f13])).
% 0.25/0.36 thf(f19,plain,(
% 0.25/0.36 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)))) | ($true != (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.25/0.36 inference(cnf_transformation,[],[f15])).
% 0.25/0.36 thf(f20,plain,(
% 0.25/0.36 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.25/0.36 inference(cnf_transformation,[],[f15])).
% 0.25/0.36 thf(f21,plain,(
% 0.25/0.36 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.25/0.36 inference(cnf_transformation,[],[f15])).
% 0.25/0.36 thf(f22,plain,(
% 0.25/0.36 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0))))) )),
% 0.25/0.36 inference(cnf_transformation,[],[f15])).
% 0.25/0.36 thf(f26,definition,(
% 0.25/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.25/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.25/0.36 thf(f49,plain,(
% 0.25/0.36 ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $false) | ($true != $true)),
% 0.25/0.36 inference(constrained_superposition,[],[f17,f26])).
% 0.25/0.36 thf(f52,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ X0)) = $true) | ($true != $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) = $false)) )),
% 0.25/0.36 inference(constrained_superposition,[],[f16,f26])).
% 0.25/0.36 thf(f55,plain,(
% 0.25/0.36 ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $false)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f49])).
% 0.25/0.36 thf(f58,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) = $false) | ((('const/realax/real_le' @ sK0 @ X0)) = $true)) )),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f52])).
% 0.25/0.36 thf(f91,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1))) | ($true = $false) | ($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.25/0.36 inference(constrained_superposition,[],[f58,f22])).
% 0.25/0.36 thf(f95,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1))))) )),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f91])).
% 0.25/0.36 thf(f105,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)))) )),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f95,f18])).
% 0.25/0.36 thf(f111,definition,(
% 0.25/0.36 spl5_5 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK0 @ (sK3 @ X0 @ sK1))))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.25/0.36 thf(f112,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK3 @ X0 @ sK1))))) ) | ~spl5_5),
% 0.25/0.36 inference(avatar_component_clause,[],[f111])).
% 0.25/0.36 thf(f114,definition,(
% 0.25/0.36 spl5_6 <=> ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.25/0.36 thf(f115,plain,(
% 0.25/0.36 ( ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_6),
% 0.25/0.36 inference(avatar_component_clause,[],[f114])).
% 0.25/0.36 thf(f118,definition,(
% 0.25/0.36 spl5_7 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.25/0.36 thf(f119,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_7),
% 0.25/0.36 inference(avatar_component_clause,[],[f118])).
% 0.25/0.36 thf(f121,definition,(
% 0.25/0.36 spl5_8 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.25/0.36 thf(f122,plain,(
% 0.25/0.36 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)))) ) | ~spl5_8),
% 0.25/0.36 inference(avatar_component_clause,[],[f121])).
% 0.25/0.36 thf(f123,plain,(
% 0.25/0.36 spl5_7 | spl5_8),
% 0.25/0.36 inference(avatar_split_clause,[],[f105,f121,f118])).
% 0.25/0.36 thf(f128,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)))) ) | ~spl5_5),
% 0.25/0.36 inference(constrained_superposition,[],[f21,f112])).
% 0.25/0.36 thf(f131,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_5),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f128])).
% 0.25/0.36 thf(f134,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0 @ sK1) @ sK1)))) ) | ~spl5_5),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f131,f18])).
% 0.25/0.36 thf(f137,plain,(
% 0.25/0.36 spl5_6 | ~spl5_5),
% 0.25/0.36 inference(avatar_split_clause,[],[f134,f111,f114])).
% 0.25/0.36 thf(f138,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = $false)) ) | ~spl5_6),
% 0.25/0.36 inference(constrained_superposition,[],[f115,f58])).
% 0.25/0.36 thf(f143,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ sK0 @ (sK2 @ X0 @ sK1))))) ) | ~spl5_6),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f138])).
% 0.25/0.36 thf(f153,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK0 @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.25/0.36 inference(constrained_superposition,[],[f16,f122])).
% 0.25/0.36 thf(f155,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f153])).
% 0.25/0.36 thf(f201,plain,(
% 0.25/0.36 spl5_5 | ~spl5_8),
% 0.25/0.36 inference(avatar_split_clause,[],[f155,f121,f111])).
% 0.25/0.36 thf(f222,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true != $true)) ) | ~spl5_7),
% 0.25/0.36 inference(constrained_superposition,[],[f20,f119])).
% 0.25/0.36 thf(f223,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true)) ) | ~spl5_7),
% 0.25/0.36 inference(duplicate_literal_removal,[],[f222])).
% 0.25/0.36 thf(f224,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_7),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f223])).
% 0.25/0.36 thf(f225,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_7),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f224,f18])).
% 0.25/0.36 thf(f226,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_7),
% 0.25/0.36 inference(forward_demodulation,[],[f225,f55])).
% 0.25/0.36 thf(f227,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_7),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f226])).
% 0.25/0.36 thf(f228,plain,(
% 0.25/0.36 spl5_8 | ~spl5_7),
% 0.25/0.36 inference(avatar_split_clause,[],[f227,f118,f121])).
% 0.25/0.36 thf(f233,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_5),
% 0.25/0.36 inference(constrained_superposition,[],[f19,f112])).
% 0.25/0.36 thf(f235,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true != (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK1))))) ) | ~spl5_5),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f233])).
% 0.25/0.36 thf(f238,plain,(
% 0.25/0.36 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_5),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f235,f18])).
% 0.25/0.36 thf(f273,plain,(
% 0.25/0.36 ($true != $true) | ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | (~spl5_5 | ~spl5_7)),
% 0.25/0.36 inference(constrained_superposition,[],[f238,f119])).
% 0.25/0.36 thf(f282,plain,(
% 0.25/0.36 ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | ($true != $true) | (~spl5_5 | ~spl5_7)),
% 0.25/0.36 inference(duplicate_literal_removal,[],[f273])).
% 0.25/0.36 thf(f283,plain,(
% 0.25/0.36 ($true = (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)))) | (~spl5_5 | ~spl5_7)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f282])).
% 0.25/0.36 thf(f286,plain,(
% 0.25/0.36 ($true = $false) | (~spl5_5 | ~spl5_7)),
% 0.25/0.36 inference(forward_demodulation,[],[f283,f55])).
% 0.25/0.36 thf(f287,plain,(
% 0.25/0.36 $false | (~spl5_5 | ~spl5_7)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f286])).
% 0.25/0.36 thf(f288,plain,(
% 0.25/0.36 ~spl5_5 | ~spl5_7),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f287])).
% 0.25/0.36 thf(f289,plain,(
% 0.25/0.36 spl5_7 | ~spl5_6),
% 0.25/0.36 inference(avatar_split_clause,[],[f143,f114,f118])).
% 0.25/0.36 cnf(s5, plain, spl5_7 | spl5_8, inference(sat_conversion,[],[f123])).
% 0.25/0.36 cnf(s10, plain, ~spl5_5 | spl5_6, inference(sat_conversion,[],[f137])).
% 0.25/0.36 cnf(s13, plain, spl5_5 | ~spl5_8, inference(sat_conversion,[],[f201])).
% 0.25/0.36 cnf(s17, plain, ~spl5_7 | spl5_8, inference(sat_conversion,[],[f228])).
% 0.25/0.36 cnf(s23, plain, ~spl5_5 | ~spl5_7, inference(sat_conversion,[],[f288])).
% 0.25/0.36 cnf(s24, plain, ~spl5_6 | spl5_7, inference(sat_conversion,[],[f289])).
% 0.25/0.36 cnf(s27, plain, spl5_8, inference(rat,[],[s5,s17])).
% 0.25/0.36 cnf(s28, plain, spl5_5, inference(rat,[],[s13,s27])).
% 0.25/0.36 cnf(s29, plain, ~spl5_7, inference(rat,[],[s23,s28])).
% 0.25/0.36 cnf(s30, plain, spl5_6, inference(rat,[],[s10,s28])).
% 0.25/0.36 cnf(s31, plain, $false, inference(rat,[],[s24,s29,s30])).
% 0.25/0.36 thf(f290,plain,(
% 0.25/0.36 $false),
% 0.25/0.36 inference(avatar_sat_refutation,[],[s31])).
% 0.25/0.36 % SZS output end Proof for theBenchmark
% 0.25/0.36 % (681041)------------------------------
% 0.25/0.36 % (681041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (681041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (681041)CaDiCaL version: 2.1.3
% 0.25/0.36 % (681041)Termination reason: Refutation
% 0.25/0.36 % (681041)Time elapsed: 0.016 s
% 0.25/0.36 % (681041)Peak memory usage: 13 MB
% 0.25/0.36 % (681041)Instructions burned: 30 (million)
% 0.25/0.36 % (681031)Success in time 0.04 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------