%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV236^5 : 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 : n007.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 08:38:05 AM UTC 2026
% Result : Theorem 0.28s 0.34s
% Output : Refutation 0.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV236^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:24:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.28/0.34 % (3501664)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.34 % (3501672)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=2020474220: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)
% 0.28/0.34 % (3501675)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.34 % (3501675)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
% 0.28/0.34 % (3501670)lrs+10_16_si=on:nwc=1.5:random_seed=2244355960:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.34 % (3501669)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1377416295:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.34 % (3501671)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=523011183:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.34 % (3501673)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1868859860:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.34 % (3501675)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=3805682360:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.34 % (3501674)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1329830970:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.34 % (3501671)Refutation not found, incomplete strategy
% 0.28/0.34 % (3501671)------------------------------
% 0.28/0.34 % (3501671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501671)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501671)Termination reason: Refutation not found, incomplete strategy
% 0.28/0.34 % (3501671)Time elapsed: 0.002 s
% 0.28/0.34 % (3501671)Peak memory usage: 12 MB
% 0.28/0.34 % (3501671)Instructions burned: 2 (million)
% 0.28/0.34 % (3501671)------------------------------
% 0.28/0.34 % (3501671)------------------------------
% 0.28/0.34 % (3501675)Refutation not found, incomplete strategy
% 0.28/0.34 % (3501675)------------------------------
% 0.28/0.34 % (3501675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501675)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501675)Termination reason: Refutation not found, incomplete strategy
% 0.28/0.34 % (3501675)Time elapsed: 0.006 s
% 0.28/0.34 % (3501675)Peak memory usage: 12 MB
% 0.28/0.34 % (3501675)Instructions burned: 9 (million)
% 0.28/0.34 % (3501675)------------------------------
% 0.28/0.34 % (3501675)------------------------------
% 0.28/0.34 % (3501670)Instruction limit reached!
% 0.28/0.34 % (3501670)------------------------------
% 0.28/0.34 % (3501670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501670)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501670)Termination reason: Instruction limit
% 0.28/0.34 % (3501670)Termination phase: Saturation
% 0.28/0.34 % (3501670)Time elapsed: 0.011 s
% 0.28/0.34 % (3501670)Peak memory usage: 12 MB
% 0.28/0.34 % (3501670)Instructions burned: 19 (million)
% 0.28/0.34 % (3501673)Instruction limit reached!
% 0.28/0.34 % (3501673)------------------------------
% 0.28/0.34 % (3501673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501673)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501673)Termination reason: Instruction limit
% 0.28/0.34 % (3501673)Termination phase: Saturation
% 0.28/0.34 % (3501673)Time elapsed: 0.013 s
% 0.28/0.34 % (3501673)Peak memory usage: 11 MB
% 0.28/0.34 % (3501673)Instructions burned: 24 (million)
% 0.28/0.34 % (3501683)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3041876831:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.34 % (3501684)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2646506106:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.28/0.34 % (3501685)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.34 % (3501683)Instruction limit reached!
% 0.28/0.34 % (3501683)------------------------------
% 0.28/0.34 % (3501683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501683)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501683)Termination reason: Instruction limit
% 0.28/0.34 % (3501683)Termination phase: Saturation
% 0.28/0.34 % (3501683)Time elapsed: 0.003 s
% 0.28/0.34 % (3501683)Peak memory usage: 12 MB
% 0.28/0.34 % (3501683)Instructions burned: 4 (million)
% 0.28/0.34 % (3501685)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2719372931:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.28/0.34 % (3501684)Instruction limit reached!
% 0.28/0.34 % (3501684)------------------------------
% 0.28/0.34 % (3501684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501684)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501686)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2420863246:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.28/0.34 % (3501684)Termination reason: Instruction limit
% 0.28/0.34 % (3501684)Termination phase: Saturation
% 0.28/0.34 % (3501684)Time elapsed: 0.004 s
% 0.28/0.34 % (3501684)Peak memory usage: 12 MB
% 0.28/0.34 % (3501684)Instructions burned: 6 (million)
% 0.28/0.34 % (3501685)Instruction limit reached!
% 0.28/0.34 % (3501685)------------------------------
% 0.28/0.34 % (3501685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501685)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501685)Termination reason: Instruction limit
% 0.28/0.34 % (3501685)Termination phase: Saturation
% 0.28/0.34 % (3501685)Time elapsed: 0.004 s
% 0.28/0.34 % (3501685)Peak memory usage: 12 MB
% 0.28/0.34 % (3501685)Instructions burned: 7 (million)
% 0.28/0.34 % (3501674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3501664-3501674"...
% 0.28/0.34 % (3501686)Instruction limit reached!
% 0.28/0.34 % (3501686)------------------------------
% 0.28/0.34 % (3501686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501686)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501686)Termination reason: Instruction limit
% 0.28/0.34 % (3501686)Termination phase: Saturation
% 0.28/0.34 % (3501686)Time elapsed: 0.008 s
% 0.28/0.34 % (3501686)Peak memory usage: 12 MB
% 0.28/0.34 % (3501686)Instructions burned: 12 (million)
% 0.28/0.34 % (3501674)...printing done.
% 0.28/0.34 % (3501674)Refutation found. Thanks to Tanya!
% 0.28/0.34 % SZS status Theorem for theBenchmark
% 0.28/0.34 % SZS output start Proof for theBenchmark
% 0.28/0.34 thf(type_def_5, type, a: $tType).
% 0.28/0.34 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.28/0.34 thf(func_def_0, type, cS: (a > $o)).
% 0.28/0.34 thf(func_def_1, type, cK: ((a > $o) > a > $o)).
% 0.28/0.34 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.28/0.34 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.28/0.34 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.28/0.34 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.28/0.34 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.28/0.34 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.28/0.34 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.28/0.34 thf(func_def_12, type, sK0: a).
% 0.28/0.34 thf(func_def_13, type, sK1: ((a > $o) > (a > $o) > a)).
% 0.28/0.34 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.28/0.34 thf(func_def_16, type, sK3: ((a > $o) > a)).
% 0.28/0.34 thf(func_def_17, type, sK4: a).
% 0.28/0.34 thf(func_def_18, type, sK5: ((a > $o) > a)).
% 0.28/0.34 thf(func_def_19, type, sK6: (a > $o)).
% 0.28/0.34 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.28/0.34 thf(func_def_21, type, sK7: ((a > $o) > (a > a > $o) > a)).
% 0.28/0.34 thf(f1,conjecture,(
% 0.28/0.34 ! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ cS @ X2) => (cK @ (^[X3 : a] : (? [X4 : (a > $o)] : ((X4 @ X3) & ! [X5 : a] : ((X4 @ X5) => (cS @ X5))))) @ X2))),
% 0.28/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM91_pme)).
% 0.28/0.34 thf(f2,negated_conjecture,(
% 0.28/0.34 ~(! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ cS @ X2) => (cK @ (^[X3 : a] : (? [X4 : (a > $o)] : ((X4 @ X3) & ! [X5 : a] : ((X4 @ X5) => (cS @ X5))))) @ X2)))),
% 0.28/0.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.28/0.34 thf(f3,plain,(
% 0.28/0.34 ~(! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : a] : ((cK @ X1 @ X3) => (cK @ X0 @ X3))) => ! [X4 : a] : ((cK @ cS @ X4) => (cK @ (^[X5 : a] : (? [X6 : (a > $o)] : ((X6 @ X5) & ! [X7 : a] : ((X6 @ X7) => (cS @ X7))))) @ X4)))),
% 0.28/0.34 inference(rectify,[],[f2])).
% 0.28/0.34 thf(f4,plain,(
% 0.28/0.34 ~(! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) = $true) => (((X0 @ X2)) = $true)) => ! [X3 : a] : (($true = ((cK @ X1 @ X3))) => ($true = ((cK @ X0 @ X3))))) => ! [X4 : a] : ((((cK @ cS @ X4)) = $true) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ X4)))))),
% 0.28/0.34 inference(fool_elimination,[],[f3])).
% 0.28/0.34 thf(f5,plain,(
% 0.28/0.34 ? [X4 : a] : ((((cK @ cS @ X4)) = $true) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ X4)))) & ! [X1 : (a > $o),X0 : (a > $o)] : (? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ! [X3 : a] : (($true = ((cK @ X0 @ X3))) | ($true != ((cK @ X1 @ X3)))))),
% 0.28/0.34 inference(ennf_transformation,[],[f4])).
% 0.28/0.34 thf(f6,plain,(
% 0.28/0.34 ? [X0 : a] : (($true = ((cK @ cS @ X0))) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ X0)))) & ! [X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : ((((X1 @ X3)) = $true) & ($true != ((X2 @ X3)))) | ! [X4 : a] : (($true = ((cK @ X2 @ X4))) | ($true != ((cK @ X1 @ X4)))))),
% 0.28/0.34 inference(rectify,[],[f5])).
% 0.28/0.34 thf(f7,plain,(
% 0.28/0.34 ((((cK @ cS @ sK0)) = $true) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ sK0)))) & ! [X1 : (a > $o),X2 : (a > $o)] : ((($true = ((X1 @ (sK1 @ X2 @ X1)))) & ($true != ((X2 @ (sK1 @ X2 @ X1))))) | ! [X4 : a] : (($true = ((cK @ X2 @ X4))) | ($true != ((cK @ X1 @ X4)))))),
% 0.28/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X3,sK1 @ X2 @ X1)],[f6])).
% 0.28/0.34 thf(f10,plain,(
% 0.28/0.34 ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ sK0)))),
% 0.28/0.34 inference(cnf_transformation,[],[f7])).
% 0.28/0.34 thf(f11,plain,(
% 0.28/0.34 (((cK @ cS @ sK0)) = $true)),
% 0.28/0.34 inference(cnf_transformation,[],[f7])).
% 0.28/0.34 thf(f30,plain,(
% 0.28/0.34 (cS != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0)))))) | ($true != $true)),
% 0.28/0.34 inference(constrained_superposition,[],[f10,f11])).
% 0.28/0.34 thf(f31,plain,(
% 0.28/0.34 (cS != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))))),
% 0.28/0.34 inference(trivial_inequality_removal,[],[f30])).
% 0.28/0.34 thf(f63,plain,(
% 0.28/0.34 ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ sK4)) != ((cS @ sK4)))),
% 0.28/0.34 inference(negative_extensionality,[],[f31])).
% 0.28/0.34 thf(f64,plain,(
% 0.28/0.34 ($true = ((cS @ sK4))) | ($true = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ sK4)))),
% 0.28/0.34 inference(xor_proxy_clausification,[],[f63])).
% 0.28/0.34 thf(f65,plain,(
% 0.28/0.34 ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cS @ Y2)))) & (Y1 @ Y0))))) @ sK4)) = $false) | (((cS @ sK4)) = $false)),
% 0.28/0.34 inference(xor_proxy_clausification,[],[f63])).
% 0.28/0.34 thf(f66,plain,(
% 0.28/0.34 (((cS @ sK4)) = $false) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))) & (Y0 @ sK4))))) = $false)),
% 0.28/0.34 inference(beta-eta_normalization,[],[f65])).
% 0.28/0.34 thf(f67,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))) & (Y0 @ sK4))) @ X1)) = $false) | (((cS @ sK4)) = $false)) )),
% 0.28/0.34 inference(pi_proxy_clausification,[],[f66])).
% 0.28/0.34 thf(f68,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (($false = (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cS @ Y0)))) & (X1 @ sK4)))) | (((cS @ sK4)) = $false)) )),
% 0.28/0.34 inference(beta-eta_normalization,[],[f67])).
% 0.28/0.34 thf(f69,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (($false = ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cS @ Y0)))))) | (((X1 @ sK4)) = $false) | (((cS @ sK4)) = $false)) )),
% 0.28/0.34 inference(and_proxy_clausification,[],[f68])).
% 0.28/0.34 thf(f70,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (((((^[Y0 : a]: ((X1 @ Y0) => (cS @ Y0))) @ (sK5 @ X1))) = $false) | (((cS @ sK4)) = $false) | (((X1 @ sK4)) = $false)) )),
% 0.28/0.34 inference(sigma_proxy_clausification,[],[f69])).
% 0.28/0.34 thf(f71,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (($false = (((X1 @ (sK5 @ X1)) => (cS @ (sK5 @ X1))))) | (((cS @ sK4)) = $false) | (((X1 @ sK4)) = $false)) )),
% 0.28/0.34 inference(beta-eta_normalization,[],[f70])).
% 0.28/0.34 thf(f72,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : ((((cS @ sK4)) = $false) | ($false = ((cS @ (sK5 @ X1)))) | (((X1 @ sK4)) = $false)) )),
% 0.28/0.34 inference(imp_proxy_clausification,[],[f71])).
% 0.28/0.34 thf(f73,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : ((((X1 @ sK4)) = $false) | (((cS @ sK4)) = $false) | ($true = ((X1 @ (sK5 @ X1))))) )),
% 0.28/0.34 inference(imp_proxy_clausification,[],[f71])).
% 0.28/0.34 thf(f74,plain,(
% 0.28/0.34 ($true = ((cS @ sK4))) | ($true = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))) & (Y0 @ sK4))))))),
% 0.28/0.34 inference(beta-eta_normalization,[],[f64])).
% 0.28/0.34 thf(f75,plain,(
% 0.28/0.34 ($true = (((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cS @ Y1)))) & (Y0 @ sK4))) @ sK6))) | ($true = ((cS @ sK4)))),
% 0.28/0.34 inference(sigma_proxy_clausification,[],[f74])).
% 0.28/0.34 thf(f76,plain,(
% 0.28/0.34 ($true = (((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (cS @ Y0)))) & (sK6 @ sK4)))) | ($true = ((cS @ sK4)))),
% 0.28/0.34 inference(beta-eta_normalization,[],[f75])).
% 0.28/0.34 thf(f77,plain,(
% 0.28/0.34 ($true = ((sK6 @ sK4))) | ($true = ((cS @ sK4)))),
% 0.28/0.34 inference(and_proxy_clausification,[],[f76])).
% 0.28/0.34 thf(f78,plain,(
% 0.28/0.34 ($true = ((cS @ sK4))) | ($true = ((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (cS @ Y0))))))),
% 0.28/0.34 inference(and_proxy_clausification,[],[f76])).
% 0.28/0.34 thf(f79,plain,(
% 0.28/0.34 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ((sK6 @ Y0) => (cS @ Y0))) @ X1))) | ($true = ((cS @ sK4)))) )),
% 0.28/0.34 inference(pi_proxy_clausification,[],[f78])).
% 0.28/0.34 thf(f80,plain,(
% 0.28/0.34 ( ! [X1 : a] : (($true = (((sK6 @ X1) => (cS @ X1)))) | ($true = ((cS @ sK4)))) )),
% 0.28/0.34 inference(beta-eta_normalization,[],[f79])).
% 0.28/0.34 thf(f81,plain,(
% 0.28/0.34 ( ! [X1 : a] : (($true = ((cS @ sK4))) | ($false = ((sK6 @ X1))) | ($true = ((cS @ X1)))) )),
% 0.28/0.34 inference(imp_proxy_clausification,[],[f80])).
% 0.28/0.34 thf(f83,definition,(
% 0.28/0.34 spl2_3 <=> ! [X1 : (a > $o)] : ((((X1 @ sK4)) = $false) | ($true = ((X1 @ (sK5 @ X1)))))),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.28/0.34 thf(f84,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (($true = ((X1 @ (sK5 @ X1)))) | (((X1 @ sK4)) = $false)) ) | ~spl2_3),
% 0.28/0.34 inference(avatar_component_clause,[],[f83])).
% 0.28/0.34 thf(f86,definition,(
% 0.28/0.34 spl2_4 <=> (((cS @ sK4)) = $false)),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.28/0.34 thf(f87,plain,(
% 0.28/0.34 (((cS @ sK4)) = $false) | ~spl2_4),
% 0.28/0.34 inference(avatar_component_clause,[],[f86])).
% 0.28/0.34 thf(f88,plain,(
% 0.28/0.34 spl2_3 | spl2_4),
% 0.28/0.34 inference(avatar_split_clause,[],[f73,f86,f83])).
% 0.28/0.34 thf(f90,definition,(
% 0.28/0.34 spl2_5 <=> ! [X1 : (a > $o)] : (($false = ((cS @ (sK5 @ X1)))) | (((X1 @ sK4)) = $false))),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.28/0.34 thf(f91,plain,(
% 0.28/0.34 ( ! [X1 : (a > $o)] : (($false = ((cS @ (sK5 @ X1)))) | (((X1 @ sK4)) = $false)) ) | ~spl2_5),
% 0.28/0.34 inference(avatar_component_clause,[],[f90])).
% 0.28/0.34 thf(f92,plain,(
% 0.28/0.34 spl2_5 | spl2_4),
% 0.28/0.34 inference(avatar_split_clause,[],[f72,f86,f90])).
% 0.28/0.34 thf(f94,definition,(
% 0.28/0.34 spl2_6 <=> ! [X1 : a] : (($false = ((sK6 @ X1))) | ($true = ((cS @ X1))))),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.28/0.34 thf(f95,plain,(
% 0.28/0.34 ( ! [X1 : a] : (($false = ((sK6 @ X1))) | ($true = ((cS @ X1)))) ) | ~spl2_6),
% 0.28/0.34 inference(avatar_component_clause,[],[f94])).
% 0.28/0.34 thf(f97,definition,(
% 0.28/0.34 spl2_7 <=> ($true = ((cS @ sK4)))),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.28/0.34 thf(f98,plain,(
% 0.28/0.34 ($true = ((cS @ sK4))) | ~spl2_7),
% 0.28/0.34 inference(avatar_component_clause,[],[f97])).
% 0.28/0.34 thf(f99,plain,(
% 0.28/0.34 spl2_6 | spl2_7),
% 0.28/0.34 inference(avatar_split_clause,[],[f81,f97,f94])).
% 0.28/0.34 thf(f101,definition,(
% 0.28/0.34 spl2_8 <=> ($true = ((sK6 @ sK4)))),
% 0.28/0.34 introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition])).
% 0.28/0.34 thf(f102,plain,(
% 0.28/0.34 ($true = ((sK6 @ sK4))) | ~spl2_8),
% 0.28/0.34 inference(avatar_component_clause,[],[f101])).
% 0.28/0.34 thf(f103,plain,(
% 0.28/0.34 spl2_8 | spl2_7),
% 0.28/0.34 inference(avatar_split_clause,[],[f77,f97,f101])).
% 0.28/0.34 thf(f104,plain,(
% 0.28/0.34 ($true = $false) | (~spl2_4 | ~spl2_7)),
% 0.28/0.34 inference(backward_demodulation,[],[f98,f87])).
% 0.28/0.34 thf(f105,plain,(
% 0.28/0.34 $false | (~spl2_4 | ~spl2_7)),
% 0.28/0.34 inference(trivial_inequality_removal,[],[f104])).
% 0.28/0.34 thf(f106,plain,(
% 0.28/0.34 ~spl2_4 | ~spl2_7),
% 0.28/0.34 inference(avatar_contradiction_clause,[],[f105])).
% 0.28/0.34 thf(f116,plain,(
% 0.28/0.34 (((sK5 @ (= @ sK4))) = sK4) | ~spl2_3),
% 0.28/0.34 inference(leibniz_equality_elimination,[],[f84])).
% 0.28/0.34 thf(f236,plain,(
% 0.28/0.34 (((cS @ sK4)) = $false) | ($false = ((sK4 = sK4))) | (~spl2_3 | ~spl2_5)),
% 0.28/0.34 inference(constrained_superposition,[],[f91,f116])).
% 0.28/0.34 thf(f259,plain,(
% 0.28/0.34 (sK4 != sK4) | (((cS @ sK4)) = $false) | (~spl2_3 | ~spl2_5)),
% 0.28/0.34 inference(equality_proxy_clausification,[],[f236])).
% 0.28/0.34 thf(f260,plain,(
% 0.28/0.34 (((cS @ sK4)) = $false) | (~spl2_3 | ~spl2_5)),
% 0.28/0.34 inference(trivial_inequality_removal,[],[f259])).
% 0.28/0.34 thf(f265,plain,(
% 0.28/0.34 spl2_4 | ~spl2_3 | ~spl2_5),
% 0.28/0.34 inference(avatar_split_clause,[],[f260,f90,f83,f86])).
% 0.28/0.34 thf(f436,plain,(
% 0.28/0.34 ($true = $false) | ($true = ((cS @ sK4))) | (~spl2_6 | ~spl2_8)),
% 0.28/0.34 inference(constrained_superposition,[],[f95,f102])).
% 0.28/0.34 thf(f449,plain,(
% 0.28/0.34 ($true = ((cS @ sK4))) | (~spl2_6 | ~spl2_8)),
% 0.28/0.34 inference(trivial_inequality_removal,[],[f436])).
% 0.28/0.34 thf(f462,plain,(
% 0.28/0.34 ($true = $false) | (~spl2_4 | ~spl2_6 | ~spl2_8)),
% 0.28/0.34 inference(forward_demodulation,[],[f449,f87])).
% 0.28/0.34 thf(f463,plain,(
% 0.28/0.34 $false | (~spl2_4 | ~spl2_6 | ~spl2_8)),
% 0.28/0.34 inference(trivial_inequality_removal,[],[f462])).
% 0.28/0.34 thf(f464,plain,(
% 0.28/0.34 ~spl2_4 | ~spl2_6 | ~spl2_8),
% 0.28/0.34 inference(avatar_contradiction_clause,[],[f463])).
% 0.28/0.34 cnf(s2, plain, spl2_3 | spl2_4, inference(sat_conversion,[],[f88])).
% 0.28/0.34 cnf(s3, plain, spl2_4 | spl2_5, inference(sat_conversion,[],[f92])).
% 0.28/0.34 cnf(s4, plain, spl2_6 | spl2_7, inference(sat_conversion,[],[f99])).
% 0.28/0.34 cnf(s5, plain, spl2_7 | spl2_8, inference(sat_conversion,[],[f103])).
% 0.28/0.34 cnf(s6, plain, ~spl2_4 | ~spl2_7, inference(sat_conversion,[],[f106])).
% 0.28/0.34 cnf(s10, plain, ~spl2_3 | spl2_4 | ~spl2_5, inference(sat_conversion,[],[f265])).
% 0.28/0.34 cnf(s16, plain, ~spl2_4 | ~spl2_6 | ~spl2_8, inference(sat_conversion,[],[f464])).
% 0.28/0.34 cnf(s17, plain, ~spl2_4, inference(rat,[],[s16,s4,s5,s6])).
% 0.28/0.34 cnf(s18, plain, spl2_5, inference(rat,[],[s3,s17])).
% 0.28/0.34 cnf(s19, plain, spl2_3, inference(rat,[],[s2,s17])).
% 0.28/0.34 cnf(s20, plain, $false, inference(rat,[],[s10,s17,s19,s18])).
% 0.28/0.34 thf(f465,plain,(
% 0.28/0.34 $false),
% 0.28/0.34 inference(avatar_sat_refutation,[],[s20])).
% 0.28/0.34 % SZS output end Proof for theBenchmark
% 0.28/0.34 % (3501674)------------------------------
% 0.28/0.34 % (3501674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.34 % (3501674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.34 % (3501674)CaDiCaL version: 2.1.3
% 0.28/0.34 % (3501674)Termination reason: Refutation
% 0.28/0.34 % (3501674)Time elapsed: 0.038 s
% 0.28/0.34 % (3501674)Peak memory usage: 14 MB
% 0.28/0.34 % (3501674)Instructions burned: 61 (million)
% 0.28/0.34 % (3501664)Success in time 0.082 s
% 0.28/0.34 % Vampire exiting
%------------------------------------------------------------------------------