%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV493^1 : 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 : 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 08:38:44 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV493^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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 15:53:18 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
% 0.08/0.22 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
% 0.19/0.27 % (957201)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (957211)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=407312522:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (957212)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (957212)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
% 0.19/0.27 % (957207)lrs+10_16_si=on:nwc=1.5:random_seed=2023226588:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (957208)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3057903523:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (957209)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=602893961: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)
% 0.19/0.27 % (957210)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1769218153:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (957212)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=1015475483:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (957208)Instruction limit reached!
% 0.19/0.27 % (957208)------------------------------
% 0.19/0.27 % (957208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (957208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (957208)CaDiCaL version: 2.1.3
% 0.19/0.27 % (957208)Termination reason: Instruction limit
% 0.19/0.27 % (957208)Termination phase: Saturation
% 0.19/0.27 % (957208)Time elapsed: 0.003 s
% 0.19/0.27 % (957208)Peak memory usage: 12 MB
% 0.19/0.27 % (957208)Instructions burned: 4 (million)
% 0.19/0.27 % (957211) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-957201-957211"...
% 0.19/0.27 % (957207)Instruction limit reached!
% 0.19/0.27 % (957207)------------------------------
% 0.19/0.27 % (957207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (957207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (957207)CaDiCaL version: 2.1.3
% 0.19/0.27 % (957207)Termination reason: Instruction limit
% 0.19/0.27 % (957207)Termination phase: Saturation
% 0.19/0.27 % (957207)Time elapsed: 0.011 s
% 0.19/0.27 % (957207)Peak memory usage: 12 MB
% 0.19/0.27 % (957207)Instructions burned: 19 (million)
% 0.19/0.27 % (957210)Instruction limit reached!
% 0.19/0.27 % (957210)------------------------------
% 0.19/0.27 % (957210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (957211)...printing done.
% 0.19/0.27 % (957210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (957210)CaDiCaL version: 2.1.3
% 0.19/0.27 % (957210)Termination reason: Instruction limit
% 0.19/0.27 % (957210)Termination phase: Saturation
% 0.19/0.27 % (957210)Time elapsed: 0.013 s
% 0.19/0.27 % (957210)Peak memory usage: 12 MB
% 0.19/0.27 % (957210)Instructions burned: 24 (million)
% 0.19/0.27 % (957206)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1883500347:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (957211)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.27 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_8, type, sK0: (('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_9, type, sK1: ('type/realax/real' > $o)).
% 0.19/0.27 thf(func_def_10, type, sK2: 'type/realax/real').
% 0.19/0.27 thf(func_def_11, type, sK3: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_12, type, sK4: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.19/0.27 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(func_def_15, type, sK6: 'type/realax/real').
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 ! [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)))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.19/0.27 thf(f3,axiom,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((X0 = X1) = ('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_')).
% 0.19/0.27 thf(f4,axiom,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_LEMMA_')).
% 0.19/0.27 thf(f5,conjecture,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_')).
% 0.19/0.27 thf(f6,negated_conjecture,(
% 0.19/0.27 ~ ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 ~ ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ~ ! [X0 : ('type/realax/real' > $o)] : ((((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) = $true) & ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true))))),
% 0.19/0.27 inference(fool_elimination,[],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ! [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)))))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ! [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' @ X1 @ X2)) = $true))) => (! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X4 @ X5)))) => ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true)) & ! [X3 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) => ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))))),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : ((((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ? [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X2)) = $true))))),
% 0.19/0.27 inference(fool_elimination,[],[f13])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((X0 = X1) = ('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1))),
% 0.19/0.27 inference(rectify,[],[f3])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X1 @ X0)) = $true)) <=> (X0 = X1))),
% 0.19/0.27 inference(fool_elimination,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ? [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)) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) != $true)) & (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.19/0.27 inference(ennf_transformation,[],[f8])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ? [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) != $true)) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.19/0.27 inference(flattening,[],[f17])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ! [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' @ X4 @ X5)))) | ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true)) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))))),
% 0.19/0.27 inference(ennf_transformation,[],[f10])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X5)))) | ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) = $true)) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))))),
% 0.19/0.27 inference(flattening,[],[f19])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.19/0.27 inference(ennf_transformation,[],[f14])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 0.19/0.27 inference(flattening,[],[f21])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0) @ X2))) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0) @ X0)))) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f22])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ((($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)))) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK1)))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f18])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X1 @ X0)) = $true)) | (X0 != X1)) & ((X0 = X1) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true))))),
% 0.19/0.27 inference(nnf_transformation,[],[f16])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X1 @ X0)) = $true)) | (X0 != X1)) & ((X0 = X1) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true)))),
% 0.19/0.27 inference(flattening,[],[f25])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((((('const/realax/real_le' @ X1 @ X0)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) | (X0 != X1)) & ((X0 = X1) | ((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 0.19/0.27 inference(rectify,[],[f26])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) & ((('const/realax/real_le' @ X3 @ X4)) != $true)) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))) & ! [X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))))),
% 0.19/0.27 inference(rectify,[],[f20])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK3 @ X1 @ X0)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : ((($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X3 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ X3 @ (sK4 @ X3 @ X0))))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))) & ! [X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X1,sK0 @ X0),skolemize(X1,sK0 @ X0)],[f29])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o)] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0) @ X0)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f23])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X0) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f23])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f36,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) != $true) | (X0 = X1) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f27])).
% 0.19/0.27 thf(f41,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ (sK4 @ X3 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X3 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK3 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f45,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ (sK4 @ X3 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/realax/real_le' @ X1 @ (sK3 @ X1 @ X0)))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK3 @ X1 @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X3 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f30])).
% 0.19/0.27 thf(f48,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f52,definition,(
% 0.19/0.27 spl5_1 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | spl5_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f52])).
% 0.19/0.27 thf(f55,definition,(
% 0.19/0.27 spl5_2 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.27 thf(f56,plain,(
% 0.19/0.27 ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1))) | spl5_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f55])).
% 0.19/0.27 thf(f57,plain,(
% 0.19/0.27 ~spl5_1 | ~spl5_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f35,f55,f52])).
% 0.19/0.27 thf(f59,definition,(
% 0.19/0.27 spl5_3 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.27 thf(f60,plain,(
% 0.19/0.27 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1))) | ~spl5_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f59])).
% 0.19/0.27 thf(f61,plain,(
% 0.19/0.27 ~spl5_2 | spl5_3),
% 0.19/0.27 inference(avatar_split_clause,[],[f34,f59,f55])).
% 0.19/0.27 thf(f85,plain,(
% 0.19/0.27 ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)) = $false) | ($true != $true) | spl5_2),
% 0.19/0.27 inference(constrained_superposition,[],[f56,f48])).
% 0.19/0.27 thf(f92,plain,(
% 0.19/0.27 ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1)) = $false) | spl5_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f85])).
% 0.19/0.27 thf(f97,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((X0 = X1) | ((('const/realax/real_le' @ X1 @ X0)) != $true) | ($true != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f37,f48])).
% 0.19/0.27 thf(f98,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) != $true) | (X0 = X1) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f97])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ sK1) @ sK1)))),
% 0.19/0.27 inference(constrained_superposition,[],[f31,f33])).
% 0.19/0.27 thf(f104,plain,(
% 0.19/0.27 ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f101])).
% 0.19/0.27 thf(f105,plain,(
% 0.19/0.27 ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ sK1) @ sK1)))),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f104,f36])).
% 0.19/0.27 thf(f150,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f41,f105])).
% 0.19/0.27 thf(f153,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f150])).
% 0.19/0.27 thf(f154,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1))))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f153,f36])).
% 0.19/0.27 thf(f156,definition,(
% 0.19/0.27 spl5_8 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.19/0.27 thf(f157,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_8),
% 0.19/0.27 inference(avatar_component_clause,[],[f156])).
% 0.19/0.27 thf(f159,definition,(
% 0.19/0.27 spl5_9 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.19/0.27 thf(f160,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1)))) | ~spl5_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f159])).
% 0.19/0.27 thf(f161,plain,(
% 0.19/0.27 spl5_8 | spl5_9),
% 0.19/0.27 inference(avatar_split_clause,[],[f154,f159,f156])).
% 0.19/0.27 thf(f163,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ sK1) @ (sK3 @ X0 @ sK1)))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1)))) ) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f32,f157])).
% 0.19/0.27 thf(f165,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f163])).
% 0.19/0.27 thf(f166,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f165,f36])).
% 0.19/0.27 thf(f167,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ sK1) @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f166,f33])).
% 0.19/0.27 thf(f176,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f44,f167])).
% 0.19/0.27 thf(f178,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)))) ) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f176])).
% 0.19/0.27 thf(f184,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f178,f36])).
% 0.19/0.27 thf(f188,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1)))) | ($true != $true) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f184,f105])).
% 0.19/0.27 thf(f193,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ (sK0 @ sK1)))) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f188])).
% 0.19/0.27 thf(f194,plain,(
% 0.19/0.27 spl5_9 | ~spl5_8),
% 0.19/0.27 inference(avatar_split_clause,[],[f193,f156,f159])).
% 0.19/0.27 thf(f195,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true)) ) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f46,f167])).
% 0.19/0.27 thf(f198,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f195])).
% 0.19/0.27 thf(f199,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f198,f36])).
% 0.19/0.27 thf(f200,plain,(
% 0.19/0.27 ((('const/sets/inf' @ sK1)) = ((sK0 @ sK1))) | ($true != $true) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $false) | ~spl5_9),
% 0.19/0.27 inference(constrained_superposition,[],[f98,f160])).
% 0.19/0.27 thf(f203,plain,(
% 0.19/0.27 ((('const/sets/inf' @ sK1)) = ((sK0 @ sK1))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $false) | ~spl5_9),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f200])).
% 0.19/0.27 thf(f208,definition,(
% 0.19/0.27 spl5_11 <=> ((('const/sets/inf' @ sK1)) = ((sK0 @ sK1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition])).
% 0.19/0.27 thf(f209,plain,(
% 0.19/0.27 ((('const/sets/inf' @ sK1)) = ((sK0 @ sK1))) | ~spl5_11),
% 0.19/0.27 inference(avatar_component_clause,[],[f208])).
% 0.19/0.27 thf(f212,definition,(
% 0.19/0.27 spl5_12 <=> ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $false)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition])).
% 0.19/0.27 thf(f213,plain,(
% 0.19/0.27 ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $false) | ~spl5_12),
% 0.19/0.27 inference(avatar_component_clause,[],[f212])).
% 0.19/0.27 thf(f214,plain,(
% 0.19/0.27 spl5_11 | spl5_12 | ~spl5_9),
% 0.19/0.27 inference(avatar_split_clause,[],[f203,f159,f212,f208])).
% 0.19/0.27 thf(f215,plain,(
% 0.19/0.27 ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK1) @ sK1))) | ~spl5_11),
% 0.19/0.27 inference(backward_demodulation,[],[f105,f209])).
% 0.19/0.27 thf(f221,plain,(
% 0.19/0.27 ($true = $false) | (spl5_2 | ~spl5_11)),
% 0.19/0.27 inference(forward_demodulation,[],[f215,f92])).
% 0.19/0.27 thf(f222,plain,(
% 0.19/0.27 $false | (spl5_2 | ~spl5_11)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f221])).
% 0.19/0.27 thf(f223,plain,(
% 0.19/0.27 spl5_2 | ~spl5_11),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f222])).
% 0.19/0.27 thf(f227,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ($true != $true) | ~spl5_3),
% 0.19/0.27 inference(constrained_superposition,[],[f32,f60])).
% 0.19/0.27 thf(f230,plain,(
% 0.19/0.27 ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ sK2))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ~spl5_3),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f227])).
% 0.19/0.27 thf(f233,plain,(
% 0.19/0.27 ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ sK2))) | ~spl5_3),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f230,f36])).
% 0.19/0.27 thf(f234,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ (sK0 @ sK1) @ sK2))) | ~spl5_3),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f233,f33])).
% 0.19/0.27 thf(f235,plain,(
% 0.19/0.27 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | (~spl5_3 | ~spl5_11)),
% 0.19/0.27 inference(forward_demodulation,[],[f234,f209])).
% 0.19/0.27 thf(f236,plain,(
% 0.19/0.27 $false | (spl5_1 | ~spl5_3 | ~spl5_11)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f235,f53])).
% 0.19/0.27 thf(f237,plain,(
% 0.19/0.27 spl5_1 | ~spl5_3 | ~spl5_11),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f236])).
% 0.19/0.27 thf(f245,plain,(
% 0.19/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ (sK0 @ X1) @ (sK4 @ X0 @ X1)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X2 @ X1) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f32,f43])).
% 0.19/0.27 thf(f255,plain,(
% 0.19/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X1) @ (sK4 @ X0 @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X2 @ X1) @ X1)))) )),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f245])).
% 0.19/0.27 thf(f256,plain,(
% 0.19/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ (sK0 @ X1) @ (sK4 @ X0 @ X1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f255])).
% 0.19/0.27 thf(f274,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)) = $true) | ($true != $true)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f256,f33])).
% 0.19/0.27 thf(f276,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f274])).
% 0.19/0.27 thf(f424,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true) | ((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f32,f199])).
% 0.19/0.27 thf(f429,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f424])).
% 0.19/0.27 thf(f430,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f429,f33])).
% 0.19/0.27 thf(f431,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f430,f36])).
% 0.19/0.27 thf(f463,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1)))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl5_8),
% 0.19/0.27 inference(constrained_superposition,[],[f45,f431])).
% 0.19/0.27 thf(f472,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true) | ($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f463])).
% 0.19/0.27 thf(f473,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1)))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl5_8),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f472])).
% 0.19/0.27 thf(f474,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1))))) ) | ~spl5_8),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f473,f36])).
% 0.19/0.27 thf(f475,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1))))) ) | (~spl5_8 | ~spl5_12)),
% 0.19/0.27 inference(forward_demodulation,[],[f474,f213])).
% 0.19/0.27 thf(f476,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK1))))) ) | (~spl5_8 | ~spl5_12)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f475])).
% 0.19/0.27 thf(f487,plain,(
% 0.19/0.27 ($true != $true) | (~spl5_8 | ~spl5_12)),
% 0.19/0.27 inference(constrained_superposition,[],[f476,f167])).
% 0.19/0.27 thf(f493,plain,(
% 0.19/0.27 $false | (~spl5_8 | ~spl5_12)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f487])).
% 0.19/0.27 thf(f494,plain,(
% 0.19/0.27 ~spl5_8 | ~spl5_12),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f493])).
% 0.19/0.27 thf(f497,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ sK1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true)) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f276,f36])).
% 0.19/0.27 thf(f507,definition,(
% 0.19/0.27 spl5_15 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition])).
% 0.19/0.27 thf(f508,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ (sK4 @ X0 @ sK1))) = $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) ) | ~spl5_15),
% 0.19/0.27 inference(avatar_component_clause,[],[f507])).
% 0.19/0.27 thf(f509,plain,(
% 0.19/0.27 spl5_15 | spl5_8),
% 0.19/0.27 inference(avatar_split_clause,[],[f497,f156,f507])).
% 0.19/0.27 thf(f589,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl5_15),
% 0.19/0.27 inference(constrained_superposition,[],[f42,f508])).
% 0.19/0.27 thf(f595,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true)) ) | ~spl5_15),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f589])).
% 0.19/0.27 thf(f596,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | ~spl5_15),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f595])).
% 0.19/0.27 thf(f602,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ((('const/realax/real_le' @ (sK0 @ sK1) @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl5_15),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f596,f36])).
% 0.19/0.27 thf(f605,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1))) | ($true = $false)) ) | (~spl5_12 | ~spl5_15)),
% 0.19/0.27 inference(forward_demodulation,[],[f602,f213])).
% 0.19/0.27 thf(f606,plain,(
% 0.19/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X0 @ sK1) @ sK1)))) ) | (~spl5_12 | ~spl5_15)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f605])).
% 0.19/0.27 thf(f607,plain,(
% 0.19/0.27 spl5_8 | ~spl5_12 | ~spl5_15),
% 0.19/0.27 inference(avatar_split_clause,[],[f606,f507,f212,f156])).
% 0.19/0.27 cnf(s1, plain, ~spl5_1 | ~spl5_2, inference(sat_conversion,[],[f57])).
% 0.19/0.27 cnf(s2, plain, ~spl5_2 | spl5_3, inference(sat_conversion,[],[f61])).
% 0.19/0.27 cnf(s5, plain, spl5_8 | spl5_9, inference(sat_conversion,[],[f161])).
% 0.19/0.27 cnf(s6, plain, ~spl5_8 | spl5_9, inference(sat_conversion,[],[f194])).
% 0.19/0.27 cnf(s8, plain, ~spl5_9 | spl5_11 | spl5_12, inference(sat_conversion,[],[f214])).
% 0.19/0.27 cnf(s9, plain, spl5_2 | ~spl5_11, inference(sat_conversion,[],[f223])).
% 0.19/0.27 cnf(s11, plain, spl5_1 | ~spl5_3 | ~spl5_11, inference(sat_conversion,[],[f237])).
% 0.19/0.27 cnf(s13, plain, ~spl5_8 | ~spl5_12, inference(sat_conversion,[],[f494])).
% 0.19/0.27 cnf(s15, plain, spl5_8 | spl5_15, inference(sat_conversion,[],[f509])).
% 0.19/0.27 cnf(s21, plain, spl5_8 | ~spl5_12 | ~spl5_15, inference(sat_conversion,[],[f607])).
% 0.19/0.27 cnf(s22, plain, spl5_8 | spl5_11, inference(rat,[],[s8,s21,s5,s15])).
% 0.19/0.27 cnf(s23, plain, spl5_11, inference(rat,[],[s8,s6,s13,s22])).
% 0.19/0.27 cnf(s24, plain, spl5_2, inference(rat,[],[s9,s23])).
% 0.19/0.27 cnf(s25, plain, spl5_3, inference(rat,[],[s2,s24])).
% 0.19/0.27 cnf(s26, plain, ~spl5_1, inference(rat,[],[s1,s24])).
% 0.19/0.27 cnf(s28, plain, $false, inference(rat,[],[s11,s23,s26,s25])).
% 0.19/0.27 thf(f608,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s28])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (957211)------------------------------
% 0.19/0.27 % (957211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (957211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (957211)CaDiCaL version: 2.1.3
% 0.19/0.27 % (957211)Termination reason: Refutation
% 0.19/0.27 % (957211)Time elapsed: 0.020 s
% 0.19/0.27 % (957211)Peak memory usage: 14 MB
% 0.19/0.27 % (957211)Instructions burned: 64 (million)
% 0.19/0.27 % (957201)Success in time 0.047 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------