%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA091^1 : 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 : n018.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 0.20s 0.28s
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:43:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (404715)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (404723)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=2196987547: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)
% 0.20/0.28 % (404726)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (404726)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
% 0.20/0.28 % (404720)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=393854583:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (404724)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3143987668:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (404721)lrs+10_16_si=on:nwc=1.5:random_seed=2809534863:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (404722)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2254321838:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (404725)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1589466484:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (404726)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=1818306432:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (404723) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-404715-404723"...
% 0.20/0.28 % (404722)Instruction limit reached!
% 0.20/0.28 % (404722)------------------------------
% 0.20/0.28 % (404722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (404722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (404722)CaDiCaL version: 2.1.3
% 0.20/0.28 % (404722)Termination reason: Instruction limit
% 0.20/0.28 % (404722)Termination phase: Saturation
% 0.20/0.28 % (404722)Time elapsed: 0.002 s
% 0.20/0.28 % (404722)Peak memory usage: 11 MB
% 0.20/0.28 % (404722)Instructions burned: 3 (million)
% 0.20/0.28 % (404723)...printing done.
% 0.20/0.28 % (404723)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.20/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.28 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.28 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.28 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.28 thf(func_def_7, type, sK0: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.28 thf(func_def_8, type, sK1: 'type/realax/real').
% 0.20/0.28 thf(func_def_9, type, sK2: 'type/realax/real').
% 0.20/0.28 thf(func_def_10, type, sK3: ('type/realax/real' > $o)).
% 0.20/0.28 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.20/0.28 thf(func_def_12, type, sK5: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.28 thf(func_def_13, type, sK6: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.28 thf(func_def_15, type, sK8: 'type/realax/real').
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 ! [X1 : 'type/realax/real',X0 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.20/0.28 thf(f2,axiom,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.20/0.28 thf(f3,axiom,(
% 0.20/0.28 ! [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' @ X1 @ X2))) => (! [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)))))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.20/0.28 thf(f4,conjecture,(
% 0.20/0.28 ! [X1 : 'type/realax/real',X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ('const/realax/real_le' @ X3 @ X2) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4))) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_')).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~ ! [X1 : 'type/realax/real',X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ('const/realax/real_le' @ X3 @ X2) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4))) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X2)) => ('const/realax/real_le' @ X1 @ X2))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X0)) = $true)) => ((('const/realax/real_le' @ X1 @ X2)) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [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' @ X1 @ X2))) => (! [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)))))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ! [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' @ X1 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => ($true = (('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)) = $true) => ((('const/realax/real_le' @ X4 @ X5)) = $true)) => ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true))))),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ~ ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X2) & ('const/realax/real_le' @ X1 @ X3) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X0 @ X4))) => ('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X3))),
% 0.20/0.28 inference(rectify,[],[f5])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ~ ! [X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X3 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X2)) = $true) => ((('const/realax/real_le' @ X0 @ X4)) = $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X2)) = $true)) => ((('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X3)) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f10])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) <=> ? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ? [X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X3)) != $true) & (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X4)) = $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X2)) = $true)))),
% 0.20/0.28 inference(ennf_transformation,[],[f11])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ? [X1 : 'type/realax/real',X3 : 'type/realax/real',X2 : ('type/realax/real' > $o),X0 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X4)) = $true)) & ((('const/realax/real_le' @ X1 @ X3)) = $true) & ((('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X2)) = $true))),
% 0.20/0.28 inference(flattening,[],[f14])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | (((('const/realax/real_le' @ X0 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true)))),
% 0.20/0.28 inference(ennf_transformation,[],[f7])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 ! [X1 : 'type/realax/real',X0 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) != $true))),
% 0.20/0.28 inference(flattening,[],[f16])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ! [X0 : ('type/realax/real' > $o)] : ((! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true) | ? [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ X5)) != $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | (! [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)))),
% 0.20/0.28 inference(ennf_transformation,[],[f9])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true) | ? [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ X5)) != $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) != $true)))),
% 0.20/0.28 inference(flattening,[],[f18])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.20/0.28 inference(nnf_transformation,[],[f13])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.20/0.28 inference(rectify,[],[f20])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X1)],[f21])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 ? [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X2)) != $true) | ((('const/realax/real_le' @ X3 @ X4)) = $true)) & ((('const/realax/real_le' @ X0 @ X1)) = $true) & ($true != (('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X1))) & ((('const/sets/IN' @ 'type/realax/real' @ X0 @ X2)) = $true))),
% 0.20/0.28 inference(rectify,[],[f15])).
% 0.20/0.28 thf(f24,plain,(
% 0.20/0.28 ! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK3)) != $true) | ((('const/realax/real_le' @ sK4 @ X4)) = $true)) & ((('const/realax/real_le' @ sK1 @ sK2)) = $true) & ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK2))) & ((('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK3)) = $true)),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f23])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true))),
% 0.20/0.28 inference(rectify,[],[f17])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) != $true))) & ! [X3 : 'type/realax/real'] : (($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'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ X5)) != $true)))),
% 0.20/0.28 inference(rectify,[],[f19])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ X0) @ X0))) & ((('const/realax/real_le' @ X1 @ (sK5 @ X1 @ 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'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK6 @ X4 @ X0) @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ (sK6 @ X4 @ X0))) != $true)))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK0 @ X0 @ X1),skolemize(X3,sK0 @ X0 @ X1)],[f26])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) | ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f22])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ((('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK3)) = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK2)))),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ((('const/realax/real_le' @ sK1 @ sK2)) = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ( ! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK3)) != $true) | ((('const/realax/real_le' @ sK4 @ X4)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f34,plain,(
% 0.20/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f25])).
% 0.20/0.28 thf(f35,plain,(
% 0.20/0.28 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ (sK6 @ X4 @ X0))) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f27])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK6 @ X4 @ X0) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f27])).
% 0.20/0.28 thf(f42,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0] : (((('const/sets/IN' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) != $true)) )),
% 0.20/0.28 inference(equality_resolution,[],[f29])).
% 0.20/0.28 thf(f44,definition,(
% 0.20/0.28 spl7_1 <=> ((('const/realax/real_le' @ sK1 @ sK2)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.20/0.28 thf(f46,plain,(
% 0.20/0.28 ((('const/realax/real_le' @ sK1 @ sK2)) = $true) | ~spl7_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f44])).
% 0.20/0.28 thf(f47,plain,(
% 0.20/0.28 spl7_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f32,f44])).
% 0.20/0.28 thf(f49,definition,(
% 0.20/0.28 spl7_2 <=> ((('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK3)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.20/0.28 thf(f51,plain,(
% 0.20/0.28 ((('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK3)) = $true) | ~spl7_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f49])).
% 0.20/0.28 thf(f52,plain,(
% 0.20/0.28 spl7_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f30,f49])).
% 0.20/0.28 thf(f54,definition,(
% 0.20/0.28 spl7_3 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK2)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.20/0.28 thf(f56,plain,(
% 0.20/0.28 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK2))) | spl7_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f54])).
% 0.20/0.28 thf(f57,plain,(
% 0.20/0.28 ~spl7_3),
% 0.20/0.28 inference(avatar_split_clause,[],[f31,f54])).
% 0.20/0.28 thf(f72,definition,(
% 0.20/0.28 spl7_6 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK3)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.20/0.28 thf(f73,plain,(
% 0.20/0.28 ('const/sets/EMPTY' @ 'type/realax/real' != sK3) | spl7_6),
% 0.20/0.28 inference(avatar_component_clause,[],[f72])).
% 0.20/0.28 thf(f74,plain,(
% 0.20/0.28 ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ~spl7_6),
% 0.20/0.28 inference(avatar_component_clause,[],[f72])).
% 0.20/0.28 thf(f78,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X1)) = $true) | ((('const/realax/real_le' @ sK4 @ (sK6 @ X0 @ sK3))) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) )),
% 0.20/0.28 inference(superposition,[],[f33,f36])).
% 0.20/0.28 thf(f79,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ((('const/realax/real_le' @ sK4 @ (sK6 @ X0 @ sK3))) = $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X1)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f78])).
% 0.20/0.28 thf(f81,definition,(
% 0.20/0.28 spl7_7 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK4 @ (sK6 @ X0 @ sK3))) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.20/0.28 thf(f82,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK4 @ (sK6 @ X0 @ sK3))) = $true)) ) | ~spl7_7),
% 0.20/0.28 inference(avatar_component_clause,[],[f81])).
% 0.20/0.28 thf(f84,definition,(
% 0.20/0.28 spl7_8 <=> ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X1)) = $true))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 0.20/0.28 thf(f85,plain,(
% 0.20/0.28 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3)) != $true)) ) | ~spl7_8),
% 0.20/0.28 inference(avatar_component_clause,[],[f84])).
% 0.20/0.28 thf(f86,plain,(
% 0.20/0.28 spl7_6 | spl7_7 | spl7_8),
% 0.20/0.28 inference(avatar_split_clause,[],[f79,f84,f81,f72])).
% 0.20/0.28 thf(f93,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ sK2)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)) != $true)) ) | spl7_3),
% 0.20/0.28 inference(superposition,[],[f56,f34])).
% 0.20/0.28 thf(f94,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ sK2)) != $true)) ) | spl7_3),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f93])).
% 0.20/0.28 thf(f95,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true)) ) | ~spl7_6),
% 0.20/0.28 inference(superposition,[],[f42,f74])).
% 0.20/0.28 thf(f112,plain,(
% 0.20/0.28 ($true != $true) | (~spl7_2 | ~spl7_6)),
% 0.20/0.28 inference(superposition,[],[f95,f51])).
% 0.20/0.28 thf(f114,plain,(
% 0.20/0.28 $false | (~spl7_2 | ~spl7_6)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f112])).
% 0.20/0.28 thf(f115,plain,(
% 0.20/0.28 ~spl7_2 | ~spl7_6),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f114])).
% 0.20/0.28 thf(f164,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true)) ) | ~spl7_7),
% 0.20/0.28 inference(superposition,[],[f35,f82])).
% 0.20/0.28 thf(f165,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true)) ) | ~spl7_7),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f164])).
% 0.20/0.28 thf(f167,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true)) ) | (spl7_6 | ~spl7_7)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f165,f73])).
% 0.20/0.28 thf(f169,plain,(
% 0.20/0.28 spl7_8 | spl7_6 | ~spl7_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f167,f81,f72,f84])).
% 0.20/0.28 thf(f173,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true) | ($true != $true) | ((('const/realax/real_le' @ X0 @ sK2)) != $true)) ) | (spl7_3 | ~spl7_8)),
% 0.20/0.28 inference(superposition,[],[f94,f85])).
% 0.20/0.28 thf(f180,plain,(
% 0.20/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true) | ((('const/realax/real_le' @ X0 @ sK2)) != $true)) ) | (spl7_3 | ~spl7_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f173])).
% 0.20/0.28 thf(f283,plain,(
% 0.20/0.28 ((('const/realax/real_le' @ sK1 @ sK2)) != $true) | ($true != $true) | (~spl7_2 | spl7_3 | ~spl7_8)),
% 0.20/0.28 inference(superposition,[],[f180,f51])).
% 0.20/0.28 thf(f287,plain,(
% 0.20/0.28 ((('const/realax/real_le' @ sK1 @ sK2)) != $true) | (~spl7_2 | spl7_3 | ~spl7_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f283])).
% 0.20/0.28 thf(f291,plain,(
% 0.20/0.28 $false | (~spl7_1 | ~spl7_2 | spl7_3 | ~spl7_8)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f287,f46])).
% 0.20/0.28 thf(f292,plain,(
% 0.20/0.28 ~spl7_1 | ~spl7_2 | spl7_3 | ~spl7_8),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f291])).
% 0.20/0.28 cnf(s1, plain, spl7_1, inference(sat_conversion,[],[f47])).
% 0.20/0.28 cnf(s2, plain, spl7_2, inference(sat_conversion,[],[f52])).
% 0.20/0.28 cnf(s3, plain, ~spl7_3, inference(sat_conversion,[],[f57])).
% 0.20/0.28 cnf(s6, plain, spl7_6 | spl7_7 | spl7_8, inference(sat_conversion,[],[f86])).
% 0.20/0.28 cnf(s7, plain, ~spl7_2 | ~spl7_6, inference(sat_conversion,[],[f115])).
% 0.20/0.28 cnf(s13, plain, spl7_6 | ~spl7_7 | spl7_8, inference(sat_conversion,[],[f169])).
% 0.20/0.28 cnf(s20, plain, ~spl7_1 | ~spl7_2 | spl7_3 | ~spl7_8, inference(sat_conversion,[],[f292])).
% 0.20/0.28 cnf(s23, plain, ~spl7_6, inference(rat,[],[s7,s2])).
% 0.20/0.28 cnf(s26, plain, ~spl7_8, inference(rat,[],[s20,s2,s3,s1])).
% 0.20/0.28 cnf(s27, plain, ~spl7_7, inference(rat,[],[s13,s23,s26])).
% 0.20/0.28 cnf(s28, plain, $false, inference(rat,[],[s6,s23,s26,s27])).
% 0.20/0.28 thf(f304,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s28])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (404723)------------------------------
% 0.20/0.28 % (404723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (404723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (404723)CaDiCaL version: 2.1.3
% 0.20/0.28 % (404723)Termination reason: Refutation
% 0.20/0.28 % (404723)Time elapsed: 0.011 s
% 0.20/0.28 % (404723)Peak memory usage: 13 MB
% 0.20/0.28 % (404723)Instructions burned: 32 (million)
% 0.20/0.28 % (404715)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------