%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO272^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:47:19 AM UTC 2026
% Result : Theorem 0.30s 0.28s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO272^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:42:32 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.28 % (325650)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.28 % (325655)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3382447625:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.28 % (325661)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.28 % (325661)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
% 0.30/0.28 % (325656)lrs+10_16_si=on:nwc=1.5:random_seed=483136113:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.28 % (325657)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1886785322:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.28 % (325659)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2826178070:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.28 % (325660)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4109416111:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.28 % (325661)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=3910158922:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.28 % (325658)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=422067870: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)
% 0.30/0.28 % (325657)Instruction limit reached!
% 0.30/0.28 % (325657)------------------------------
% 0.30/0.28 % (325657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325657)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325657)Termination reason: Instruction limit
% 0.30/0.28 % (325657)Termination phase: Saturation
% 0.30/0.28 % (325657)Time elapsed: 0.002 s
% 0.30/0.28 % (325657)Peak memory usage: 12 MB
% 0.30/0.28 % (325657)Instructions burned: 3 (million)
% 0.30/0.28 % (325656)Instruction limit reached!
% 0.30/0.28 % (325656)------------------------------
% 0.30/0.28 % (325656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325656)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325656)Termination reason: Instruction limit
% 0.30/0.28 % (325656)Termination phase: Saturation
% 0.30/0.28 % (325656)Time elapsed: 0.010 s
% 0.30/0.28 % (325656)Peak memory usage: 12 MB
% 0.30/0.28 % (325656)Instructions burned: 20 (million)
% 0.30/0.28 % (325659)Instruction limit reached!
% 0.30/0.28 % (325659)------------------------------
% 0.30/0.28 % (325659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325659)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325659)Termination reason: Instruction limit
% 0.30/0.28 % (325659)Termination phase: Saturation
% 0.30/0.28 % (325659)Time elapsed: 0.014 s
% 0.30/0.28 % (325659)Peak memory usage: 12 MB
% 0.30/0.28 % (325659)Instructions burned: 24 (million)
% 0.30/0.28 % (325655)Instruction limit reached!
% 0.30/0.28 % (325655)------------------------------
% 0.30/0.28 % (325655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325655)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325655)Termination reason: Instruction limit
% 0.30/0.28 % (325655)Termination phase: Saturation
% 0.30/0.28 % (325655)Time elapsed: 0.025 s
% 0.30/0.28 % (325655)Peak memory usage: 12 MB
% 0.30/0.28 % (325655)Instructions burned: 87 (million)
% 0.30/0.28 % (325669)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1176909729:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.28 % (325669)Instruction limit reached!
% 0.30/0.28 % (325669)------------------------------
% 0.30/0.28 % (325669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325669)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325669)Termination reason: Instruction limit
% 0.30/0.28 % (325669)Termination phase: Saturation
% 0.30/0.28 % (325669)Time elapsed: 0.002 s
% 0.30/0.28 % (325669)Peak memory usage: 12 MB
% 0.30/0.28 % (325669)Instructions burned: 2 (million)
% 0.30/0.28 % (325677)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=871150682:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/0.28 % (325675)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.28 % (325673)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3818157856:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.28 % (325677)Instruction limit reached!
% 0.30/0.28 % (325677)------------------------------
% 0.30/0.28 % (325677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325677)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325677)Termination reason: Instruction limit
% 0.30/0.28 % (325677)Termination phase: Saturation
% 0.30/0.28 % (325677)Time elapsed: 0.004 s
% 0.30/0.28 % (325677)Peak memory usage: 12 MB
% 0.30/0.28 % (325677)Instructions burned: 14 (million)
% 0.30/0.28 % (325661) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-325650-325661"...
% 0.30/0.28 % (325675)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3910756038:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.28 % (325673)Instruction limit reached!
% 0.30/0.28 % (325673)------------------------------
% 0.30/0.28 % (325673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.28 % (325673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.28 % (325673)CaDiCaL version: 2.1.3
% 0.30/0.28 % (325673)Termination reason: Instruction limit
% 0.30/0.28 % (325673)Termination phase: Saturation
% 0.30/0.28 % (325673)Time elapsed: 0.004 s
% 0.30/0.28 % (325673)Peak memory usage: 12 MB
% 0.30/0.28 % (325673)Instructions burned: 5 (million)
% 0.30/0.28 % (325661)...printing done.
% 0.30/0.28 % (325661)Refutation found. Thanks to Tanya!
% 0.30/0.28 % SZS status Theorem for theBenchmark
% 0.30/0.28 % SZS output start Proof for theBenchmark
% 0.30/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.30/0.28 thf(func_def_0, type, cHALF: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_1, type, cDOUBLE: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_2, type, cS: ($i > $i)).
% 0.30/0.28 thf(func_def_7, type, sP0: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_8, type, sK1: ($i > $i > $i > $i > $o)).
% 0.30/0.28 thf(func_def_9, type, sK2: (($i > $i > $o) > $i)).
% 0.30/0.28 thf(func_def_10, type, sK3: (($i > $i > $o) > $i)).
% 0.30/0.28 thf(func_def_13, type, sF6: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_14, type, sF7: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_16, type, sF9: $o).
% 0.30/0.28 thf(func_def_17, type, sF10: $o).
% 0.30/0.28 thf(func_def_18, type, sF11: $o).
% 0.30/0.28 thf(func_def_19, type, sF12: $o).
% 0.30/0.28 thf(func_def_20, type, sF13: ($i > $i)).
% 0.30/0.28 thf(func_def_21, type, sF14: ($i > $i)).
% 0.30/0.28 thf(func_def_22, type, sF15: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_23, type, sF16: ($i > $i > $o)).
% 0.30/0.28 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
% 0.30/0.28 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 0.30/0.28 thf(func_def_27, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.30/0.28 thf(f1,conjecture,(
% 0.30/0.28 ((cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $i > $o)] : ((! [X4 : $i,X3 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)) <=> (cDOUBLE @ X0 @ X1)) & ! [X4 : $i,X3 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4)))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0))),
% 0.30/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM301A)).
% 0.30/0.28 thf(f2,negated_conjecture,(
% 0.30/0.28 ~(((cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $i > $o)] : ((! [X4 : $i,X3 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)) <=> (cDOUBLE @ X0 @ X1)) & ! [X4 : $i,X3 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4)))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0)))),
% 0.30/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.30/0.28 thf(f3,plain,(
% 0.30/0.28 ~(((cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : (! [X2 : ($i > $i > $o)] : ((! [X3 : $i,X4 : $i] : ((X2 @ X4 @ X3) => (X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) & (X2 @ c0 @ c0)) => (X2 @ X1 @ X0)) <=> (cDOUBLE @ X1 @ X0)) & ! [X5 : $i,X6 : $i] : ((cHALF @ X6 @ X5) => (cHALF @ (cS @ (cS @ X6)) @ (cS @ X5)))) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X7 @ X8) => (cHALF @ X8 @ X7)))),
% 0.30/0.28 inference(rectify,[],[f2])).
% 0.30/0.28 thf(f4,plain,(
% 0.30/0.28 ~(((((cHALF @ (cS @ c0) @ c0)) = $true) & ! [X1 : $i,X0 : $i] : ((((cDOUBLE @ X1 @ X0)) = $true) <=> ! [X2 : ($i > $i > $o)] : (((((X2 @ c0 @ c0)) = $true) & ! [X4 : $i,X3 : $i] : ((((X2 @ X4 @ X3)) = $true) => (((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) = $true))) => (((X2 @ X1 @ X0)) = $true))) & ! [X5 : $i,X6 : $i] : ((((cHALF @ X6 @ X5)) = $true) => (((cHALF @ (cS @ (cS @ X6)) @ (cS @ X5))) = $true)) & (((cHALF @ c0 @ c0)) = $true)) => ! [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) => (((cHALF @ X8 @ X7)) = $true)))),
% 0.30/0.28 inference(fool_elimination,[],[f3])).
% 0.30/0.28 thf(f5,plain,(
% 0.30/0.28 ? [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) & (((cHALF @ X8 @ X7)) != $true)) & ((((cHALF @ (cS @ c0) @ c0)) = $true) & ! [X1 : $i,X0 : $i] : ((((cDOUBLE @ X1 @ X0)) = $true) <=> ! [X2 : ($i > $i > $o)] : ((((X2 @ X1 @ X0)) = $true) | ((((X2 @ c0 @ c0)) != $true) | ? [X4 : $i,X3 : $i] : ((((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) != $true) & (((X2 @ X4 @ X3)) = $true))))) & ! [X6 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X6)) @ (cS @ X5))) = $true) | (((cHALF @ X6 @ X5)) != $true)) & (((cHALF @ c0 @ c0)) = $true))),
% 0.30/0.28 inference(ennf_transformation,[],[f4])).
% 0.30/0.28 thf(f6,plain,(
% 0.30/0.28 ! [X0 : $i,X1 : $i] : (! [X2 : ($i > $i > $o)] : ((((X2 @ c0 @ c0)) != $true) | (((X2 @ X1 @ X0)) = $true) | ? [X4 : $i,X3 : $i] : ((((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) != $true) & (((X2 @ X4 @ X3)) = $true))) <=> (((cDOUBLE @ X1 @ X0)) = $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ? [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) & (((cHALF @ X8 @ X7)) != $true)) & ! [X6 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X6)) @ (cS @ X5))) = $true) | (((cHALF @ X6 @ X5)) != $true))),
% 0.30/0.28 inference(flattening,[],[f5])).
% 0.30/0.28 thf(f7,definition,(
% 0.30/0.28 ! [X0 : $i,X1 : $i] : (($true = ((sP0 @ X1 @ X0))) <=> ! [X2 : ($i > $i > $o)] : ((((X2 @ c0 @ c0)) != $true) | (((X2 @ X1 @ X0)) = $true) | ? [X4 : $i,X3 : $i] : ((((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) != $true) & (((X2 @ X4 @ X3)) = $true))))),
% 0.30/0.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.30/0.28 thf(f8,plain,(
% 0.30/0.28 ! [X0 : $i,X1 : $i] : (($true = ((sP0 @ X1 @ X0))) <=> (((cDOUBLE @ X1 @ X0)) = $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ? [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) & (((cHALF @ X8 @ X7)) != $true)) & ! [X6 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X6)) @ (cS @ X5))) = $true) | (((cHALF @ X6 @ X5)) != $true))),
% 0.30/0.28 inference(definition_folding,[],[f6,f7])).
% 0.30/0.29 thf(f9,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | ? [X2 : ($i > $i > $o)] : ((((X2 @ c0 @ c0)) = $true) & (((X2 @ X1 @ X0)) != $true) & ! [X4 : $i,X3 : $i] : ((((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) = $true) | (((X2 @ X4 @ X3)) != $true)))) & (! [X2 : ($i > $i > $o)] : ((((X2 @ c0 @ c0)) != $true) | (((X2 @ X1 @ X0)) = $true) | ? [X4 : $i,X3 : $i] : ((((X2 @ (cS @ X4) @ (cS @ (cS @ X3)))) != $true) & (((X2 @ X4 @ X3)) = $true))) | ($true != ((sP0 @ X1 @ X0)))))),
% 0.30/0.29 inference(nnf_transformation,[],[f7])).
% 0.30/0.29 thf(f10,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | ? [X2 : ($i > $i > $o)] : ((((X2 @ c0 @ c0)) = $true) & (((X2 @ X1 @ X0)) != $true) & ! [X3 : $i,X4 : $i] : ((((X2 @ (cS @ X3) @ (cS @ (cS @ X4)))) = $true) | (((X2 @ X3 @ X4)) != $true)))) & (! [X5 : ($i > $i > $o)] : ((((X5 @ c0 @ c0)) != $true) | (((X5 @ X1 @ X0)) = $true) | ? [X6 : $i,X7 : $i] : ((((X5 @ (cS @ X6) @ (cS @ (cS @ X7)))) != $true) & (((X5 @ X6 @ X7)) = $true))) | ($true != ((sP0 @ X1 @ X0)))))),
% 0.30/0.29 inference(rectify,[],[f9])).
% 0.30/0.29 thf(f11,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | ((((sK1 @ X1 @ X0 @ c0 @ c0)) = $true) & (((sK1 @ X1 @ X0 @ X1 @ X0)) != $true) & ! [X3 : $i,X4 : $i] : (($true = ((sK1 @ X1 @ X0 @ (cS @ X3) @ (cS @ (cS @ X4))))) | (((sK1 @ X1 @ X0 @ X3 @ X4)) != $true)))) & (! [X5 : ($i > $i > $o)] : ((((X5 @ c0 @ c0)) != $true) | (((X5 @ X1 @ X0)) = $true) | (($true != ((X5 @ (cS @ (sK2 @ X5)) @ (cS @ (cS @ (sK3 @ X5)))))) & (((X5 @ (sK2 @ X5) @ (sK3 @ X5))) = $true))) | ($true != ((sP0 @ X1 @ X0)))))),
% 0.30/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X7,sK3 @ X5),skolemize(X7,sK3 @ X5),skolemize(X7,sK3 @ X5)],[f10])).
% 0.30/0.29 thf(f12,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | (((cDOUBLE @ X1 @ X0)) != $true)) & ((((cDOUBLE @ X1 @ X0)) = $true) | ($true != ((sP0 @ X1 @ X0))))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ? [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) & (((cHALF @ X8 @ X7)) != $true)) & ! [X6 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X6)) @ (cS @ X5))) = $true) | (((cHALF @ X6 @ X5)) != $true))),
% 0.30/0.29 inference(nnf_transformation,[],[f8])).
% 0.30/0.29 thf(f13,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | (((cDOUBLE @ X1 @ X0)) != $true)) & ((((cDOUBLE @ X1 @ X0)) = $true) | ($true != ((sP0 @ X1 @ X0))))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ? [X2 : $i,X3 : $i] : ((((cDOUBLE @ X3 @ X2)) = $true) & (((cHALF @ X2 @ X3)) != $true)) & ! [X4 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X4)) @ (cS @ X5))) = $true) | (((cHALF @ X4 @ X5)) != $true))),
% 0.30/0.29 inference(rectify,[],[f12])).
% 0.30/0.29 thf(f14,plain,(
% 0.30/0.29 ! [X0 : $i,X1 : $i] : ((($true = ((sP0 @ X1 @ X0))) | (((cDOUBLE @ X1 @ X0)) != $true)) & ((((cDOUBLE @ X1 @ X0)) = $true) | ($true != ((sP0 @ X1 @ X0))))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ((((cDOUBLE @ sK5 @ sK4)) = $true) & (((cHALF @ sK4 @ sK5)) != $true)) & ! [X4 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X4)) @ (cS @ X5))) = $true) | (((cHALF @ X4 @ X5)) != $true))),
% 0.30/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4),skolemize(X3,sK5)],[f13])).
% 0.30/0.29 thf(f15,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : ((((X5 @ (sK2 @ X5) @ (sK3 @ X5))) = $true) | (((X5 @ X1 @ X0)) = $true) | (((X5 @ c0 @ c0)) != $true) | ($true != ((sP0 @ X1 @ X0)))) )),
% 0.30/0.29 inference(cnf_transformation,[],[f11])).
% 0.30/0.29 thf(f16,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : (($true != ((X5 @ (cS @ (sK2 @ X5)) @ (cS @ (cS @ (sK3 @ X5)))))) | (((X5 @ X1 @ X0)) = $true) | (((X5 @ c0 @ c0)) != $true) | ($true != ((sP0 @ X1 @ X0)))) )),
% 0.30/0.29 inference(cnf_transformation,[],[f11])).
% 0.30/0.29 thf(f20,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X4)) @ (cS @ X5))) = $true) | (((cHALF @ X4 @ X5)) != $true)) )),
% 0.30/0.29 inference(cnf_transformation,[],[f14])).
% 0.30/0.29 thf(f21,plain,(
% 0.30/0.29 (((cHALF @ sK4 @ sK5)) != $true)),
% 0.30/0.29 inference(cnf_transformation,[],[f14])).
% 0.30/0.29 thf(f22,plain,(
% 0.30/0.29 (((cDOUBLE @ sK5 @ sK4)) = $true)),
% 0.30/0.29 inference(cnf_transformation,[],[f14])).
% 0.30/0.29 thf(f23,plain,(
% 0.30/0.29 (((cHALF @ c0 @ c0)) = $true)),
% 0.30/0.29 inference(cnf_transformation,[],[f14])).
% 0.30/0.29 thf(f26,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((sP0 @ X1 @ X0))) | (((cDOUBLE @ X1 @ X0)) != $true)) )),
% 0.30/0.29 inference(cnf_transformation,[],[f14])).
% 0.30/0.29 thf(f28,definition,(
% 0.30/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.30/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.30/0.29 thf(f29,definition,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF6 @ X0 @ X1)) = ((sP0 @ X1 @ X0)))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.30/0.29 thf(f30,definition,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF7 @ X0 @ X1)) = ((cDOUBLE @ X1 @ X0)))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 0.30/0.29 thf(f31,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((cDOUBLE @ X1 @ X0)) = ((sF7 @ X0 @ X1)))) )),
% 0.30/0.29 inference(reorient_equations,[],[f30])).
% 0.30/0.29 thf(f32,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF6 @ X0 @ X1)) = $true) | (((sF7 @ X0 @ X1)) != $true)) )),
% 0.30/0.29 inference(definition_folding,[],[f26,f31,f29])).
% 0.30/0.29 thf(f39,definition,(
% 0.30/0.29 (sF10 = ((cHALF @ c0 @ c0)))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 0.30/0.29 thf(f40,plain,(
% 0.30/0.29 (((cHALF @ c0 @ c0)) = sF10)),
% 0.30/0.29 inference(reorient_equations,[],[f39])).
% 0.30/0.29 thf(f41,plain,(
% 0.30/0.29 (sF10 = $true)),
% 0.30/0.29 inference(definition_folding,[],[f23,f40])).
% 0.30/0.29 thf(f42,definition,(
% 0.30/0.29 (sF11 = ((cDOUBLE @ sK5 @ sK4)))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 0.30/0.29 thf(f43,plain,(
% 0.30/0.29 (sF11 = $true)),
% 0.30/0.29 inference(definition_folding,[],[f22,f42])).
% 0.30/0.29 thf(f44,definition,(
% 0.30/0.29 (sF12 = ((cHALF @ sK4 @ sK5)))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 0.30/0.29 thf(f45,plain,(
% 0.30/0.29 (((cHALF @ sK4 @ sK5)) = sF12)),
% 0.30/0.29 inference(reorient_equations,[],[f44])).
% 0.30/0.29 thf(f46,plain,(
% 0.30/0.29 (sF12 != $true)),
% 0.30/0.29 inference(definition_folding,[],[f21,f45])).
% 0.30/0.29 thf(f47,definition,(
% 0.30/0.29 ( ! [X4 : $i] : ((((sF13 @ X4)) = ((cS @ X4)))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 0.30/0.29 thf(f48,plain,(
% 0.30/0.29 ( ! [X4 : $i] : ((((cS @ X4)) = ((sF13 @ X4)))) )),
% 0.30/0.29 inference(reorient_equations,[],[f47])).
% 0.30/0.29 thf(f49,definition,(
% 0.30/0.29 ( ! [X4 : $i] : ((((sF14 @ X4)) = ((cS @ (sF13 @ X4))))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 0.30/0.29 thf(f50,definition,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((sF15 @ X5 @ X4)) = ((cHALF @ (sF14 @ X4) @ (sF13 @ X5))))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 0.30/0.29 thf(f51,definition,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((sF16 @ X5 @ X4)) = ((cHALF @ X4 @ X5)))) )),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
% 0.30/0.29 thf(f52,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((cHALF @ X4 @ X5)) = ((sF16 @ X5 @ X4)))) )),
% 0.30/0.29 inference(reorient_equations,[],[f51])).
% 0.30/0.29 thf(f53,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((sF15 @ X5 @ X4)) = $true) | (((sF16 @ X5 @ X4)) != $true)) )),
% 0.30/0.29 inference(definition_folding,[],[f20,f52,f50,f48,f49,f48])).
% 0.30/0.29 thf(f55,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((sP0 @ X1 @ X0))) | ($false = ((sF6 @ X0 @ X1)))) )),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f29])).
% 0.30/0.29 thf(f56,plain,(
% 0.30/0.29 (((cHALF @ c0 @ c0)) = $true) | ($false = sF10)),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f40])).
% 0.30/0.29 thf(f59,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : ((((cHALF @ (sF14 @ X4) @ (sF13 @ X5))) = $true) | ($false = ((sF15 @ X5 @ X4)))) )),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f50])).
% 0.30/0.29 thf(f63,plain,(
% 0.30/0.29 ($false = ((cHALF @ sK4 @ sK5))) | (sF12 = $true)),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f45])).
% 0.30/0.29 thf(f64,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : (($false = ((sF16 @ X5 @ X4))) | (((cHALF @ X4 @ X5)) = $true)) )),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f52])).
% 0.30/0.29 thf(f65,plain,(
% 0.30/0.29 ( ! [X4 : $i,X5 : $i] : (($false = ((cHALF @ X4 @ X5))) | (((sF16 @ X5 @ X4)) = $true)) )),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f52])).
% 0.30/0.29 thf(f67,plain,(
% 0.30/0.29 (((cDOUBLE @ sK5 @ sK4)) = $true) | ($false = sF11)),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f42])).
% 0.30/0.29 thf(f69,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($false = ((cDOUBLE @ X1 @ X0))) | (((sF7 @ X0 @ X1)) = $true)) )),
% 0.30/0.29 inference(iff_proxy_clausification,[],[f31])).
% 0.30/0.29 thf(f71,definition,(
% 0.30/0.29 spl17_1 <=> (sF10 = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition])).
% 0.30/0.29 thf(f73,plain,(
% 0.30/0.29 (sF10 = $true) | ~spl17_1),
% 0.30/0.29 inference(avatar_component_clause,[],[f71])).
% 0.30/0.29 thf(f80,definition,(
% 0.30/0.29 spl17_3 <=> ($false = sF10)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition])).
% 0.30/0.29 thf(f82,plain,(
% 0.30/0.29 ($false = sF10) | ~spl17_3),
% 0.30/0.29 inference(avatar_component_clause,[],[f80])).
% 0.30/0.29 thf(f84,definition,(
% 0.30/0.29 spl17_4 <=> (((cHALF @ c0 @ c0)) = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition])).
% 0.30/0.29 thf(f86,plain,(
% 0.30/0.29 (((cHALF @ c0 @ c0)) = $true) | ~spl17_4),
% 0.30/0.29 inference(avatar_component_clause,[],[f84])).
% 0.30/0.29 thf(f87,plain,(
% 0.30/0.29 spl17_3 | spl17_4),
% 0.30/0.29 inference(avatar_split_clause,[],[f56,f84,f80])).
% 0.30/0.29 thf(f107,definition,(
% 0.30/0.29 spl17_9 <=> (sF12 = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_9])],[avatar_definition])).
% 0.30/0.29 thf(f111,definition,(
% 0.30/0.29 spl17_10 <=> ($false = ((cHALF @ sK4 @ sK5)))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition])).
% 0.30/0.29 thf(f113,plain,(
% 0.30/0.29 ($false = ((cHALF @ sK4 @ sK5))) | ~spl17_10),
% 0.30/0.29 inference(avatar_component_clause,[],[f111])).
% 0.30/0.29 thf(f114,plain,(
% 0.30/0.29 spl17_9 | spl17_10),
% 0.30/0.29 inference(avatar_split_clause,[],[f63,f111,f107])).
% 0.30/0.29 thf(f125,definition,(
% 0.30/0.29 spl17_13 <=> (((cDOUBLE @ sK5 @ sK4)) = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition])).
% 0.30/0.29 thf(f127,plain,(
% 0.30/0.29 (((cDOUBLE @ sK5 @ sK4)) = $true) | ~spl17_13),
% 0.30/0.29 inference(avatar_component_clause,[],[f125])).
% 0.30/0.29 thf(f129,definition,(
% 0.30/0.29 spl17_14 <=> ($false = sF11)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_14])],[avatar_definition])).
% 0.30/0.29 thf(f131,plain,(
% 0.30/0.29 ($false = sF11) | ~spl17_14),
% 0.30/0.29 inference(avatar_component_clause,[],[f129])).
% 0.30/0.29 thf(f132,plain,(
% 0.30/0.29 spl17_13 | spl17_14),
% 0.30/0.29 inference(avatar_split_clause,[],[f67,f129,f125])).
% 0.30/0.29 thf(f138,definition,(
% 0.30/0.29 spl17_16 <=> (sF11 = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_16])],[avatar_definition])).
% 0.30/0.29 thf(f140,plain,(
% 0.30/0.29 (sF11 = $true) | ~spl17_16),
% 0.30/0.29 inference(avatar_component_clause,[],[f138])).
% 0.30/0.29 thf(f143,plain,(
% 0.30/0.29 spl17_1),
% 0.30/0.29 inference(avatar_split_clause,[],[f41,f71])).
% 0.30/0.29 thf(f144,plain,(
% 0.30/0.29 spl17_16),
% 0.30/0.29 inference(avatar_split_clause,[],[f43,f138])).
% 0.30/0.29 thf(f145,plain,(
% 0.30/0.29 ~spl17_9),
% 0.30/0.29 inference(avatar_split_clause,[],[f46,f107])).
% 0.30/0.29 thf(f146,plain,(
% 0.30/0.29 ($false = $true) | (~spl17_1 | ~spl17_3)),
% 0.30/0.29 inference(forward_demodulation,[],[f82,f73])).
% 0.30/0.29 thf(f147,plain,(
% 0.30/0.29 $false | (~spl17_1 | ~spl17_3)),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f146])).
% 0.30/0.29 thf(f148,plain,(
% 0.30/0.29 ~spl17_1 | ~spl17_3),
% 0.30/0.29 inference(avatar_contradiction_clause,[],[f147])).
% 0.30/0.29 thf(f169,plain,(
% 0.30/0.29 ( ! [X4 : $i] : ((((sF14 @ X4)) = ((sF13 @ (sF13 @ X4))))) )),
% 0.30/0.29 inference(forward_demodulation,[],[f49,f48])).
% 0.30/0.29 thf(f185,plain,(
% 0.30/0.29 ($false = $true) | (~spl17_14 | ~spl17_16)),
% 0.30/0.29 inference(forward_demodulation,[],[f131,f140])).
% 0.30/0.29 thf(f186,plain,(
% 0.30/0.29 $false | (~spl17_14 | ~spl17_16)),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f185])).
% 0.30/0.29 thf(f187,plain,(
% 0.30/0.29 ~spl17_14 | ~spl17_16),
% 0.30/0.29 inference(avatar_contradiction_clause,[],[f186])).
% 0.30/0.29 thf(f209,plain,(
% 0.30/0.29 ($true = ((sF16 @ c0 @ c0))) | ($false = $true) | ~spl17_4),
% 0.30/0.29 inference(constrained_superposition,[],[f86,f65])).
% 0.30/0.29 thf(f212,plain,(
% 0.30/0.29 ($true = ((sF16 @ c0 @ c0))) | ~spl17_4),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f209])).
% 0.30/0.29 thf(f240,plain,(
% 0.30/0.29 (((sF7 @ sK4 @ sK5)) = $true) | ($false = $true) | ~spl17_13),
% 0.30/0.29 inference(constrained_superposition,[],[f69,f127])).
% 0.30/0.29 thf(f246,plain,(
% 0.30/0.29 (((sF7 @ sK4 @ sK5)) = $true) | ~spl17_13),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f240])).
% 0.30/0.29 thf(f262,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($true != ((sF16 @ c0 @ c0))) | (((sF16 @ X0 @ X1)) = $true) | (((cHALF @ (sK3 @ sF16) @ (sK2 @ sF16))) = $true) | ($true != ((sP0 @ X0 @ X1)))) )),
% 0.30/0.29 inference(constrained_superposition,[],[f64,f15])).
% 0.30/0.29 thf(f271,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF16 @ X0 @ X1)) = $true) | (((cHALF @ (sK3 @ sF16) @ (sK2 @ sF16))) = $true) | ($true != ((sF16 @ c0 @ c0))) | ($true != ((sP0 @ X0 @ X1)))) )),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f262])).
% 0.30/0.29 thf(f301,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF16 @ X0 @ X1)) = $true) | (((cHALF @ (sK3 @ sF16) @ (sK2 @ sF16))) = $true) | ($true != ((sP0 @ X0 @ X1)))) ) | ~spl17_4),
% 0.30/0.29 inference(forward_subsumption_resolution,[],[f271,f212])).
% 0.30/0.29 thf(f304,definition,(
% 0.30/0.29 spl17_23 <=> (((cHALF @ (sK3 @ sF16) @ (sK2 @ sF16))) = $true)),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_23])],[avatar_definition])).
% 0.30/0.29 thf(f306,plain,(
% 0.30/0.29 (((cHALF @ (sK3 @ sF16) @ (sK2 @ sF16))) = $true) | ~spl17_23),
% 0.30/0.29 inference(avatar_component_clause,[],[f304])).
% 0.30/0.29 thf(f308,definition,(
% 0.30/0.29 spl17_24 <=> ! [X0 : $i,X1 : $i] : ((((sF16 @ X0 @ X1)) = $true) | ($true != ((sP0 @ X0 @ X1))))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_24])],[avatar_definition])).
% 0.30/0.29 thf(f309,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF16 @ X0 @ X1)) = $true) | ($true != ((sP0 @ X0 @ X1)))) ) | ~spl17_24),
% 0.30/0.29 inference(avatar_component_clause,[],[f308])).
% 0.30/0.29 thf(f320,plain,(
% 0.30/0.29 spl17_23 | spl17_24 | ~spl17_4),
% 0.30/0.29 inference(avatar_split_clause,[],[f301,f84,f308,f304])).
% 0.30/0.29 thf(f345,plain,(
% 0.30/0.29 (((sF16 @ (sK2 @ sF16) @ (sK3 @ sF16))) = $true) | ($false = $true) | ~spl17_23),
% 0.30/0.29 inference(constrained_superposition,[],[f306,f65])).
% 0.30/0.29 thf(f347,plain,(
% 0.30/0.29 (((sF16 @ (sK2 @ sF16) @ (sK3 @ sF16))) = $true) | ~spl17_23),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f345])).
% 0.30/0.29 thf(f353,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : ((((X5 @ c0 @ c0)) != $true) | (((X5 @ X1 @ X0)) = $true) | ($true != ((sP0 @ X1 @ X0))) | (((X5 @ (sF13 @ (sK2 @ X5)) @ (cS @ (cS @ (sK3 @ X5))))) != $true)) )),
% 0.30/0.29 inference(forward_demodulation,[],[f16,f48])).
% 0.30/0.29 thf(f354,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : ((((X5 @ X1 @ X0)) = $true) | (((X5 @ c0 @ c0)) != $true) | ($true != ((sP0 @ X1 @ X0))) | (((X5 @ (sF13 @ (sK2 @ X5)) @ (sF13 @ (cS @ (sK3 @ X5))))) != $true)) )),
% 0.30/0.29 inference(forward_demodulation,[],[f353,f48])).
% 0.30/0.29 thf(f355,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : ((((X5 @ (sF13 @ (sK2 @ X5)) @ (sF13 @ (sF13 @ (sK3 @ X5))))) != $true) | (((X5 @ X1 @ X0)) = $true) | ($true != ((sP0 @ X1 @ X0))) | (((X5 @ c0 @ c0)) != $true)) )),
% 0.30/0.29 inference(forward_demodulation,[],[f354,f48])).
% 0.30/0.29 thf(f356,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i,X5 : ($i > $i > $o)] : (($true != ((X5 @ (sF13 @ (sK2 @ X5)) @ (sF14 @ (sK3 @ X5))))) | (((X5 @ c0 @ c0)) != $true) | ($true != ((sP0 @ X1 @ X0))) | (((X5 @ X1 @ X0)) = $true)) )),
% 0.30/0.29 inference(forward_demodulation,[],[f355,f169])).
% 0.30/0.29 thf(f384,plain,(
% 0.30/0.29 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ c0 @ c0)) != $true) | ($true != $true) | ($false = ((X0 @ (sF13 @ (sK2 @ X0)) @ (sF14 @ (sK3 @ X0))))) | ($true != ((sP0 @ X1 @ X2))) | (((X0 @ X1 @ X2)) = $true)) )),
% 0.30/0.29 inference(constrained_superposition,[],[f356,f28])).
% 0.30/0.29 thf(f391,plain,(
% 0.30/0.29 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : (($false = ((X0 @ (sF13 @ (sK2 @ X0)) @ (sF14 @ (sK3 @ X0))))) | ($true != ((sP0 @ X1 @ X2))) | (((X0 @ c0 @ c0)) != $true) | (((X0 @ X1 @ X2)) = $true)) )),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f384])).
% 0.30/0.29 thf(f538,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF16 @ (sF13 @ X1) @ (sF14 @ X0))) = $true) | ($false = $true) | ($false = ((sF15 @ X1 @ X0)))) )),
% 0.30/0.29 inference(constrained_superposition,[],[f59,f65])).
% 0.30/0.29 thf(f542,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((sF16 @ (sF13 @ X1) @ (sF14 @ X0))) = $true) | ($false = ((sF15 @ X1 @ X0)))) )),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f538])).
% 0.30/0.29 thf(f592,definition,(
% 0.30/0.29 spl17_34 <=> ($false = ((sF15 @ (sK2 @ sF16) @ (sK3 @ sF16))))),
% 0.30/0.29 introduced(definition,[new_symbols(definition,[spl17_34])],[avatar_definition])).
% 0.30/0.29 thf(f594,plain,(
% 0.30/0.29 ($false = ((sF15 @ (sK2 @ sF16) @ (sK3 @ sF16)))) | ~spl17_34),
% 0.30/0.29 inference(avatar_component_clause,[],[f592])).
% 0.30/0.29 thf(f710,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($true != ((sP0 @ X0 @ X1))) | (((cHALF @ X1 @ X0)) = $true)) ) | ~spl17_24),
% 0.30/0.29 inference(constrained_superposition,[],[f64,f309])).
% 0.30/0.29 thf(f719,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : ((((cHALF @ X1 @ X0)) = $true) | ($true != ((sP0 @ X0 @ X1)))) ) | ~spl17_24),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f710])).
% 0.30/0.29 thf(f731,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((sF16 @ c0 @ c0))) | ($true != ((sP0 @ X0 @ X1))) | ($false = ((sF15 @ (sK2 @ sF16) @ (sK3 @ sF16)))) | ($false = $true) | (((sF16 @ X0 @ X1)) = $true)) )),
% 0.30/0.29 inference(constrained_superposition,[],[f391,f542])).
% 0.30/0.29 thf(f766,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((sP0 @ X0 @ X1))) | ($false = ((sF15 @ (sK2 @ sF16) @ (sK3 @ sF16)))) | ($true != ((sF16 @ c0 @ c0))) | (((sF16 @ X0 @ X1)) = $true)) )),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f731])).
% 0.30/0.29 thf(f812,plain,(
% 0.30/0.29 ($true != ((sP0 @ sK5 @ sK4))) | ($false = $true) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(constrained_superposition,[],[f113,f719])).
% 0.30/0.29 thf(f815,plain,(
% 0.30/0.29 ($true != ((sP0 @ sK5 @ sK4))) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f812])).
% 0.30/0.29 thf(f848,plain,(
% 0.30/0.29 ($false = ((sF6 @ sK4 @ sK5))) | ($true != $true) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(constrained_superposition,[],[f815,f55])).
% 0.30/0.29 thf(f851,plain,(
% 0.30/0.29 ($false = ((sF6 @ sK4 @ sK5))) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f848])).
% 0.30/0.29 thf(f853,plain,(
% 0.30/0.29 ($false = $true) | (((sF7 @ sK4 @ sK5)) != $true) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(constrained_superposition,[],[f851,f32])).
% 0.30/0.29 thf(f858,plain,(
% 0.30/0.29 (((sF7 @ sK4 @ sK5)) != $true) | (~spl17_10 | ~spl17_24)),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f853])).
% 0.30/0.29 thf(f861,plain,(
% 0.30/0.29 $false | (~spl17_10 | ~spl17_13 | ~spl17_24)),
% 0.30/0.29 inference(forward_subsumption_resolution,[],[f858,f246])).
% 0.30/0.29 thf(f862,plain,(
% 0.30/0.29 ~spl17_10 | ~spl17_13 | ~spl17_24),
% 0.30/0.29 inference(avatar_contradiction_clause,[],[f861])).
% 0.30/0.29 thf(f864,plain,(
% 0.30/0.29 ( ! [X0 : $i,X1 : $i] : (($false = ((sF15 @ (sK2 @ sF16) @ (sK3 @ sF16)))) | ($true != ((sP0 @ X0 @ X1))) | (((sF16 @ X0 @ X1)) = $true)) ) | ~spl17_4),
% 0.30/0.29 inference(forward_subsumption_resolution,[],[f766,f212])).
% 0.30/0.29 thf(f866,plain,(
% 0.30/0.29 spl17_24 | spl17_34 | ~spl17_4),
% 0.30/0.29 inference(avatar_split_clause,[],[f864,f84,f592,f308])).
% 0.30/0.29 thf(f876,plain,(
% 0.30/0.29 (((sF16 @ (sK2 @ sF16) @ (sK3 @ sF16))) != $true) | ($false = $true) | ~spl17_34),
% 0.30/0.29 inference(constrained_superposition,[],[f594,f53])).
% 0.30/0.29 thf(f880,plain,(
% 0.30/0.29 (((sF16 @ (sK2 @ sF16) @ (sK3 @ sF16))) != $true) | ~spl17_34),
% 0.30/0.29 inference(trivial_inequality_removal,[],[f876])).
% 0.30/0.29 thf(f885,plain,(
% 0.30/0.29 $false | (~spl17_23 | ~spl17_34)),
% 0.30/0.29 inference(forward_subsumption_resolution,[],[f880,f347])).
% 0.30/0.29 thf(f886,plain,(
% 0.30/0.29 ~spl17_23 | ~spl17_34),
% 0.30/0.29 inference(avatar_contradiction_clause,[],[f885])).
% 0.30/0.29 cnf(s2, plain, spl17_3 | spl17_4, inference(sat_conversion,[],[f87])).
% 0.30/0.29 cnf(s5, plain, spl17_9 | spl17_10, inference(sat_conversion,[],[f114])).
% 0.30/0.29 cnf(s7, plain, spl17_13 | spl17_14, inference(sat_conversion,[],[f132])).
% 0.30/0.29 cnf(s10, plain, spl17_1, inference(sat_conversion,[],[f143])).
% 0.30/0.29 cnf(s11, plain, spl17_16, inference(sat_conversion,[],[f144])).
% 0.30/0.29 cnf(s12, plain, ~spl17_9, inference(sat_conversion,[],[f145])).
% 0.30/0.29 cnf(s13, plain, ~spl17_1 | ~spl17_3, inference(sat_conversion,[],[f148])).
% 0.30/0.29 cnf(s18, plain, ~spl17_14 | ~spl17_16, inference(sat_conversion,[],[f187])).
% 0.30/0.29 cnf(s26, plain, ~spl17_4 | spl17_23 | spl17_24, inference(sat_conversion,[],[f320])).
% 0.30/0.29 cnf(s43, plain, ~spl17_10 | ~spl17_13 | ~spl17_24, inference(sat_conversion,[],[f862])).
% 0.30/0.29 cnf(s45, plain, ~spl17_4 | spl17_24 | spl17_34, inference(sat_conversion,[],[f866])).
% 0.30/0.29 cnf(s46, plain, ~spl17_23 | ~spl17_34, inference(sat_conversion,[],[f886])).
% 0.30/0.29 cnf(s54, plain, ~spl17_14, inference(rat,[],[s18,s11])).
% 0.30/0.29 cnf(s55, plain, ~spl17_3, inference(rat,[],[s13,s10])).
% 0.30/0.29 cnf(s57, plain, spl17_13, inference(rat,[],[s7,s54])).
% 0.30/0.29 cnf(s59, plain, spl17_10, inference(rat,[],[s5,s12])).
% 0.30/0.29 cnf(s60, plain, ~spl17_24, inference(rat,[],[s43,s57,s59])).
% 0.30/0.29 cnf(s62, plain, spl17_4, inference(rat,[],[s2,s55])).
% 0.30/0.29 cnf(s63, plain, spl17_34, inference(rat,[],[s45,s60,s62])).
% 0.30/0.29 cnf(s65, plain, spl17_23, inference(rat,[],[s26,s60,s62])).
% 0.30/0.29 cnf(s67, plain, $false, inference(rat,[],[s46,s63,s65])).
% 0.30/0.29 thf(f889,plain,(
% 0.30/0.29 $false),
% 0.30/0.29 inference(avatar_sat_refutation,[],[s67])).
% 0.30/0.29 % SZS output end Proof for theBenchmark
% 0.30/0.29 % (325661)------------------------------
% 0.30/0.29 % (325661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.29 % (325661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.29 % (325661)CaDiCaL version: 2.1.3
% 0.30/0.29 % (325661)Termination reason: Refutation
% 0.30/0.29 % (325661)Time elapsed: 0.035 s
% 0.30/0.29 % (325661)Peak memory usage: 13 MB
% 0.30/0.29 % (325661)Instructions burned: 62 (million)
% 0.30/0.29 % (325650)Success in time 0.059 s
% 0.30/0.29 % Vampire exiting
%------------------------------------------------------------------------------