%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU773^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:31:17 AM UTC 2026
% Result : Theorem 0.09s 0.17s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU773^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:23:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 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
% 0.09/0.17 % (177509)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.17 % (177520)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.17 % (177520)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
% 0.09/0.17 % (177519)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4050088972:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.17 % (177517)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=1717967263: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)
% 0.09/0.17 % (177516)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2042424517:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.17 % (177514)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1760893392:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.17 % (177515)lrs+10_16_si=on:nwc=1.5:random_seed=2860676849:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.17 % (177518)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1946999234:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.17 % (177520)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=3874558363:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.17 % (177516)Instruction limit reached!
% 0.09/0.17 % (177516)------------------------------
% 0.09/0.17 % (177516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (177516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (177516)CaDiCaL version: 2.1.3
% 0.09/0.17 % (177516)Termination reason: Instruction limit
% 0.09/0.17 % (177516)Termination phase: Saturation
% 0.09/0.17 % (177516)Time elapsed: 0.001 s
% 0.09/0.17 % (177516)Peak memory usage: 11 MB
% 0.09/0.17 % (177516)Instructions burned: 3 (million)
% 0.09/0.17 % (177514) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-177509-177514"...
% 0.09/0.17 % (177515) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-177509-177515"...
% 0.09/0.17 % (177517) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-177509-177517"...
% 0.09/0.17 % (177514)...printing done.
% 0.09/0.17 % (177518) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-177509-177518"...
% 0.09/0.17 % (177515)...printing done.
% 0.09/0.17 % (177519) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-177509-177519"...
% 0.09/0.17 % (177514)Refutation found. Thanks to Tanya!
% 0.09/0.17 % SZS status Theorem for theBenchmark
% 0.09/0.17 % SZS output start Proof for theBenchmark
% 0.09/0.17 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.17 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.09/0.17 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.09/0.17 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.09/0.17 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.09/0.17 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.09/0.17 thf(func_def_6, type, subbreln: $o).
% 0.09/0.17 thf(func_def_7, type, breln1: ($i > $i > $o)).
% 0.09/0.17 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.17 thf(func_def_18, type, sK4: ($i > $i > $i > $i > $i)).
% 0.09/0.17 thf(func_def_19, type, sK5: ($i > $i > $i > $i > $i)).
% 0.09/0.17 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.09/0.17 thf(f1,axiom,(
% 0.09/0.17 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 0.09/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 0.09/0.17 thf(f2,axiom,(
% 0.09/0.17 (! [X1 : $i,X0 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 0.09/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln)).
% 0.09/0.17 thf(f3,axiom,(
% 0.09/0.17 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 0.09/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1)).
% 0.09/0.17 thf(f4,conjecture,(
% 0.09/0.17 subbreln => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2))))),
% 0.09/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln1)).
% 0.09/0.17 thf(f5,negated_conjecture,(
% 0.09/0.17 ~(subbreln => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2)))))),
% 0.09/0.17 inference(negated_conjecture,[status(cth)],[f4])).
% 0.09/0.17 thf(f6,plain,(
% 0.09/0.17 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : $i] : ((breln @ X1 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 0.09/0.17 inference(rectify,[],[f2])).
% 0.09/0.17 thf(f7,plain,(
% 0.09/0.17 ! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X0 @ X2)) = $true) => ! [X3 : $i] : ((((breln @ X1 @ X0 @ X3)) = $true) => (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X0)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X2)) = $true) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => (((subset @ X2 @ X3)) = $true)))) <=> (subbreln = $true)),
% 0.09/0.17 inference(fool_elimination,[],[f6])).
% 0.09/0.17 thf(f8,plain,(
% 0.09/0.17 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.09/0.17 inference(fool_elimination,[],[f1])).
% 0.09/0.17 thf(f9,plain,(
% 0.09/0.17 ~(subbreln => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X0 @ X2)))))),
% 0.09/0.17 inference(rectify,[],[f5])).
% 0.09/0.17 thf(f10,plain,(
% 0.09/0.17 ~((subbreln = $true) => ! [X0 : $i,X1 : $i] : ((((breln1 @ X1 @ X0)) = $true) => ! [X2 : $i] : ((((breln1 @ X1 @ X2)) = $true) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ((((in @ (kpair @ X3 @ X4) @ X0)) = $true) => (((in @ (kpair @ X3 @ X4) @ X2)) = $true)))) => (((subset @ X0 @ X2)) = $true)))))),
% 0.09/0.17 inference(fool_elimination,[],[f9])).
% 0.09/0.17 thf(f11,plain,(
% 0.09/0.17 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.09/0.17 inference(fool_elimination,[],[f3])).
% 0.09/0.17 thf(f12,plain,(
% 0.09/0.17 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((((subset @ X0 @ X2)) != $true) & ! [X3 : $i] : (! [X4 : $i] : (((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X0)) != $true)) | (((in @ X4 @ X1)) != $true)) | (((in @ X3 @ X1)) != $true))) & (((breln1 @ X1 @ X2)) = $true)) & (((breln1 @ X1 @ X0)) = $true)) & (subbreln = $true)),
% 0.09/0.17 inference(ennf_transformation,[],[f10])).
% 0.09/0.17 thf(f13,plain,(
% 0.09/0.17 (subbreln = $true) & ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((breln1 @ X1 @ X2)) = $true) & ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X0)) != $true) | (((in @ X4 @ X1)) != $true))) & (((subset @ X0 @ X2)) != $true)) & (((breln1 @ X1 @ X0)) = $true))),
% 0.09/0.17 inference(flattening,[],[f12])).
% 0.09/0.17 thf(f14,plain,(
% 0.09/0.17 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((((subset @ X2 @ X3)) = $true) | ? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & (((in @ X5 @ X0)) = $true)) & (((in @ X4 @ X1)) = $true))) | (((breln @ X1 @ X0 @ X3)) != $true)) | (((breln @ X1 @ X0 @ X2)) != $true)) <=> (subbreln = $true)),
% 0.09/0.17 inference(ennf_transformation,[],[f7])).
% 0.09/0.17 thf(f15,plain,(
% 0.09/0.17 (subbreln = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) != $true) | ! [X3 : $i] : ((((breln @ X1 @ X0 @ X3)) != $true) | (((subset @ X2 @ X3)) = $true) | ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true) & (((in @ X5 @ X0)) = $true)))))),
% 0.09/0.17 inference(flattening,[],[f14])).
% 0.09/0.17 thf(f16,plain,(
% 0.09/0.17 ((subbreln = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) = $true) & ? [X3 : $i] : ((((breln @ X1 @ X0 @ X3)) = $true) & (((subset @ X2 @ X3)) != $true) & ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | (((in @ X5 @ X0)) != $true)))))) & (! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) != $true) | ! [X3 : $i] : ((((breln @ X1 @ X0 @ X3)) != $true) | (((subset @ X2 @ X3)) = $true) | ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true) & (((in @ X5 @ X0)) = $true))))) | (subbreln != $true))),
% 0.09/0.17 inference(nnf_transformation,[],[f15])).
% 0.09/0.17 thf(f17,plain,(
% 0.09/0.17 ((subbreln = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X2 @ X1)) = $true) & ? [X3 : $i] : ((((breln @ X0 @ X2 @ X3)) = $true) & ($true != ((subset @ X1 @ X3))) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X1)) != $true) | (((in @ X5 @ X2)) != $true)))))) & (! [X6 : $i,X7 : $i,X8 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | ! [X9 : $i] : ((((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | ? [X10 : $i] : ((((in @ X10 @ X6)) = $true) & ? [X11 : $i] : ((((in @ (kpair @ X10 @ X11) @ X9)) != $true) & (((in @ (kpair @ X10 @ X11) @ X7)) = $true) & (((in @ X11 @ X8)) = $true))))) | (subbreln != $true))),
% 0.09/0.17 inference(rectify,[],[f16])).
% 0.09/0.17 thf(f18,plain,(
% 0.09/0.17 ((subbreln = $true) | ((((breln @ sK0 @ sK2 @ sK1)) = $true) & ((((breln @ sK0 @ sK2 @ sK3)) = $true) & (((subset @ sK1 @ sK3)) != $true) & ! [X4 : $i] : ((((in @ X4 @ sK0)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK3)) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK1))) | (((in @ X5 @ sK2)) != $true)))))) & (! [X6 : $i,X7 : $i,X8 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | ! [X9 : $i] : ((((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | ((((in @ (sK4 @ X9 @ X8 @ X7 @ X6) @ X6)) = $true) & ((((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X9)) != $true) & (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X7)) = $true) & (((in @ (sK5 @ X9 @ X8 @ X7 @ X6) @ X8)) = $true))))) | (subbreln != $true))),
% 0.09/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X11,sK5 @ X9 @ X8 @ X7 @ X6),skolemize(X11,sK5 @ X9 @ X8 @ X7 @ X6)],[f17])).
% 0.09/0.17 thf(f19,plain,(
% 0.09/0.17 (subbreln = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((breln1 @ X0 @ X2)) = $true) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true) | (((in @ X4 @ X0)) != $true))) & (((subset @ X1 @ X2)) != $true)) & (((breln1 @ X0 @ X1)) = $true))),
% 0.09/0.17 inference(rectify,[],[f13])).
% 0.09/0.17 thf(f20,plain,(
% 0.09/0.17 (subbreln = $true) & (((((breln1 @ sK6 @ sK8)) = $true) & ! [X3 : $i] : ((((in @ X3 @ sK6)) != $true) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ sK8)) = $true) | (((in @ (kpair @ X3 @ X4) @ sK7)) != $true) | (((in @ X4 @ sK6)) != $true))) & (((subset @ sK7 @ sK8)) != $true)) & (((breln1 @ sK6 @ sK7)) = $true))),
% 0.09/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f19])).
% 0.09/0.17 thf(f21,plain,(
% 0.09/0.17 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.09/0.17 inference(cnf_transformation,[],[f11])).
% 0.09/0.17 thf(f22,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | (((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (sK5 @ X9 @ X8 @ X7 @ X6) @ X8)) = $true) | (subbreln != $true)) )),
% 0.09/0.17 inference(cnf_transformation,[],[f18])).
% 0.09/0.17 thf(f23,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | (((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X7)) = $true) | (subbreln != $true)) )),
% 0.09/0.17 inference(cnf_transformation,[],[f18])).
% 0.09/0.17 thf(f24,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | (((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X9)) != $true) | (subbreln != $true)) )),
% 0.09/0.17 inference(cnf_transformation,[],[f18])).
% 0.09/0.17 thf(f25,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | (((breln @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (sK4 @ X9 @ X8 @ X7 @ X6) @ X6)) = $true) | (subbreln != $true)) )),
% 0.09/0.17 inference(cnf_transformation,[],[f18])).
% 0.09/0.17 thf(f30,plain,(
% 0.09/0.17 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.09/0.17 inference(cnf_transformation,[],[f8])).
% 0.09/0.17 thf(f31,plain,(
% 0.09/0.17 (((breln1 @ sK6 @ sK7)) = $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f20])).
% 0.09/0.17 thf(f32,plain,(
% 0.09/0.17 (((subset @ sK7 @ sK8)) != $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f20])).
% 0.09/0.17 thf(f33,plain,(
% 0.09/0.17 ( ! [X3 : $i,X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ sK7)) != $true) | (((in @ (kpair @ X3 @ X4) @ sK8)) = $true) | (((in @ X4 @ sK6)) != $true) | (((in @ X3 @ sK6)) != $true)) )),
% 0.09/0.17 inference(cnf_transformation,[],[f20])).
% 0.09/0.17 thf(f34,plain,(
% 0.09/0.17 (((breln1 @ sK6 @ sK8)) = $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f20])).
% 0.09/0.17 thf(f35,plain,(
% 0.09/0.17 (subbreln = $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f20])).
% 0.09/0.17 thf(f38,plain,(
% 0.09/0.17 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 0.09/0.17 inference(definition_unfolding,[],[f21,f30])).
% 0.09/0.17 thf(f43,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | ($true != $true) | (((in @ (sK4 @ X9 @ X8 @ X7 @ X6) @ X6)) = $true)) )),
% 0.09/0.17 inference(definition_unfolding,[],[f25,f30,f30,f35])).
% 0.09/0.17 thf(f44,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X9)) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | ($true != $true)) )),
% 0.09/0.17 inference(definition_unfolding,[],[f24,f30,f30,f35])).
% 0.09/0.17 thf(f45,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X7)) = $true) | (((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | ($true != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true)) )),
% 0.09/0.17 inference(definition_unfolding,[],[f23,f30,f30,f35])).
% 0.09/0.17 thf(f46,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | ($true != $true) | (((in @ (sK5 @ X9 @ X8 @ X7 @ X6) @ X8)) = $true)) )),
% 0.09/0.17 inference(definition_unfolding,[],[f22,f30,f30,f35])).
% 0.09/0.17 thf(f47,plain,(
% 0.09/0.17 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK6 @ sK8)) = $true)),
% 0.09/0.17 inference(definition_unfolding,[],[f34,f38])).
% 0.09/0.17 thf(f48,plain,(
% 0.09/0.17 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK6 @ sK7)) = $true)),
% 0.09/0.17 inference(definition_unfolding,[],[f31,f38])).
% 0.09/0.17 thf(f49,plain,(
% 0.09/0.17 (((subset @ sK7 @ (cartprod @ sK6 @ sK6))) = $true)),
% 0.09/0.17 inference(beta-eta_normalization,[],[f48])).
% 0.09/0.17 thf(f50,plain,(
% 0.09/0.17 (((subset @ sK8 @ (cartprod @ sK6 @ sK6))) = $true)),
% 0.09/0.17 inference(beta-eta_normalization,[],[f47])).
% 0.09/0.17 thf(f51,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X7)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f45])).
% 0.09/0.17 thf(f52,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X9 @ (cartprod @ X6 @ X8))) != $true) | (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X7)) = $true) | (((subset @ X7 @ X9)) = $true) | (((subset @ X7 @ (cartprod @ X6 @ X8))) != $true)) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f51])).
% 0.09/0.17 thf(f53,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | (((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X9)) != $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f44])).
% 0.09/0.17 thf(f54,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((in @ (kpair @ (sK4 @ X9 @ X8 @ X7 @ X6) @ (sK5 @ X9 @ X8 @ X7 @ X6)) @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | (((subset @ X7 @ (cartprod @ X6 @ X8))) != $true) | (((subset @ X9 @ (cartprod @ X6 @ X8))) != $true)) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f53])).
% 0.09/0.17 thf(f55,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (sK5 @ X9 @ X8 @ X7 @ X6) @ X8)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f46])).
% 0.09/0.17 thf(f56,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X9 @ (cartprod @ X6 @ X8))) != $true) | (((subset @ X7 @ (cartprod @ X6 @ X8))) != $true) | (((in @ (sK5 @ X9 @ X8 @ X7 @ X6) @ X8)) = $true) | (((subset @ X7 @ X9)) = $true)) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f55])).
% 0.09/0.17 thf(f57,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X9)) != $true) | (((subset @ X7 @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X8 @ X7)) != $true) | (((in @ (sK4 @ X9 @ X8 @ X7 @ X6) @ X6)) = $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f43])).
% 0.09/0.17 thf(f58,plain,(
% 0.09/0.17 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((((subset @ X9 @ (cartprod @ X6 @ X8))) != $true) | (((subset @ X7 @ X9)) = $true) | (((in @ (sK4 @ X9 @ X8 @ X7 @ X6) @ X6)) = $true) | (((subset @ X7 @ (cartprod @ X6 @ X8))) != $true)) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f57])).
% 0.09/0.17 thf(f60,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true = ((in @ (sK5 @ sK8 @ sK6 @ X0 @ sK6) @ sK6))) | ($true != $true) | (((subset @ X0 @ sK8)) = $true) | ($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6))))) )),
% 0.09/0.17 inference(constrained_superposition,[],[f56,f50])).
% 0.09/0.17 thf(f62,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6)))) | ($true = ((in @ (sK5 @ sK8 @ sK6 @ X0 @ sK6) @ sK6))) | (((subset @ X0 @ sK8)) = $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f60])).
% 0.09/0.17 thf(f85,plain,(
% 0.09/0.17 (((subset @ sK7 @ sK8)) = $true) | ($true != $true) | ($true = ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)))),
% 0.09/0.17 inference(constrained_superposition,[],[f62,f49])).
% 0.09/0.17 thf(f88,plain,(
% 0.09/0.17 ($true = ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6))) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f85])).
% 0.09/0.17 thf(f98,plain,(
% 0.09/0.17 ($true = ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)))),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f88,f32])).
% 0.09/0.17 thf(f100,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6)))) | ($true != $true) | ($true = ((in @ (sK4 @ sK8 @ sK6 @ X0 @ sK6) @ sK6))) | (((subset @ X0 @ sK8)) = $true)) )),
% 0.09/0.17 inference(constrained_superposition,[],[f58,f50])).
% 0.09/0.17 thf(f102,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6)))) | ($true = ((in @ (sK4 @ sK8 @ sK6 @ X0 @ sK6) @ sK6))) | (((subset @ X0 @ sK8)) = $true)) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f100])).
% 0.09/0.17 thf(f112,plain,(
% 0.09/0.17 ($true != $true) | (((in @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)) = $true) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(constrained_superposition,[],[f102,f49])).
% 0.09/0.17 thf(f114,plain,(
% 0.09/0.17 (((subset @ sK7 @ sK8)) = $true) | (((in @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)) = $true)),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f112])).
% 0.09/0.17 thf(f116,plain,(
% 0.09/0.17 (((in @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f114,f32])).
% 0.09/0.17 thf(f123,plain,(
% 0.09/0.17 ( ! [X0 : $i] : ((((subset @ X0 @ sK8)) = $true) | ($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6)))) | ($true = ((in @ (kpair @ (sK4 @ sK8 @ sK6 @ X0 @ sK6) @ (sK5 @ sK8 @ sK6 @ X0 @ sK6)) @ X0))) | ($true != $true)) )),
% 0.09/0.17 inference(constrained_superposition,[],[f52,f50])).
% 0.09/0.17 thf(f125,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK6 @ sK6)))) | (((subset @ X0 @ sK8)) = $true) | ($true = ((in @ (kpair @ (sK4 @ sK8 @ sK6 @ X0 @ sK6) @ (sK5 @ sK8 @ sK6 @ X0 @ sK6)) @ X0)))) )),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f123])).
% 0.09/0.17 thf(f130,plain,(
% 0.09/0.17 (((subset @ sK7 @ sK8)) = $true) | ($true != $true) | (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK7)) = $true)),
% 0.09/0.17 inference(constrained_superposition,[],[f125,f49])).
% 0.09/0.17 thf(f133,plain,(
% 0.09/0.17 (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK7)) = $true) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f130])).
% 0.09/0.17 thf(f134,plain,(
% 0.09/0.17 (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK7)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f133,f32])).
% 0.09/0.17 thf(f135,plain,(
% 0.09/0.17 (((in @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)) != $true) | ($true != $true) | (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK8)) = $true) | ($true != ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)))),
% 0.09/0.17 inference(constrained_superposition,[],[f33,f134])).
% 0.09/0.17 thf(f136,plain,(
% 0.09/0.17 (((in @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)) != $true) | (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK8)) = $true) | ($true != ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6)))),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f135])).
% 0.09/0.17 thf(f137,plain,(
% 0.09/0.17 ($true != ((in @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6) @ sK6))) | (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK8)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f136,f116])).
% 0.09/0.17 thf(f138,plain,(
% 0.09/0.17 (((in @ (kpair @ (sK4 @ sK8 @ sK6 @ sK7 @ sK6) @ (sK5 @ sK8 @ sK6 @ sK7 @ sK6)) @ sK8)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f137,f98])).
% 0.09/0.17 thf(f139,plain,(
% 0.09/0.17 (((subset @ sK7 @ (cartprod @ sK6 @ sK6))) != $true) | ($true != $true) | (((subset @ sK8 @ (cartprod @ sK6 @ sK6))) != $true) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(constrained_superposition,[],[f54,f138])).
% 0.09/0.17 thf(f140,plain,(
% 0.09/0.17 (((subset @ sK7 @ (cartprod @ sK6 @ sK6))) != $true) | (((subset @ sK8 @ (cartprod @ sK6 @ sK6))) != $true) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f139])).
% 0.09/0.17 thf(f141,plain,(
% 0.09/0.17 (((subset @ sK8 @ (cartprod @ sK6 @ sK6))) != $true) | (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f140,f49])).
% 0.09/0.17 thf(f142,plain,(
% 0.09/0.17 (((subset @ sK7 @ sK8)) = $true)),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f141,f50])).
% 0.09/0.17 thf(f143,plain,(
% 0.09/0.17 $false),
% 0.09/0.17 inference(forward_subsumption_resolution,[],[f142,f32])).
% 0.09/0.17 % SZS output end Proof for theBenchmark
% 0.09/0.17 % (177514)------------------------------
% 0.09/0.17 % (177514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (177514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (177514)CaDiCaL version: 2.1.3
% 0.09/0.17 % (177514)Termination reason: Refutation
% 0.09/0.17 % (177514)Time elapsed: 0.005 s
% 0.09/0.17 % (177514)Peak memory usage: 12 MB
% 0.09/0.17 % (177514)Instructions burned: 18 (million)
% 0.09/0.17 % (177509)Success in time 0.032 s
% 0.09/0.17 % Vampire exiting
%------------------------------------------------------------------------------