%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV138^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:37:53 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV138^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n008.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 15:16:54 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (3286040)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3286050)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1083400713:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3286047)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=508696453:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (3286046)lrs+10_16_si=on:nwc=1.5:random_seed=3401898044:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (3286045)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=852530509:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3286047)Instruction limit reached!
% 0.20/0.28 % (3286047)------------------------------
% 0.20/0.28 % (3286047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3286047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3286047)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3286047)Termination reason: Instruction limit
% 0.20/0.29 % (3286047)Termination phase: Saturation
% 0.20/0.29 % (3286047)Time elapsed: 0.003 s
% 0.20/0.29 % (3286047)Peak memory usage: 12 MB
% 0.20/0.29 % (3286047)Instructions burned: 3 (million)
% 0.20/0.29 % (3286049)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3970222213:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3286046)Instruction limit reached!
% 0.20/0.29 % (3286046)------------------------------
% 0.20/0.29 % (3286046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3286046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3286046)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3286046)Termination reason: Instruction limit
% 0.20/0.29 % (3286046)Termination phase: Saturation
% 0.20/0.29 % (3286046)Time elapsed: 0.011 s
% 0.20/0.29 % (3286046)Peak memory usage: 12 MB
% 0.20/0.29 % (3286046)Instructions burned: 18 (million)
% 0.20/0.29 % (3286048)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=4027118943:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.29 % (3286051)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3286051)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.29 % (3286045) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3286040-3286045"...
% 0.20/0.29 % (3286051)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=2951662480:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3286050)Instruction limit reached!
% 0.20/0.29 % (3286050)------------------------------
% 0.20/0.29 % (3286050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3286050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3286050)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3286050)Termination reason: Instruction limit
% 0.20/0.29 % (3286050)Termination phase: Saturation
% 0.20/0.29 % (3286050)Time elapsed: 0.023 s
% 0.20/0.29 % (3286050)Peak memory usage: 13 MB
% 0.20/0.29 % (3286050)Instructions burned: 77 (million)
% 0.20/0.29 % (3286045)...printing done.
% 0.20/0.29 % (3286045)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, a: $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_3, type, sK0: a).
% 0.20/0.29 thf(func_def_4, type, sK1: a).
% 0.20/0.29 thf(func_def_5, type, sK2: (a > a > $o)).
% 0.20/0.29 thf(func_def_6, type, sK3: a).
% 0.20/0.29 thf(func_def_7, type, sK4: (a > $o)).
% 0.20/0.29 thf(func_def_8, type, sK5: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_9, type, sK6: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_10, type, sK7: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_11, type, sK8: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_12, type, sK9: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_13, type, sK10: ((a > $o) > a)).
% 0.20/0.29 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ! [X1 : a,X0 : (a > a > $o),X3 : a,X2 : a] : ((! [X4 : (a > $o)] : ((! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5))) => (X4 @ X3)) & ! [X4 : (a > $o)] : ((! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X2))) => ! [X4 : (a > $o)] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X3)))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM150_pme)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~ ! [X1 : a,X0 : (a > a > $o),X3 : a,X2 : a] : ((! [X4 : (a > $o)] : ((! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5))) => (X4 @ X3)) & ! [X4 : (a > $o)] : ((! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X2))) => ! [X4 : (a > $o)] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X3)))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~ ! [X0 : a,X1 : (a > a > $o),X2 : a,X3 : a] : ((! [X4 : (a > $o)] : ((! [X5 : a,X6 : a] : (((X4 @ X6) & (X1 @ X6 @ X5)) => (X4 @ X5)) & ! [X7 : a] : ((X1 @ X3 @ X7) => (X4 @ X7))) => (X4 @ X2)) & ! [X8 : (a > $o)] : ((! [X9 : a,X10 : a] : (((X1 @ X10 @ X9) & (X8 @ X10)) => (X8 @ X9)) & ! [X11 : a] : ((X1 @ X0 @ X11) => (X8 @ X11))) => (X8 @ X3))) => ! [X12 : (a > $o)] : ((! [X13 : a] : ((X1 @ X0 @ X13) => (X12 @ X13)) & ! [X14 : a,X15 : a] : (((X1 @ X15 @ X14) & (X12 @ X15)) => (X12 @ X14))) => (X12 @ X2)))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~ ! [X0 : a,X2 : a,X3 : a,X1 : (a > a > $o)] : ((! [X4 : (a > $o)] : ((! [X6 : a,X5 : a] : (((((X4 @ X6)) = $true) & (((X1 @ X6 @ X5)) = $true)) => (((X4 @ X5)) = $true)) & ! [X7 : a] : ((((X1 @ X3 @ X7)) = $true) => (((X4 @ X7)) = $true))) => (((X4 @ X2)) = $true)) & ! [X8 : (a > $o)] : ((! [X11 : a] : ((((X1 @ X0 @ X11)) = $true) => (((X8 @ X11)) = $true)) & ! [X10 : a,X9 : a] : (((((X8 @ X10)) = $true) & (((X1 @ X10 @ X9)) = $true)) => (((X8 @ X9)) = $true))) => (((X8 @ X3)) = $true))) => ! [X12 : (a > $o)] : ((! [X13 : a] : ((((X1 @ X0 @ X13)) = $true) => (((X12 @ X13)) = $true)) & ! [X15 : a,X14 : a] : (((((X1 @ X15 @ X14)) = $true) & (((X12 @ X15)) = $true)) => (((X12 @ X14)) = $true))) => (((X12 @ X2)) = $true)))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ? [X0 : a,X2 : a,X3 : a,X1 : (a > a > $o)] : (? [X12 : (a > $o)] : ((((X12 @ X2)) != $true) & (! [X13 : a] : ((((X1 @ X0 @ X13)) != $true) | (((X12 @ X13)) = $true)) & ! [X15 : a,X14 : a] : ((((X12 @ X14)) = $true) | ((((X1 @ X15 @ X14)) != $true) | (((X12 @ X15)) != $true))))) & (! [X4 : (a > $o)] : ((((X4 @ X2)) = $true) | (? [X6 : a,X5 : a] : ((((X4 @ X5)) != $true) & ((((X4 @ X6)) = $true) & (((X1 @ X6 @ X5)) = $true))) | ? [X7 : a] : ((((X1 @ X3 @ X7)) = $true) & (((X4 @ X7)) != $true)))) & ! [X8 : (a > $o)] : ((((X8 @ X3)) = $true) | (? [X11 : a] : ((((X1 @ X0 @ X11)) = $true) & (((X8 @ X11)) != $true)) | ? [X10 : a,X9 : a] : ((((X8 @ X9)) != $true) & ((((X8 @ X10)) = $true) & (((X1 @ X10 @ X9)) = $true)))))))),
% 0.20/0.29 inference(ennf_transformation,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ? [X3 : a,X2 : a,X1 : (a > a > $o),X0 : a] : (? [X12 : (a > $o)] : ((((X12 @ X2)) != $true) & ! [X13 : a] : ((((X1 @ X0 @ X13)) != $true) | (((X12 @ X13)) = $true)) & ! [X15 : a,X14 : a] : ((((X12 @ X14)) = $true) | (((X1 @ X15 @ X14)) != $true) | (((X12 @ X15)) != $true))) & ! [X4 : (a > $o)] : ((((X4 @ X2)) = $true) | ? [X7 : a] : ((((X1 @ X3 @ X7)) = $true) & (((X4 @ X7)) != $true)) | ? [X6 : a,X5 : a] : ((((X4 @ X6)) = $true) & (((X1 @ X6 @ X5)) = $true) & (((X4 @ X5)) != $true))) & ! [X8 : (a > $o)] : ((((X8 @ X3)) = $true) | ? [X9 : a,X10 : a] : ((((X8 @ X9)) != $true) & (((X8 @ X10)) = $true) & (((X1 @ X10 @ X9)) = $true)) | ? [X11 : a] : ((((X1 @ X0 @ X11)) = $true) & (((X8 @ X11)) != $true))))),
% 0.20/0.29 inference(flattening,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ? [X0 : a,X1 : a,X2 : (a > a > $o),X3 : a] : (? [X4 : (a > $o)] : ((((X4 @ X1)) != $true) & ! [X5 : a] : ((((X2 @ X3 @ X5)) != $true) | (((X4 @ X5)) = $true)) & ! [X6 : a,X7 : a] : ((((X4 @ X7)) = $true) | (((X2 @ X6 @ X7)) != $true) | (((X4 @ X6)) != $true))) & ! [X8 : (a > $o)] : (($true = ((X8 @ X1))) | ? [X9 : a] : ((((X2 @ X0 @ X9)) = $true) & (((X8 @ X9)) != $true)) | ? [X10 : a,X11 : a] : ((((X8 @ X10)) = $true) & (((X2 @ X10 @ X11)) = $true) & (((X8 @ X11)) != $true))) & ! [X12 : (a > $o)] : ((((X12 @ X0)) = $true) | ? [X13 : a,X14 : a] : ((((X12 @ X13)) != $true) & (((X12 @ X14)) = $true) & (((X2 @ X14 @ X13)) = $true)) | ? [X15 : a] : ((((X2 @ X3 @ X15)) = $true) & (((X12 @ X15)) != $true))))),
% 0.20/0.29 inference(rectify,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ((((sK4 @ sK1)) != $true) & ! [X5 : a] : ((((sK2 @ sK3 @ X5)) != $true) | (((sK4 @ X5)) = $true)) & ! [X6 : a,X7 : a] : ((((sK4 @ X7)) = $true) | (((sK2 @ X6 @ X7)) != $true) | (((sK4 @ X6)) != $true))) & ! [X8 : (a > $o)] : ((((X8 @ sK1)) = $true) | ((((sK2 @ sK0 @ (sK5 @ X8))) = $true) & (((X8 @ (sK5 @ X8))) != $true)) | ((((X8 @ (sK6 @ X8))) = $true) & (((sK2 @ (sK6 @ X8) @ (sK7 @ X8))) = $true) & (((X8 @ (sK7 @ X8))) != $true))) & ! [X12 : (a > $o)] : ((((X12 @ sK0)) = $true) | ((((X12 @ (sK8 @ X12))) != $true) & (((X12 @ (sK9 @ X12))) = $true) & (((sK2 @ (sK9 @ X12) @ (sK8 @ X12))) = $true)) | ((((sK2 @ sK3 @ (sK10 @ X12))) = $true) & (((X12 @ (sK10 @ X12))) != $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12)],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((X12 @ (sK10 @ X12))) != $true) | (((sK2 @ (sK9 @ X12) @ (sK8 @ X12))) = $true) | (((X12 @ sK0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((sK2 @ (sK9 @ X12) @ (sK8 @ X12))) = $true) | (((sK2 @ sK3 @ (sK10 @ X12))) = $true) | (((X12 @ sK0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((X12 @ (sK10 @ X12))) != $true) | (((X12 @ sK0)) = $true) | (((X12 @ (sK9 @ X12))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((sK2 @ sK3 @ (sK10 @ X12))) = $true) | (((X12 @ (sK9 @ X12))) = $true) | (((X12 @ sK0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((X12 @ (sK10 @ X12))) != $true) | (((X12 @ (sK8 @ X12))) != $true) | (((X12 @ sK0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ( ! [X12 : (a > $o)] : ((((X12 @ (sK8 @ X12))) != $true) | (((sK2 @ sK3 @ (sK10 @ X12))) = $true) | (((X12 @ sK0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((X8 @ (sK7 @ X8))) != $true) | (((X8 @ (sK5 @ X8))) != $true) | (((X8 @ sK1)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((X8 @ (sK5 @ X8))) != $true) | (((sK2 @ (sK6 @ X8) @ (sK7 @ X8))) = $true) | (((X8 @ sK1)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((X8 @ (sK5 @ X8))) != $true) | (((X8 @ (sK6 @ X8))) = $true) | (((X8 @ sK1)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((X8 @ (sK7 @ X8))) != $true) | (((X8 @ sK1)) = $true) | (((sK2 @ sK0 @ (sK5 @ X8))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((sK2 @ (sK6 @ X8) @ (sK7 @ X8))) = $true) | (((X8 @ sK1)) = $true) | (((sK2 @ sK0 @ (sK5 @ X8))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ( ! [X8 : (a > $o)] : ((((sK2 @ sK0 @ (sK5 @ X8))) = $true) | (((X8 @ (sK6 @ X8))) = $true) | (((X8 @ sK1)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ( ! [X6 : a,X7 : a] : ((((sK2 @ X6 @ X7)) != $true) | (((sK4 @ X6)) != $true) | (((sK4 @ X7)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ( ! [X5 : a] : ((((sK2 @ sK3 @ X5)) != $true) | (((sK4 @ X5)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 (((sK4 @ sK1)) != $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f121,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((X0 @ sK0)) = $true) | (((X0 @ (sK9 @ X0))) = $true) | ($true = ((sK4 @ (sK10 @ X0)))) | ($true != $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f22,f12])).
% 0.20/0.29 thf(f129,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((X0 @ sK0)) = $true) | ($true = ((sK4 @ (sK10 @ X0)))) | (((X0 @ (sK9 @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f121])).
% 0.20/0.29 thf(f138,definition,(
% 0.20/0.29 spl11_6 <=> ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK10 @ X0)))) | (((X0 @ (sK9 @ X0))) = $true) | (((X0 @ sK0)) = $true))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition])).
% 0.20/0.29 thf(f139,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK10 @ X0)))) | (((X0 @ (sK9 @ X0))) = $true) | (((X0 @ sK0)) = $true)) ) | ~spl11_6),
% 0.20/0.29 inference(avatar_component_clause,[],[f138])).
% 0.20/0.29 thf(f145,plain,(
% 0.20/0.29 spl11_6),
% 0.20/0.29 inference(avatar_split_clause,[],[f129,f138])).
% 0.20/0.29 thf(f205,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((sK4 @ (sK5 @ X0))) = $true) | (((X0 @ sK1)) = $true) | (((sK4 @ sK0)) != $true) | (((X0 @ (sK6 @ X0))) = $true) | ($true != $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f20])).
% 0.20/0.29 thf(f214,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((X0 @ sK1)) = $true) | (((sK4 @ sK0)) != $true) | (((X0 @ (sK6 @ X0))) = $true) | (((sK4 @ (sK5 @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f205])).
% 0.20/0.29 thf(f220,definition,(
% 0.20/0.29 spl11_11 <=> (((sK4 @ sK0)) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition])).
% 0.20/0.29 thf(f221,plain,(
% 0.20/0.29 (((sK4 @ sK0)) = $true) | ~spl11_11),
% 0.20/0.29 inference(avatar_component_clause,[],[f220])).
% 0.20/0.29 thf(f222,plain,(
% 0.20/0.29 (((sK4 @ sK0)) != $true) | spl11_11),
% 0.20/0.29 inference(avatar_component_clause,[],[f220])).
% 0.20/0.29 thf(f224,definition,(
% 0.20/0.29 spl11_12 <=> ! [X0 : (a > $o)] : ((((X0 @ sK1)) = $true) | (((sK4 @ (sK5 @ X0))) = $true) | (((X0 @ (sK6 @ X0))) = $true))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition])).
% 0.20/0.29 thf(f225,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((sK4 @ (sK5 @ X0))) = $true) | (((X0 @ (sK6 @ X0))) = $true) | (((X0 @ sK1)) = $true)) ) | ~spl11_12),
% 0.20/0.29 inference(avatar_component_clause,[],[f224])).
% 0.20/0.29 thf(f226,plain,(
% 0.20/0.29 ~spl11_11 | spl11_12),
% 0.20/0.29 inference(avatar_split_clause,[],[f214,f224,f220])).
% 0.20/0.29 thf(f320,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : (($true != $true) | (((sK2 @ sK3 @ (sK10 @ X0))) = $true) | (((sK4 @ (sK9 @ X0))) != $true) | (((sK4 @ (sK8 @ X0))) = $true) | (((X0 @ sK0)) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f10])).
% 0.20/0.29 thf(f321,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((sK4 @ (sK9 @ X0))) != $true) | (((sK2 @ sK3 @ (sK10 @ X0))) = $true) | (((sK4 @ (sK8 @ X0))) = $true) | (((X0 @ sK0)) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f320])).
% 0.20/0.29 thf(f323,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : (($true != $true) | (((sK4 @ (sK6 @ X0))) != $true) | (((sK2 @ sK0 @ (sK5 @ X0))) = $true) | (((sK4 @ (sK7 @ X0))) = $true) | (((X0 @ sK1)) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f19])).
% 0.20/0.29 thf(f328,plain,(
% 0.20/0.29 ( ! [X0 : (a > $o)] : ((((sK4 @ (sK6 @ X0))) != $true) | (((X0 @ sK1)) = $true) | (((sK2 @ sK0 @ (sK5 @ X0))) = $true) | (((sK4 @ (sK7 @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f323])).
% 0.20/0.29 thf(f329,plain,(
% 0.20/0.29 (((sK4 @ sK0)) = $true) | ($true != $true) | ($true = ((sK2 @ sK3 @ (sK10 @ sK4)))) | (((sK4 @ (sK8 @ sK4))) = $true) | (((sK4 @ sK0)) = $true) | (((sK4 @ (sK10 @ sK4))) = $true) | ~spl11_6),
% 0.20/0.29 inference(constrained_superposition,[],[f321,f139])).
% 0.20/0.29 thf(f332,plain,(
% 0.20/0.29 (((sK4 @ sK0)) = $true) | ($true != $true) | ($true = ((sK2 @ sK3 @ (sK10 @ sK4)))) | (((sK4 @ (sK10 @ sK4))) = $true) | (((sK4 @ (sK8 @ sK4))) = $true) | ~spl11_6),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f329])).
% 0.20/0.29 thf(f333,plain,(
% 0.20/0.29 ($true = ((sK2 @ sK3 @ (sK10 @ sK4)))) | (((sK4 @ (sK8 @ sK4))) = $true) | (((sK4 @ (sK10 @ sK4))) = $true) | (((sK4 @ sK0)) = $true) | ~spl11_6),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f332])).
% 0.20/0.29 thf(f334,plain,(
% 0.20/0.29 (((sK4 @ (sK10 @ sK4))) = $true) | (((sK4 @ sK0)) = $true) | ($true = ((sK2 @ sK3 @ (sK10 @ sK4)))) | ~spl11_6),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f333,f14])).
% 0.20/0.29 thf(f335,plain,(
% 0.20/0.29 (((sK4 @ sK1)) = $true) | ($true != $true) | (((sK4 @ (sK5 @ sK4))) = $true) | (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | (((sK4 @ (sK7 @ sK4))) = $true) | (((sK4 @ sK1)) = $true) | ~spl11_12),
% 0.20/0.29 inference(constrained_superposition,[],[f328,f225])).
% 0.20/0.29 thf(f336,plain,(
% 0.20/0.29 (((sK4 @ sK1)) = $true) | (((sK4 @ (sK7 @ sK4))) = $true) | (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | ($true != $true) | (((sK4 @ (sK5 @ sK4))) = $true) | ~spl11_12),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f335])).
% 0.20/0.29 thf(f337,plain,(
% 0.20/0.29 (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | (((sK4 @ (sK7 @ sK4))) = $true) | (((sK4 @ (sK5 @ sK4))) = $true) | (((sK4 @ sK1)) = $true) | ~spl11_12),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f336])).
% 0.20/0.29 thf(f338,plain,(
% 0.20/0.29 (((sK4 @ sK1)) = $true) | (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | (((sK4 @ (sK5 @ sK4))) = $true) | ~spl11_12),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f337,f18])).
% 0.20/0.29 thf(f339,plain,(
% 0.20/0.29 (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | (((sK4 @ (sK5 @ sK4))) = $true) | ~spl11_12),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f338,f23])).
% 0.20/0.29 thf(f341,definition,(
% 0.20/0.29 spl11_20 <=> (((sK4 @ (sK5 @ sK4))) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition])).
% 0.20/0.29 thf(f342,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) != $true) | spl11_20),
% 0.20/0.29 inference(avatar_component_clause,[],[f341])).
% 0.20/0.29 thf(f343,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) = $true) | ~spl11_20),
% 0.20/0.29 inference(avatar_component_clause,[],[f341])).
% 0.20/0.29 thf(f345,definition,(
% 0.20/0.29 spl11_21 <=> (((sK2 @ sK0 @ (sK5 @ sK4))) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition])).
% 0.20/0.29 thf(f347,plain,(
% 0.20/0.29 (((sK2 @ sK0 @ (sK5 @ sK4))) = $true) | ~spl11_21),
% 0.20/0.29 inference(avatar_component_clause,[],[f345])).
% 0.20/0.29 thf(f348,plain,(
% 0.20/0.29 spl11_20 | spl11_21 | ~spl11_12),
% 0.20/0.29 inference(avatar_split_clause,[],[f339,f224,f345,f341])).
% 0.20/0.29 thf(f349,plain,(
% 0.20/0.29 ($true != $true) | (((sK4 @ sK1)) = $true) | (((sK2 @ (sK6 @ sK4) @ (sK7 @ sK4))) = $true) | ~spl11_20),
% 0.20/0.29 inference(constrained_superposition,[],[f16,f343])).
% 0.20/0.29 thf(f350,plain,(
% 0.20/0.29 ($true != $true) | (((sK4 @ (sK6 @ sK4))) = $true) | (((sK4 @ sK1)) = $true) | ~spl11_20),
% 0.20/0.29 inference(constrained_superposition,[],[f17,f343])).
% 0.20/0.29 thf(f351,plain,(
% 0.20/0.29 (((sK4 @ (sK6 @ sK4))) = $true) | (((sK4 @ sK1)) = $true) | ~spl11_20),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f350])).
% 0.20/0.29 thf(f352,plain,(
% 0.20/0.29 (((sK2 @ (sK6 @ sK4) @ (sK7 @ sK4))) = $true) | (((sK4 @ sK1)) = $true) | ~spl11_20),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f349])).
% 0.20/0.29 thf(f353,plain,(
% 0.20/0.29 (((sK4 @ (sK6 @ sK4))) = $true) | ~spl11_20),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f351,f23])).
% 0.20/0.29 thf(f354,plain,(
% 0.20/0.29 (((sK2 @ (sK6 @ sK4) @ (sK7 @ sK4))) = $true) | ~spl11_20),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f352,f23])).
% 0.20/0.29 thf(f360,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) = $true) | ($true != $true) | (((sK4 @ sK0)) != $true) | ~spl11_21),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f347])).
% 0.20/0.29 thf(f361,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) = $true) | (((sK4 @ sK0)) != $true) | ~spl11_21),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f360])).
% 0.20/0.29 thf(f362,plain,(
% 0.20/0.29 ($true != $true) | (((sK4 @ (sK7 @ sK4))) = $true) | (((sK4 @ (sK6 @ sK4))) != $true) | ~spl11_20),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f354])).
% 0.20/0.29 thf(f363,plain,(
% 0.20/0.29 (((sK4 @ (sK7 @ sK4))) = $true) | (((sK4 @ (sK6 @ sK4))) != $true) | ~spl11_20),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f362])).
% 0.20/0.29 thf(f364,plain,(
% 0.20/0.29 (((sK4 @ (sK7 @ sK4))) = $true) | ~spl11_20),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f363,f353])).
% 0.20/0.29 thf(f366,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) != $true) | ($true != $true) | (((sK4 @ sK1)) = $true) | ~spl11_20),
% 0.20/0.29 inference(constrained_superposition,[],[f15,f364])).
% 0.20/0.29 thf(f367,plain,(
% 0.20/0.29 (((sK4 @ sK1)) = $true) | (((sK4 @ (sK5 @ sK4))) != $true) | ~spl11_20),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f366])).
% 0.20/0.29 thf(f369,plain,(
% 0.20/0.29 (((sK4 @ (sK5 @ sK4))) != $true) | ~spl11_20),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f367,f23])).
% 0.20/0.29 thf(f370,plain,(
% 0.20/0.29 $false | ~spl11_20),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f369,f343])).
% 0.20/0.29 thf(f371,plain,(
% 0.20/0.29 ~spl11_20),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f370])).
% 0.20/0.29 thf(f372,plain,(
% 0.20/0.29 (((sK4 @ sK0)) != $true) | (spl11_20 | ~spl11_21)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f361,f342])).
% 0.20/0.29 thf(f373,plain,(
% 0.20/0.29 $false | (~spl11_11 | spl11_20 | ~spl11_21)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f372,f221])).
% 0.20/0.29 thf(f374,plain,(
% 0.20/0.29 ~spl11_11 | spl11_20 | ~spl11_21),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f373])).
% 0.20/0.29 thf(f381,plain,(
% 0.20/0.29 ($true = ((sK2 @ sK3 @ (sK10 @ sK4)))) | (((sK4 @ (sK10 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f334,f222])).
% 0.20/0.29 thf(f382,plain,(
% 0.20/0.29 (((sK4 @ (sK10 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f381,f22])).
% 0.20/0.29 thf(f392,plain,(
% 0.20/0.29 (((sK2 @ (sK9 @ sK4) @ (sK8 @ sK4))) = $true) | (((sK4 @ sK0)) = $true) | ($true != $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(constrained_superposition,[],[f9,f382])).
% 0.20/0.29 thf(f393,plain,(
% 0.20/0.29 (((sK4 @ (sK8 @ sK4))) != $true) | ($true != $true) | (((sK4 @ sK0)) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(constrained_superposition,[],[f13,f382])).
% 0.20/0.29 thf(f394,plain,(
% 0.20/0.29 ($true != $true) | (((sK4 @ (sK9 @ sK4))) = $true) | (((sK4 @ sK0)) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(constrained_superposition,[],[f11,f382])).
% 0.20/0.29 thf(f395,plain,(
% 0.20/0.29 (((sK4 @ sK0)) = $true) | (((sK4 @ (sK9 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f394])).
% 0.20/0.29 thf(f396,plain,(
% 0.20/0.29 (((sK4 @ sK0)) = $true) | (((sK2 @ (sK9 @ sK4) @ (sK8 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f392])).
% 0.20/0.29 thf(f397,plain,(
% 0.20/0.29 (((sK4 @ (sK8 @ sK4))) != $true) | (((sK4 @ sK0)) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f393])).
% 0.20/0.29 thf(f398,plain,(
% 0.20/0.29 (((sK4 @ (sK9 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f395,f222])).
% 0.20/0.29 thf(f399,plain,(
% 0.20/0.29 (((sK2 @ (sK9 @ sK4) @ (sK8 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f396,f222])).
% 0.20/0.29 thf(f400,plain,(
% 0.20/0.29 (((sK4 @ (sK8 @ sK4))) != $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f397,f222])).
% 0.20/0.29 thf(f409,plain,(
% 0.20/0.29 (((sK4 @ (sK8 @ sK4))) = $true) | ($true != $true) | (((sK4 @ (sK9 @ sK4))) != $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f399])).
% 0.20/0.29 thf(f410,plain,(
% 0.20/0.29 (((sK4 @ (sK9 @ sK4))) != $true) | (((sK4 @ (sK8 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f409])).
% 0.20/0.29 thf(f411,plain,(
% 0.20/0.29 (((sK4 @ (sK8 @ sK4))) = $true) | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f410,f398])).
% 0.20/0.29 thf(f412,plain,(
% 0.20/0.29 $false | (~spl11_6 | spl11_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f411,f400])).
% 0.20/0.29 thf(f413,plain,(
% 0.20/0.29 ~spl11_6 | spl11_11),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f412])).
% 0.20/0.29 cnf(s5, plain, spl11_6, inference(sat_conversion,[],[f145])).
% 0.20/0.29 cnf(s7, plain, ~spl11_11 | spl11_12, inference(sat_conversion,[],[f226])).
% 0.20/0.29 cnf(s16, plain, ~spl11_12 | spl11_20 | spl11_21, inference(sat_conversion,[],[f348])).
% 0.20/0.29 cnf(s18, plain, ~spl11_20, inference(sat_conversion,[],[f371])).
% 0.20/0.29 cnf(s19, plain, ~spl11_11 | spl11_20 | ~spl11_21, inference(sat_conversion,[],[f374])).
% 0.20/0.29 cnf(s22, plain, ~spl11_6 | spl11_11, inference(sat_conversion,[],[f413])).
% 0.20/0.29 cnf(s23, plain, ~spl11_12 | spl11_21, inference(rat,[],[s16,s18])).
% 0.20/0.29 cnf(s24, plain, spl11_11, inference(rat,[],[s22,s5])).
% 0.20/0.29 cnf(s25, plain, ~spl11_21, inference(rat,[],[s19,s18,s24])).
% 0.20/0.29 cnf(s26, plain, spl11_12, inference(rat,[],[s7,s24])).
% 0.20/0.29 cnf(s27, plain, $false, inference(rat,[],[s23,s25,s26])).
% 0.20/0.29 thf(f414,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s27])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3286045)------------------------------
% 0.20/0.29 % (3286045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3286045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3286045)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3286045)Termination reason: Refutation
% 0.20/0.29 % (3286045)Time elapsed: 0.017 s
% 0.20/0.29 % (3286045)Peak memory usage: 13 MB
% 0.20/0.29 % (3286045)Instructions burned: 27 (million)
% 0.20/0.29 % (3286040)Success in time 0.052 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------