0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.12/0.39 % Computer : n015.cluster.edu 0.12/0.39 % Model : x86_64 x86_64 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.39 % Memory : 8046.5625MB 0.12/0.39 % OS : Linux 6.8.0-71-generic 0.12/0.39 % CPULimit : 1440 0.12/0.39 % WCLimit : 180 0.12/0.39 % DateTime : Mon Jul 27 12:23:35 UTC 2026 0.12/0.39 % CPUTime : 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.12/0.43 Running higher-order theorem proving 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.51 % (998006)Detected a higher-order problem, will run a greedy HOL sequence. 0.19/0.51 % (998017)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.19/0.51 % (998017)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 0.19/0.51 % (998017)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=3250110772:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.19/0.51 % (998014)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=3104124765: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_1799 on theBenchmark for (1799ds/634Mi) 0.19/0.51 % (998013)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3030898530:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.19/0.51 % (998012)lrs+10_16_si=on:nwc=1.5:random_seed=4238131412:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.19/0.51 % (998011)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=218546679:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.19/0.51 % (998016)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2300880747:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.19/0.51 % (998015)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2307041344:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.19/0.51 % (998013)Refutation not found, incomplete strategy 0.19/0.51 % (998013)------------------------------ 0.19/0.51 % (998013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.51 % (998013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.51 % (998013)CaDiCaL version: 2.1.3 0.19/0.51 % (998013)Termination reason: Refutation not found, incomplete strategy 0.19/0.51 % (998013)Time elapsed: 0.003 s 0.19/0.51 % (998013)Peak memory usage: 12 MB 0.19/0.51 % (998013)Instructions burned: 4 (million) 0.19/0.51 % (998013)------------------------------ 0.19/0.51 % (998013)------------------------------ 0.19/0.51 % (998017)Refutation not found, incomplete strategy 0.19/0.51 % (998017)------------------------------ 0.19/0.51 % (998017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.51 % (998017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.51 % (998017)CaDiCaL version: 2.1.3 0.19/0.51 % (998017)Termination reason: Refutation not found, incomplete strategy 0.19/0.51 % (998017)Time elapsed: 0.013 s 0.19/0.51 % (998017)Peak memory usage: 13 MB 0.19/0.51 % (998017)Instructions burned: 41 (million) 0.19/0.51 % (998017)------------------------------ 0.19/0.51 % (998017)------------------------------ 0.19/0.51 % (998012)Instruction limit reached! 0.19/0.51 % (998012)------------------------------ 0.19/0.51 % (998012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.51 % (998012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.51 % (998012)CaDiCaL version: 2.1.3 0.19/0.51 % (998012)Termination reason: Instruction limit 0.19/0.51 % (998012)Termination phase: Saturation 0.19/0.51 % (998012)Time elapsed: 0.010 s 0.19/0.51 % (998012)Peak memory usage: 12 MB 0.19/0.51 % (998012)Instructions burned: 19 (million) 0.19/0.51 % (998015)Instruction limit reached! 0.19/0.51 % (998015)------------------------------ 0.19/0.51 % (998015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.51 % (998015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.51 % (998015)CaDiCaL version: 2.1.3 0.19/0.51 % (998015)Termination reason: Instruction limit 0.19/0.51 % (998015)Termination phase: Saturation 0.19/0.51 % (998015)Time elapsed: 0.014 s 0.19/0.51 % (998015)Peak memory usage: 12 MB 0.19/0.51 % (998015)Instructions burned: 24 (million) 0.19/0.51 % (998014) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-998006-998014"... 0.19/0.51 % (998014)...printing done. 0.19/0.51 % (998014)Refutation found. Thanks to Tanya! 0.19/0.51 % SZS status Theorem for theBenchmark 0.19/0.51 % SZS output start Proof for theBenchmark 0.19/0.51 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 0.19/0.51 thf(func_def_0, type, in: ($i > $i > $o)). 0.19/0.51 thf(func_def_1, type, subset: ($i > $i > $o)). 0.19/0.51 thf(func_def_2, type, subsetI1: $o). 0.19/0.51 thf(func_def_4, type, kpair: ($i > $i > $i)). 0.19/0.51 thf(func_def_5, type, cartprod: ($i > $i > $i)). 0.19/0.51 thf(func_def_6, type, breln: ($i > $i > $i > $o)). 0.19/0.51 thf(func_def_7, type, brelnall1: $o). 0.19/0.51 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)). 0.19/0.51 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)). 0.19/0.51 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)). 0.19/0.51 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 0.19/0.51 thf(func_def_14, type, sK0: (($i > $o) > $i > $i > $i > $i)). 0.19/0.51 thf(func_def_15, type, sK1: (($i > $o) > $i > $i > $i > $i)). 0.19/0.51 thf(func_def_19, type, sK5: ($i > $o)). 0.19/0.51 thf(func_def_27, type, sK13: ($i > $i > $i)). 0.19/0.51 thf(func_def_28, type, vNOT: ($o > $o)). 0.19/0.51 thf(func_def_30, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 0.19/0.51 thf(f1,axiom,( 0.19/0.51 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)), 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)). 0.19/0.51 thf(f3,axiom,( 0.19/0.51 (! [X1 : $i,X0 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))) = brelnall1)), 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1)). 0.19/0.51 thf(f4,conjecture,( 0.19/0.51 subsetI1 => (brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))))), 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln)). 0.19/0.51 thf(f5,negated_conjecture,( 0.19/0.51 ~(subsetI1 => (brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3))))))), 0.19/0.51 inference(negated_conjecture,[status(cth)],[f4])). 0.19/0.51 thf(f6,plain,( 0.19/0.51 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)), 0.19/0.51 inference(rectify,[],[f1])). 0.19/0.51 thf(f7,plain,( 0.19/0.51 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0))))), 0.19/0.51 inference(fool_elimination,[],[f6])). 0.19/0.51 thf(f8,plain,( 0.19/0.51 ~(subsetI1 => (brelnall1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : $i] : ((breln @ X1 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X0 @ X3))))))), 0.19/0.51 inference(rectify,[],[f5])). 0.19/0.51 thf(f9,plain,( 0.19/0.51 ~((subsetI1 = $true) => ((brelnall1 = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((breln @ X1 @ X2 @ X3)) = $true) => (! [X4 : $i] : (($true = ((in @ X4 @ X1))) => ! [X5 : $i] : (($true = ((in @ X5 @ X2))) => ((((in @ (kpair @ X4 @ X5) @ X0)) = $true) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => ($true = ((subset @ X0 @ X3))))))))), 0.19/0.51 inference(fool_elimination,[],[f8])). 0.19/0.51 thf(f10,plain,( 0.19/0.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))) = brelnall1)), 0.19/0.51 inference(rectify,[],[f3])). 0.19/0.51 thf(f11,plain,( 0.19/0.51 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) => ! [X3 : ($i > $o)] : (! [X4 : $i] : (($true = ((in @ X4 @ X1))) => ! [X5 : $i] : (($true = ((in @ X5 @ X0))) => ((((in @ (kpair @ X4 @ X5) @ X2)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : (($true = ((in @ X6 @ X2))) => ($true = ((X3 @ X6)))))) <=> (brelnall1 = $true)), 0.19/0.51 inference(fool_elimination,[],[f10])). 0.19/0.51 thf(f13,plain,( 0.19/0.51 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))), 0.19/0.51 inference(ennf_transformation,[],[f7])). 0.19/0.51 thf(f14,plain,( 0.19/0.51 (? [X2 : $i,X0 : $i,X1 : $i] : (? [X3 : $i] : ((($true != ((subset @ X0 @ X3))) & ! [X4 : $i] : (! [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true)) | ($true != ((in @ X5 @ X2)))) | ($true != ((in @ X4 @ X1))))) & (((breln @ X1 @ X2 @ X3)) = $true)) & (((breln @ X1 @ X2 @ X0)) = $true)) & (brelnall1 = $true)) & (subsetI1 = $true)), 0.19/0.51 inference(ennf_transformation,[],[f9])). 0.19/0.51 thf(f15,plain,( 0.19/0.51 (brelnall1 = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) & ? [X3 : $i] : ((((breln @ X1 @ X2 @ X3)) = $true) & ($true != ((subset @ X0 @ X3))) & ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true) | ($true != ((in @ X5 @ X2))))))) & (subsetI1 = $true)), 0.19/0.51 inference(flattening,[],[f14])). 0.19/0.51 thf(f16,plain,( 0.19/0.51 ! [X1 : $i,X2 : $i,X0 : $i] : (! [X3 : ($i > $o)] : (! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))) | ? [X4 : $i] : (? [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X5 @ X0)))) & ($true = ((in @ X4 @ X1))))) | ($true != ((breln @ X1 @ X0 @ X2)))) <=> (brelnall1 = $true)), 0.19/0.51 inference(ennf_transformation,[],[f11])). 0.19/0.51 thf(f17,plain,( 0.19/0.51 ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X1 @ X0 @ X2))) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X0))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))))) <=> (brelnall1 = $true)), 0.19/0.51 inference(flattening,[],[f16])). 0.19/0.51 thf(f18,plain,( 0.19/0.51 (! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X1 @ X0 @ X2))) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X0))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) & ? [X3 : ($i > $o)] : (! [X4 : $i] : (! [X5 : $i] : (($true != ((in @ X5 @ X0))) | (((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true)) | ($true != ((in @ X4 @ X1)))) & ? [X6 : $i] : (($true != ((X3 @ X6))) & ($true = ((in @ X6 @ X2)))))))), 0.19/0.51 inference(nnf_transformation,[],[f17])). 0.19/0.51 thf(f19,plain,( 0.19/0.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X2 @ X0)) != $true) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X2))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X0)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X8 @ X9 @ X7)) = $true) & ? [X10 : ($i > $o)] : (! [X11 : $i] : (! [X12 : $i] : (($true != ((in @ X12 @ X9))) | (((X10 @ (kpair @ X11 @ X12))) = $true) | ($true != ((in @ (kpair @ X11 @ X12) @ X7)))) | (((in @ X11 @ X8)) != $true)) & ? [X13 : $i] : (($true != ((X10 @ X13))) & ($true = ((in @ X13 @ X7)))))))), 0.19/0.51 inference(rectify,[],[f18])). 0.19/0.51 thf(f20,plain,( 0.19/0.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X2 @ X0)) != $true) | ! [X3 : ($i > $o)] : (((($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) & (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) & ($true = ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X0)))) & (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true)) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | (($true = ((breln @ sK3 @ sK4 @ sK2))) & (! [X11 : $i] : (! [X12 : $i] : (($true != ((in @ X12 @ sK4))) | (((sK5 @ (kpair @ X11 @ X12))) = $true) | ($true != ((in @ (kpair @ X11 @ X12) @ sK2)))) | (((in @ X11 @ sK3)) != $true)) & (($true != ((sK5 @ sK6))) & ($true = ((in @ sK6 @ sK2)))))))), 0.19/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4,sK5,sK6]),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0),skolemize(X7,sK2),skolemize(X8,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f19])). 0.19/0.51 thf(f21,plain,( 0.19/0.51 (brelnall1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) & ? [X3 : $i] : (($true = ((breln @ X1 @ X0 @ X3))) & (((subset @ X2 @ X3)) != $true) & ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | ($true != ((in @ X5 @ X0))))))) & (subsetI1 = $true)), 0.19/0.51 inference(rectify,[],[f15])). 0.19/0.51 thf(f22,plain,( 0.19/0.51 (brelnall1 = $true) & (($true = ((breln @ sK8 @ sK7 @ sK9))) & (($true = ((breln @ sK8 @ sK7 @ sK10))) & ($true != ((subset @ sK9 @ sK10))) & ! [X4 : $i] : ((((in @ X4 @ sK8)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK10)) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK9))) | (((in @ X5 @ sK7)) != $true))))) & (subsetI1 = $true)), 0.19/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f21])). 0.19/0.51 thf(f23,plain,( 0.19/0.51 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true))), 0.19/0.51 inference(nnf_transformation,[],[f13])). 0.19/0.51 thf(f24,plain,( 0.19/0.51 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ? [X5 : $i] : (($true = ((in @ X5 @ X3))) & ($true != ((in @ X5 @ X4))))) | (subsetI1 != $true))), 0.19/0.51 inference(rectify,[],[f23])). 0.19/0.51 thf(f25,plain,( 0.19/0.51 ((subsetI1 = $true) | (($true != ((subset @ sK11 @ sK12))) & ! [X2 : $i] : (($true != ((in @ X2 @ sK11))) | ($true = ((in @ X2 @ sK12)))))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (($true = ((in @ (sK13 @ X4 @ X3) @ X3))) & ($true != ((in @ (sK13 @ X4 @ X3) @ X4))))) | (subsetI1 != $true))), 0.19/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,vAPP]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0)],[f24])). 0.19/0.51 thf(f30,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (brelnall1 != $true) | (((breln @ X1 @ X2 @ X0)) != $true)) )), 0.19/0.51 inference(cnf_transformation,[],[f20])). 0.19/0.51 thf(f32,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : (($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | (brelnall1 != $true) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | ($true = ((X3 @ X6)))) )), 0.19/0.51 inference(cnf_transformation,[],[f20])). 0.19/0.51 thf(f33,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((brelnall1 != $true) | ($true = ((X3 @ X6))) | ($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true != ((in @ X6 @ X0)))) )), 0.19/0.51 inference(cnf_transformation,[],[f20])). 0.19/0.51 thf(f34,plain,( 0.19/0.51 (subsetI1 = $true)), 0.19/0.51 inference(cnf_transformation,[],[f22])). 0.19/0.51 thf(f35,plain,( 0.19/0.51 ( ! [X4 : $i,X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK10)) = $true) | (((in @ X4 @ sK8)) != $true) | (((in @ X5 @ sK7)) != $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK9)))) )), 0.19/0.51 inference(cnf_transformation,[],[f22])). 0.19/0.51 thf(f36,plain,( 0.19/0.51 ($true != ((subset @ sK9 @ sK10)))), 0.19/0.51 inference(cnf_transformation,[],[f22])). 0.19/0.51 thf(f38,plain,( 0.19/0.51 ($true = ((breln @ sK8 @ sK7 @ sK9)))), 0.19/0.51 inference(cnf_transformation,[],[f22])). 0.19/0.51 thf(f39,plain,( 0.19/0.51 (brelnall1 = $true)), 0.19/0.51 inference(cnf_transformation,[],[f22])). 0.19/0.51 thf(f41,plain,( 0.19/0.51 ( ! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (subsetI1 != $true) | ($true != ((in @ (sK13 @ X4 @ X3) @ X4)))) )), 0.19/0.51 inference(cnf_transformation,[],[f25])). 0.19/0.51 thf(f42,plain,( 0.19/0.51 ( ! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ($true = ((in @ (sK13 @ X4 @ X3) @ X3))) | (subsetI1 != $true)) )), 0.19/0.51 inference(cnf_transformation,[],[f25])). 0.19/0.51 thf(f47,definition,( 0.19/0.51 spl14_1 <=> (subsetI1 = $true)), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])). 0.19/0.51 thf(f56,definition,( 0.19/0.51 spl14_3 <=> (brelnall1 = $true)), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])). 0.19/0.51 thf(f69,definition,( 0.19/0.51 spl14_6 <=> ! [X6 : $i,X0 : $i,X3 : ($i > $o),X2 : $i,X1 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0))))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition])). 0.19/0.51 thf(f70,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (((breln @ X1 @ X2 @ X0)) != $true)) ) | ~spl14_6), 0.19/0.51 inference(avatar_component_clause,[],[f69])). 0.19/0.51 thf(f71,plain,( 0.19/0.51 spl14_6 | ~spl14_3), 0.19/0.51 inference(avatar_split_clause,[],[f30,f56,f69])). 0.19/0.51 thf(f78,definition,( 0.19/0.51 spl14_8 <=> ! [X3 : ($i > $o),X0 : $i,X6 : $i,X2 : $i,X1 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition])). 0.19/0.51 thf(f79,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : (($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))) ) | ~spl14_8), 0.19/0.51 inference(avatar_component_clause,[],[f78])). 0.19/0.51 thf(f80,plain,( 0.19/0.51 ~spl14_3 | spl14_8), 0.19/0.51 inference(avatar_split_clause,[],[f33,f78,f56])). 0.19/0.51 thf(f92,definition,( 0.19/0.51 spl14_11 <=> ! [X2 : $i,X3 : ($i > $o),X0 : $i,X6 : $i,X1 : $i] : (($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | (((breln @ X1 @ X2 @ X0)) != $true))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition])). 0.19/0.51 thf(f93,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | ($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6)))) ) | ~spl14_11), 0.19/0.51 inference(avatar_component_clause,[],[f92])). 0.19/0.51 thf(f94,plain,( 0.19/0.51 spl14_11 | ~spl14_3), 0.19/0.51 inference(avatar_split_clause,[],[f32,f56,f92])). 0.19/0.51 thf(f96,definition,( 0.19/0.51 spl14_12 <=> ($true = ((subset @ sK9 @ sK10)))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition])). 0.19/0.51 thf(f98,plain,( 0.19/0.51 ($true != ((subset @ sK9 @ sK10))) | spl14_12), 0.19/0.51 inference(avatar_component_clause,[],[f96])). 0.19/0.51 thf(f99,plain,( 0.19/0.51 ~spl14_12), 0.19/0.51 inference(avatar_split_clause,[],[f36,f96])). 0.19/0.51 thf(f113,plain,( 0.19/0.51 spl14_1), 0.19/0.51 inference(avatar_split_clause,[],[f34,f47])). 0.19/0.51 thf(f115,definition,( 0.19/0.51 spl14_16 <=> ! [X4 : $i,X3 : $i] : (($true = ((subset @ X3 @ X4))) | ($true = ((in @ (sK13 @ X4 @ X3) @ X3))))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition])). 0.19/0.51 thf(f116,plain,( 0.19/0.51 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK13 @ X4 @ X3) @ X3))) | ($true = ((subset @ X3 @ X4)))) ) | ~spl14_16), 0.19/0.51 inference(avatar_component_clause,[],[f115])). 0.19/0.51 thf(f117,plain,( 0.19/0.51 spl14_16 | ~spl14_1), 0.19/0.51 inference(avatar_split_clause,[],[f42,f47,f115])). 0.19/0.51 thf(f119,definition,( 0.19/0.51 spl14_17 <=> ! [X4 : $i,X3 : $i] : (($true = ((subset @ X3 @ X4))) | ($true != ((in @ (sK13 @ X4 @ X3) @ X4))))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition])). 0.19/0.51 thf(f120,plain,( 0.19/0.51 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK13 @ X4 @ X3) @ X4))) | ($true = ((subset @ X3 @ X4)))) ) | ~spl14_17), 0.19/0.51 inference(avatar_component_clause,[],[f119])). 0.19/0.51 thf(f121,plain,( 0.19/0.51 spl14_17 | ~spl14_1), 0.19/0.51 inference(avatar_split_clause,[],[f41,f47,f119])). 0.19/0.51 thf(f122,plain,( 0.19/0.51 spl14_3), 0.19/0.51 inference(avatar_split_clause,[],[f39,f56])). 0.19/0.51 thf(f124,definition,( 0.19/0.51 spl14_18 <=> ($true = ((breln @ sK8 @ sK7 @ sK9)))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition])). 0.19/0.51 thf(f126,plain,( 0.19/0.51 ($true = ((breln @ sK8 @ sK7 @ sK9))) | ~spl14_18), 0.19/0.51 inference(avatar_component_clause,[],[f124])). 0.19/0.51 thf(f127,plain,( 0.19/0.51 spl14_18), 0.19/0.51 inference(avatar_split_clause,[],[f38,f124])). 0.19/0.51 thf(f137,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((kpair @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3))) = X0) | ($true != ((breln @ X2 @ X1 @ X3))) | ($true != ((in @ X0 @ X3)))) ) | ~spl14_11), 0.19/0.51 inference(leibniz_equality_elimination,[],[f93])). 0.19/0.51 thf(f162,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK7))) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK8))) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X0 @ X3))) | ($true != ((breln @ X2 @ X1 @ X3)))) ) | ~spl14_11), 0.19/0.51 inference(superposition,[],[f35,f137])). 0.19/0.51 thf(f170,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2))) | ($true != $true) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ X3 @ X2))) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | (((in @ X0 @ sK9)) != $true) | ($true = ((in @ X0 @ sK10)))) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(superposition,[],[f162,f79])). 0.19/0.51 thf(f171,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8)))) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(duplicate_literal_removal,[],[f170])). 0.19/0.51 thf(f172,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ sK10))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ X3 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)))) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(trivial_inequality_removal,[],[f171])). 0.19/0.51 thf(f173,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((~ (X3 = X0))) = $true) | ($true != ((in @ X3 @ X2))) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2)))) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(beta-eta_normalization,[],[f172])). 0.19/0.51 thf(f174,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($false = ((X3 = X0))) | (((in @ X0 @ sK9)) != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X0 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ X3 @ X2)))) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(not_proxy_clausification,[],[f173])). 0.19/0.51 thf(f175,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ X3 @ X2))) | (((in @ X0 @ sK9)) != $true) | (X0 != X3)) ) | (~spl14_8 | ~spl14_11)), 0.19/0.51 inference(equality_proxy_clausification,[],[f174])). 0.19/0.51 thf(f206,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ sK9)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | ($true != ((in @ X3 @ X1))) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true = ((in @ X0 @ sK10))) | ($true != $true) | (X0 != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(superposition,[],[f175,f70])). 0.19/0.51 thf(f207,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != $true) | (X0 != X2) | (((in @ X2 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X1)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(duplicate_literal_removal,[],[f206])). 0.19/0.51 thf(f208,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != ((in @ X3 @ X1))) | (((in @ X2 @ X1)) != $true) | (X0 != X2) | (((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(trivial_inequality_removal,[],[f207])). 0.19/0.51 thf(f209,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | (X0 != X2) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X2 @ X1)) != $true) | (((~ (X3 = X0))) = $true) | ($true != ((in @ X3 @ X1)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(beta-eta_normalization,[],[f208])). 0.19/0.51 thf(f210,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 != X2) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X1))) | ($false = ((X3 = X0))) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(not_proxy_clausification,[],[f209])). 0.19/0.51 thf(f211,plain,( 0.19/0.51 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((breln @ sK8 @ sK7 @ X1)) != $true) | ($true != ((in @ X3 @ X1))) | (((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | (((in @ X2 @ X1)) != $true) | (X0 != X3) | (X0 != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)), 0.19/0.51 inference(equality_proxy_clausification,[],[f210])). 0.19/0.51 thf(f213,plain,( 0.19/0.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ sK10))) | (X1 != X2) | ($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9))) | ($true != $true) | (X0 != X1) | (((in @ X2 @ sK9)) != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)), 0.19/0.51 inference(superposition,[],[f211,f126])). 0.19/0.51 thf(f219,plain,( 0.19/0.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ sK9)) != $true) | (X0 != X1) | (((in @ X0 @ sK9)) != $true) | ($true != $true) | (X1 != X2) | ($true != ((in @ X1 @ sK9))) | ($true = ((in @ X1 @ sK10)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)), 0.19/0.51 inference(duplicate_literal_removal,[],[f213])). 0.19/0.51 thf(f220,plain,( 0.19/0.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ sK10))) | ($true != ((in @ X1 @ sK9))) | (((in @ X2 @ sK9)) != $true) | (((in @ X0 @ sK9)) != $true) | (X1 != X2) | (X0 != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)), 0.19/0.51 inference(trivial_inequality_removal,[],[f219])). 0.19/0.51 thf(f221,plain,( 0.19/0.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK9))) | ($true != $true) | (((in @ X2 @ sK9)) != $true) | (((in @ (sK13 @ sK10 @ X0) @ sK9)) != $true) | (((sK13 @ sK10 @ X0)) != X2) | ($true = ((subset @ X0 @ sK10))) | (((sK13 @ sK10 @ X0)) != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(superposition,[],[f120,f220])). 0.19/0.51 thf(f222,plain,( 0.19/0.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK13 @ sK10 @ X0) @ sK9)) != $true) | ($true = ((subset @ X0 @ sK10))) | ($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ X0)) != X1) | (((in @ X2 @ sK9)) != $true) | (((sK13 @ sK10 @ X0)) != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(trivial_inequality_removal,[],[f221])). 0.19/0.51 thf(f223,plain,( 0.19/0.51 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | (((sK13 @ sK10 @ sK9)) != X0) | (((sK13 @ sK10 @ sK9)) != X1) | ($true = ((subset @ sK9 @ sK10))) | ($true = ((subset @ sK9 @ sK10))) | ($true != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(superposition,[],[f222,f116])). 0.19/0.51 thf(f224,plain,( 0.19/0.51 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ sK9 @ sK10))) | (((sK13 @ sK10 @ sK9)) != X1) | ($true != $true) | (((sK13 @ sK10 @ sK9)) != X0) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(duplicate_literal_removal,[],[f223])). 0.19/0.51 thf(f225,plain,( 0.19/0.51 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ sK9 @ sK10))) | (((sK13 @ sK10 @ sK9)) != X0) | ($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | (((sK13 @ sK10 @ sK9)) != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(trivial_inequality_removal,[],[f224])). 0.19/0.51 thf(f226,plain,( 0.19/0.51 ( ! [X0 : $i,X1 : $i] : ((((sK13 @ sK10 @ sK9)) != X1) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ sK9)) != X0)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18)), 0.19/0.51 inference(forward_subsumption_resolution,[],[f225,f98])). 0.19/0.51 thf(f228,definition,( 0.19/0.51 spl14_19 <=> ! [X1 : $i] : ((((sK13 @ sK10 @ sK9)) != X1) | ($true != ((in @ X1 @ sK9))))), 0.19/0.51 introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition])). 0.19/0.51 thf(f229,plain,( 0.19/0.51 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ sK9)) != X1)) ) | ~spl14_19), 0.19/0.51 inference(avatar_component_clause,[],[f228])). 0.19/0.51 thf(f230,plain,( 0.19/0.51 spl14_19 | spl14_19 | ~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18), 0.19/0.51 inference(avatar_split_clause,[],[f226,f124,f119,f115,f96,f92,f78,f69,f228,f228])). 0.19/0.51 thf(f256,plain,( 0.19/0.51 ( ! [X0 : $i] : ((((sK13 @ X0 @ sK9)) != ((sK13 @ sK10 @ sK9))) | ($true = ((subset @ sK9 @ X0))) | ($true != $true)) ) | (~spl14_16 | ~spl14_19)), 0.19/0.51 inference(superposition,[],[f229,f116])). 0.19/0.51 thf(f263,plain,( 0.19/0.51 ( ! [X0 : $i] : ((((sK13 @ X0 @ sK9)) != ((sK13 @ sK10 @ sK9))) | ($true = ((subset @ sK9 @ X0)))) ) | (~spl14_16 | ~spl14_19)), 0.19/0.51 inference(trivial_inequality_removal,[],[f256])). 0.19/0.51 thf(f264,plain,( 0.19/0.51 ($true = ((subset @ sK9 @ sK10))) | (~spl14_16 | ~spl14_19)), 0.19/0.51 inference(equality_resolution,[],[f263])). 0.19/0.51 thf(f265,plain,( 0.19/0.51 $false | (spl14_12 | ~spl14_16 | ~spl14_19)), 0.19/0.51 inference(forward_subsumption_resolution,[],[f264,f98])). 0.19/0.51 thf(f266,plain,( 0.19/0.51 spl14_12 | ~spl14_16 | ~spl14_19), 0.19/0.51 inference(avatar_contradiction_clause,[],[f265])). 0.19/0.51 cnf(s4, plain, ~spl14_3 | spl14_6, inference(sat_conversion,[],[f71])). 0.19/0.51 cnf(s6, plain, ~spl14_3 | spl14_8, inference(sat_conversion,[],[f80])). 0.19/0.51 cnf(s9, plain, ~spl14_3 | spl14_11, inference(sat_conversion,[],[f94])). 0.19/0.51 cnf(s10, plain, ~spl14_12, inference(sat_conversion,[],[f99])). 0.19/0.51 cnf(s14, plain, spl14_1, inference(sat_conversion,[],[f113])). 0.19/0.51 cnf(s15, plain, ~spl14_1 | spl14_16, inference(sat_conversion,[],[f117])). 0.19/0.51 cnf(s16, plain, ~spl14_1 | spl14_17, inference(sat_conversion,[],[f121])). 0.19/0.51 cnf(s17, plain, spl14_3, inference(sat_conversion,[],[f122])). 0.19/0.51 cnf(s18, plain, spl14_18, inference(sat_conversion,[],[f127])). 0.19/0.51 cnf(s19, plain, spl14_19 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18 | ~spl14_6 | spl14_19, inference(sat_conversion,[],[f230])). 0.19/0.51 cnf(s20, plain, ~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18 | spl14_19, inference(rat,[],[s19])). 0.19/0.51 cnf(s21, plain, spl14_12 | ~spl14_16 | ~spl14_19, inference(sat_conversion,[],[f266])). 0.19/0.51 cnf(s22, plain, spl14_17, inference(rat,[],[s16,s14])). 0.19/0.51 cnf(s23, plain, spl14_16, inference(rat,[],[s15,s14])). 0.19/0.51 cnf(s25, plain, ~spl14_19, inference(rat,[],[s21,s23,s10])). 0.19/0.51 cnf(s26, plain, spl14_11, inference(rat,[],[s9,s17])). 0.19/0.51 cnf(s27, plain, spl14_8, inference(rat,[],[s6,s17])). 0.19/0.51 cnf(s28, plain, ~spl14_6, inference(rat,[],[s20,s25,s18,s22,s23,s10,s26,s27])). 0.19/0.51 cnf(s29, plain, $false, inference(rat,[],[s4,s28,s17])). 0.19/0.51 thf(f267,plain,( 0.19/0.51 $false), 0.19/0.51 inference(avatar_sat_refutation,[],[s29])). 0.19/0.51 % SZS output end Proof for theBenchmark 0.19/0.51 % (998014)------------------------------ 0.19/0.51 % (998014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.51 % (998014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.51 % (998014)CaDiCaL version: 2.1.3 0.19/0.51 % (998014)Termination reason: Refutation 0.19/0.51 % (998014)Time elapsed: 0.019 s 0.19/0.51 % (998014)Peak memory usage: 13 MB 0.19/0.51 % (998014)Instructions burned: 31 (million) 0.19/0.51 % (998006)Success in time 0.059 s 0.19/0.51 % Vampire exiting 0.19/0.51 EOF