%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV508^1 : 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 08:38:46 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV508^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:57:11 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
% 0.21/0.31 % (260888)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (260897)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3438985707:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (260893)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=120865003:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (260895)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1017291700:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (260894)lrs+10_16_si=on:nwc=1.5:random_seed=20276549:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (260896)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=2925713183: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)
% 0.21/0.31 % (260898)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=895826271:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (260897)Instruction limit reached!
% 0.21/0.31 % (260897)------------------------------
% 0.21/0.31 % (260897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260897)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260897)Termination reason: Instruction limit
% 0.21/0.31 % (260897)Termination phase: Saturation
% 0.21/0.31 % (260897)Time elapsed: 0.008 s
% 0.21/0.31 % (260897)Peak memory usage: 12 MB
% 0.21/0.31 % (260897)Instructions burned: 27 (million)
% 0.21/0.31 % (260895)Instruction limit reached!
% 0.21/0.31 % (260895)------------------------------
% 0.21/0.31 % (260895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260895)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260895)Termination reason: Instruction limit
% 0.21/0.31 % (260895)Termination phase: Saturation
% 0.21/0.31 % (260895)Time elapsed: 0.003 s
% 0.21/0.31 % (260895)Peak memory usage: 12 MB
% 0.21/0.31 % (260895)Instructions burned: 4 (million)
% 0.21/0.31 % (260899)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (260899)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
% 0.21/0.31 % (260894)Instruction limit reached!
% 0.21/0.31 % (260894)------------------------------
% 0.21/0.31 % (260894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260894)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260894)Termination reason: Instruction limit
% 0.21/0.31 % (260894)Termination phase: Saturation
% 0.21/0.31 % (260894)Time elapsed: 0.011 s
% 0.21/0.31 % (260894)Peak memory usage: 12 MB
% 0.21/0.31 % (260894)Instructions burned: 18 (million)
% 0.21/0.31 % (260906)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3723718032:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (260899)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=3071667224:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (260906)Instruction limit reached!
% 0.21/0.31 % (260906)------------------------------
% 0.21/0.31 % (260906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260906)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260906)Termination reason: Instruction limit
% 0.21/0.31 % (260906)Termination phase: Saturation
% 0.21/0.31 % (260906)Time elapsed: 0.001 s
% 0.21/0.31 % (260906)Peak memory usage: 12 MB
% 0.21/0.31 % (260906)Instructions burned: 2 (million)
% 0.21/0.31 % (260907)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=807102471:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (260893) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-260888-260893"...
% 0.21/0.31 % (260911)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2465721694:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.31 % (260907)Instruction limit reached!
% 0.21/0.31 % (260907)------------------------------
% 0.21/0.31 % (260907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260907)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260907)Termination reason: Instruction limit
% 0.21/0.31 % (260907)Termination phase: Saturation
% 0.21/0.31 % (260907)Time elapsed: 0.004 s
% 0.21/0.31 % (260907)Peak memory usage: 12 MB
% 0.21/0.31 % (260907)Instructions burned: 6 (million)
% 0.21/0.31 % (260908)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (260893)...printing done.
% 0.21/0.31 % (260893)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(type_def_7, type, sK0: $tType).
% 0.21/0.31 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.21/0.31 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.31 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.31 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.31 thf(func_def_4, type, 'const/realax/real_lt': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.31 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.31 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.21/0.31 thf(func_def_10, type, sK1: (sK0 > 'type/realax/real')).
% 0.21/0.31 thf(func_def_11, type, sK2: (sK0 > $o)).
% 0.21/0.31 thf(func_def_12, type, sK3: (sK0 > 'type/realax/real')).
% 0.21/0.31 thf(func_def_13, type, sK4: !>[X0: $tType]:(((X0 > 'type/realax/real') > (X0 > 'type/realax/real') > (X0 > $o) > X0))).
% 0.21/0.31 thf(func_def_14, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.21/0.31 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_16, type, sK6: sK0).
% 0.21/0.31 thf(f2,axiom,(
% 0.21/0.31 ! [X0 : $tType,X3 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X1 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & ? [X4 : X0] : (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) & ('const/sets/IN' @ X0 @ X4 @ X3))) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_LT_')).
% 0.21/0.31 thf(f3,axiom,(
% 0.21/0.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_LT_IMP_LE_')).
% 0.21/0.31 thf(f4,axiom,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o)] : ((X1 != 'const/sets/EMPTY' @ X0) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.21/0.31 thf(f5,conjecture,(
% 0.21/0.31 ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & (X3 != 'const/sets/EMPTY' @ X0)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_LT_ALL_')).
% 0.21/0.31 thf(f6,negated_conjecture,(
% 0.21/0.31 ~ ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & (X3 != 'const/sets/EMPTY' @ X0)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.31 thf(f7,plain,(
% 0.21/0.31 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) => ('const/realax/real_lt' @ (X3 @ X4) @ (X1 @ X4))) & ('const/sets/FINITE' @ X0 @ X2) & ('const/sets/EMPTY' @ X0 != X2)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X2 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))),
% 0.21/0.31 inference(rectify,[],[f6])).
% 0.21/0.31 thf(f8,plain,(
% 0.21/0.31 ~ ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ X2))) => ($true = (('const/realax/real_lt' @ (X3 @ X4) @ (X1 @ X4))))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true) & ('const/sets/EMPTY' @ X0 != X2)) => ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X2 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))))),
% 0.21/0.31 inference(fool_elimination,[],[f7])).
% 0.21/0.31 thf(f9,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o)] : ((X1 != 'const/sets/EMPTY' @ X0) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 0.21/0.31 inference(rectify,[],[f4])).
% 0.21/0.31 thf(f10,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) <=> ? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true))),
% 0.21/0.31 inference(fool_elimination,[],[f9])).
% 0.21/0.31 thf(f11,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X3 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X1) & ? [X5 : X0] : (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5)) & ('const/sets/IN' @ X0 @ X5 @ X1))) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2)))),
% 0.21/0.31 inference(rectify,[],[f2])).
% 0.21/0.31 thf(f12,plain,(
% 0.21/0.31 ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : ((($true = (('const/sets/FINITE' @ X0 @ X1))) & ! [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ X1))) => ((('const/realax/real_le' @ (X3 @ X4) @ (X2 @ X4))) = $true)) & ? [X5 : X0] : (($true = (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5)))) & ($true = (('const/sets/IN' @ X0 @ X5 @ X1))))) => ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true))),
% 0.21/0.31 inference(fool_elimination,[],[f11])).
% 0.21/0.31 thf(f13,plain,(
% 0.21/0.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 0.21/0.31 inference(rectify,[],[f3])).
% 0.21/0.31 thf(f14,plain,(
% 0.21/0.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X1)) = $true) => ((('const/realax/real_le' @ X0 @ X1)) = $true))),
% 0.21/0.31 inference(fool_elimination,[],[f13])).
% 0.21/0.31 thf(f15,plain,(
% 0.21/0.31 ? [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > 'type/realax/real')] : (($true != (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X2 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))) & (! [X4 : X0] : (($true = (('const/realax/real_lt' @ (X3 @ X4) @ (X1 @ X4)))) | ($true != (('const/sets/IN' @ X0 @ X4 @ X2)))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true) & ('const/sets/EMPTY' @ X0 != X2)))),
% 0.21/0.31 inference(ennf_transformation,[],[f8])).
% 0.21/0.31 thf(f16,plain,(
% 0.21/0.31 ? [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) & ('const/sets/EMPTY' @ X0 != X2) & ($true != (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X2 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))) & ! [X4 : X0] : (($true = (('const/realax/real_lt' @ (X3 @ X4) @ (X1 @ X4)))) | ($true != (('const/sets/IN' @ X0 @ X4 @ X2)))))),
% 0.21/0.31 inference(flattening,[],[f15])).
% 0.21/0.31 thf(f17,plain,(
% 0.21/0.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) = $true) | ((('const/realax/real_lt' @ X0 @ X1)) != $true))),
% 0.21/0.31 inference(ennf_transformation,[],[f14])).
% 0.21/0.31 thf(f18,plain,(
% 0.21/0.31 ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true) | (($true != (('const/sets/FINITE' @ X0 @ X1))) | ? [X4 : X0] : (((('const/realax/real_le' @ (X3 @ X4) @ (X2 @ X4))) != $true) & ($true = (('const/sets/IN' @ X0 @ X4 @ X1)))) | ! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X1))) | ($true != (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5)))))))),
% 0.21/0.31 inference(ennf_transformation,[],[f12])).
% 0.21/0.31 thf(f19,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real')] : (? [X4 : X0] : (((('const/realax/real_le' @ (X3 @ X4) @ (X2 @ X4))) != $true) & ($true = (('const/sets/IN' @ X0 @ X4 @ X1)))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true) | ($true != (('const/sets/FINITE' @ X0 @ X1))) | ! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X1))) | ($true != (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5))))))),
% 0.21/0.31 inference(flattening,[],[f18])).
% 0.21/0.31 thf(f20,plain,(
% 0.21/0.31 ($true = (('const/sets/FINITE' @ sK0 @ sK2))) & (sK2 != 'const/sets/EMPTY' @ sK0) & ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) != $true) & ! [X4 : sK0] : (($true = (('const/realax/real_lt' @ (sK3 @ X4) @ (sK1 @ X4)))) | ($true != (('const/sets/IN' @ sK0 @ X4 @ sK2))))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16])).
% 0.21/0.31 thf(f21,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real')] : ((((('const/realax/real_le' @ (X3 @ (sK4 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK4 @ X0 @ X3 @ X2 @ X1)))) != $true) & ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ X1)) = $true)) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true) | ($true != (('const/sets/FINITE' @ X0 @ X1))) | ! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X1))) | ($true != (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5))))))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X0 @ X3 @ X2 @ X1)],[f19])).
% 0.21/0.31 thf(f22,plain,(
% 0.21/0.31 ! [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)))),
% 0.21/0.31 inference(nnf_transformation,[],[f10])).
% 0.21/0.31 thf(f23,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (? [X3 : X0] : ($true = (('const/sets/IN' @ X0 @ X3 @ X1))) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.21/0.31 inference(rectify,[],[f22])).
% 0.21/0.31 thf(f24,plain,(
% 0.21/0.31 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X0 @ X3 @ X2 @ X1)],[f23])).
% 0.21/0.31 thf(f25,plain,(
% 0.21/0.31 ( ! [X4 : sK0] : (($true != (('const/sets/IN' @ sK0 @ X4 @ sK2))) | ($true = (('const/realax/real_lt' @ (sK3 @ X4) @ (sK1 @ X4))))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f20])).
% 0.21/0.31 thf(f26,plain,(
% 0.21/0.31 ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) != $true)),
% 0.21/0.31 inference(cnf_transformation,[],[f20])).
% 0.21/0.31 thf(f27,plain,(
% 0.21/0.31 (sK2 != 'const/sets/EMPTY' @ sK0)),
% 0.21/0.31 inference(cnf_transformation,[],[f20])).
% 0.21/0.31 thf(f28,plain,(
% 0.21/0.31 ($true = (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.21/0.31 inference(cnf_transformation,[],[f20])).
% 0.21/0.31 thf(f29,plain,(
% 0.21/0.31 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o),X5 : X0] : (($true != (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5)))) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ X1)) = $true) | ($true != (('const/sets/IN' @ X0 @ X5 @ X1))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true) | ($true != (('const/sets/FINITE' @ X0 @ X1)))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f21])).
% 0.21/0.31 thf(f30,plain,(
% 0.21/0.31 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o),X5 : X0] : (((('const/realax/real_le' @ (X3 @ (sK4 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK4 @ X0 @ X3 @ X2 @ X1)))) != $true) | ($true != (('const/realax/real_lt' @ (X3 @ X5) @ (X2 @ X5)))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true) | ($true != (('const/sets/IN' @ X0 @ X5 @ X1))) | ($true != (('const/sets/FINITE' @ X0 @ X1)))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f21])).
% 0.21/0.31 thf(f32,plain,(
% 0.21/0.31 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f24])).
% 0.21/0.31 thf(f34,plain,(
% 0.21/0.31 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $true)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f17])).
% 0.21/0.31 thf(f65,plain,(
% 0.21/0.31 ($true = (('const/realax/real_lt' @ (sK3 @ (sK5 @ sK0 @ sK2)) @ (sK1 @ (sK5 @ sK0 @ sK2))))) | ($true != $true) | (sK2 = 'const/sets/EMPTY' @ sK0)),
% 0.21/0.31 inference(constrained_superposition,[],[f25,f32])).
% 0.21/0.31 thf(f66,plain,(
% 0.21/0.31 (sK2 = 'const/sets/EMPTY' @ sK0) | ($true = (('const/realax/real_lt' @ (sK3 @ (sK5 @ sK0 @ sK2)) @ (sK1 @ (sK5 @ sK0 @ sK2)))))),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f65])).
% 0.21/0.31 thf(f67,plain,(
% 0.21/0.31 ($true = (('const/realax/real_lt' @ (sK3 @ (sK5 @ sK0 @ sK2)) @ (sK1 @ (sK5 @ sK0 @ sK2)))))),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f66,f27])).
% 0.21/0.31 thf(f86,plain,(
% 0.21/0.31 ( ! [X0 : (sK0 > $o)] : (($true != (('const/sets/FINITE' @ sK0 @ X0))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ X0 @ sK3) @ ('const/iterate/sum' @ sK0 @ X0 @ sK1)))) | ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ X0) @ X0))) | ($true != (('const/sets/IN' @ sK0 @ (sK5 @ sK0 @ sK2) @ X0))) | ($true != $true)) )),
% 0.21/0.31 inference(constrained_superposition,[],[f29,f67])).
% 0.21/0.31 thf(f87,plain,(
% 0.21/0.31 ( ! [X0 : (sK0 > $o)] : (($true != (('const/sets/IN' @ sK0 @ (sK5 @ sK0 @ sK2) @ X0))) | ($true != (('const/sets/FINITE' @ sK0 @ X0))) | ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ X0) @ X0))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ X0 @ sK3) @ ('const/iterate/sum' @ sK0 @ X0 @ sK1))))) )),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f86])).
% 0.21/0.31 thf(f108,plain,(
% 0.21/0.31 (sK2 = 'const/sets/EMPTY' @ sK0) | ($true != $true) | ($true != (('const/sets/FINITE' @ sK0 @ sK2))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) = $true) | ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2) @ sK2)))),
% 0.21/0.31 inference(constrained_superposition,[],[f87,f32])).
% 0.21/0.31 thf(f109,plain,(
% 0.21/0.31 ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) = $true) | (sK2 = 'const/sets/EMPTY' @ sK0) | ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2) @ sK2))) | ($true != (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f108])).
% 0.21/0.31 thf(f110,plain,(
% 0.21/0.31 ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2) @ sK2))) | ($true != (('const/sets/FINITE' @ sK0 @ sK2))) | (sK2 = 'const/sets/EMPTY' @ sK0)),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f109,f26])).
% 0.21/0.31 thf(f111,plain,(
% 0.21/0.31 (sK2 = 'const/sets/EMPTY' @ sK0) | ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2) @ sK2)))),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f110,f28])).
% 0.21/0.31 thf(f112,plain,(
% 0.21/0.31 ($true = (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2) @ sK2)))),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f111,f27])).
% 0.21/0.31 thf(f113,plain,(
% 0.21/0.31 ($true != $true) | ((('const/realax/real_lt' @ (sK3 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)) @ (sK1 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)))) = $true)),
% 0.21/0.31 inference(constrained_superposition,[],[f25,f112])).
% 0.21/0.31 thf(f114,plain,(
% 0.21/0.31 ((('const/realax/real_lt' @ (sK3 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)) @ (sK1 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)))) = $true)),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f113])).
% 0.21/0.31 thf(f116,plain,(
% 0.21/0.31 ($true != $true) | ($true = (('const/realax/real_le' @ (sK3 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)) @ (sK1 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)))))),
% 0.21/0.31 inference(constrained_superposition,[],[f34,f114])).
% 0.21/0.31 thf(f118,plain,(
% 0.21/0.31 ($true = (('const/realax/real_le' @ (sK3 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)) @ (sK1 @ (sK4 @ sK0 @ sK3 @ sK1 @ sK2)))))),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f116])).
% 0.21/0.31 thf(f182,plain,(
% 0.21/0.31 ( ! [X0 : sK0] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) = $true) | ($true != (('const/realax/real_lt' @ (sK3 @ X0) @ (sK1 @ X0)))) | ($true != $true) | ((('const/sets/IN' @ sK0 @ X0 @ sK2)) != $true) | ($true != (('const/sets/FINITE' @ sK0 @ sK2)))) )),
% 0.21/0.31 inference(constrained_superposition,[],[f30,f118])).
% 0.21/0.31 thf(f183,plain,(
% 0.21/0.31 ( ! [X0 : sK0] : (($true != (('const/realax/real_lt' @ (sK3 @ X0) @ (sK1 @ X0)))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1))) = $true) | ($true != (('const/sets/FINITE' @ sK0 @ sK2))) | ((('const/sets/IN' @ sK0 @ X0 @ sK2)) != $true)) )),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f182])).
% 0.21/0.31 thf(f187,plain,(
% 0.21/0.31 ( ! [X0 : sK0] : (($true != (('const/sets/FINITE' @ sK0 @ sK2))) | ($true != (('const/realax/real_lt' @ (sK3 @ X0) @ (sK1 @ X0)))) | ((('const/sets/IN' @ sK0 @ X0 @ sK2)) != $true)) )),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f183,f26])).
% 0.21/0.31 thf(f202,plain,(
% 0.21/0.31 ( ! [X0 : sK0] : (((('const/sets/IN' @ sK0 @ X0 @ sK2)) != $true) | ($true != (('const/realax/real_lt' @ (sK3 @ X0) @ (sK1 @ X0))))) )),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f187,f28])).
% 0.21/0.31 thf(f215,plain,(
% 0.21/0.31 ( ! [X0 : sK0] : (((('const/sets/IN' @ sK0 @ X0 @ sK2)) != $true)) )),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f202,f25])).
% 0.21/0.31 thf(f226,plain,(
% 0.21/0.31 ($true != $true)),
% 0.21/0.31 inference(constrained_superposition,[],[f215,f112])).
% 0.21/0.31 thf(f227,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f226])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (260893)------------------------------
% 0.21/0.31 % (260893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (260893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (260893)CaDiCaL version: 2.1.3
% 0.21/0.31 % (260893)Termination reason: Refutation
% 0.21/0.31 % (260893)Time elapsed: 0.026 s
% 0.21/0.31 % (260893)Peak memory usage: 12 MB
% 0.21/0.31 % (260893)Instructions burned: 48 (million)
% 0.21/0.31 % (260888)Success in time 0.073 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------