0.00/0.05	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.09	% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.21/0.47	% Computer : n022.cluster.edu
0.21/0.47	% Model    : x86_64 x86_64
0.21/0.47	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.21/0.47	% Memory   : 8046.5625MB
0.21/0.47	% OS       : Linux 6.8.0-71-generic
0.21/0.47	% CPULimit : 1440
0.21/0.47	% WCLimit  : 180
0.21/0.47	% DateTime : Mon Jul 27 11:52:59 UTC 2026
0.21/0.47	% CPUTime  : 
0.21/0.47	Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.25/0.54	Running higher-order theorem proving
0.25/0.56	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
0.32/0.63	% (849642)Detected a higher-order problem, will run a greedy HOL sequence.
0.32/0.63	% (849651)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1226643296:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi)
0.32/0.63	% (849651)Instruction limit reached! 
0.32/0.63	% (849651)------------------------------
0.32/0.63	% (849651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.32/0.63	% (849651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.32/0.63	% (849653)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
0.32/0.63	% (849651)CaDiCaL version: 2.1.3
0.32/0.63	% (849651)Termination reason: Instruction limit
0.32/0.63	% (849651)Termination phase: Saturation
0.32/0.63	% (849651)Time elapsed: 0.010 s
0.32/0.63	% (849651)Peak memory usage: 12 MB
0.32/0.63	% (849651)Instructions burned: 25 (million)
0.32/0.63	% (849653)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
0.32/0.63	% (849647)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=417338581:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.32/0.63	% (849649)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3727902837:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi)
0.32/0.63	% (849653)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=4090797161:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi)
0.32/0.63	% (849650)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=2805263092: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)
0.32/0.63	% (849649)Instruction limit reached! 
0.32/0.63	% (849649)------------------------------
0.32/0.63	% (849649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.32/0.63	% (849649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.32/0.63	% (849649)CaDiCaL version: 2.1.3
0.32/0.63	% (849649)Termination reason: Instruction limit
0.32/0.63	% (849649)Termination phase: Saturation
0.32/0.63	% (849649)Time elapsed: 0.003 s
0.32/0.63	% (849649)Peak memory usage: 11 MB
0.32/0.63	% (849649)Instructions burned: 4 (million)
0.32/0.63	% (849652)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3311059074:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi)
0.32/0.63	% (849648)lrs+10_16_si=on:nwc=1.5:random_seed=630452747:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi)
0.32/0.63	% (849647) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-849642-849647"...
0.32/0.63	% (849655)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=268154723:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi)
0.32/0.63	% (849655)Instruction limit reached! 
0.32/0.63	% (849655)------------------------------
0.32/0.63	% (849655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.32/0.63	% (849655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.32/0.63	% (849647)...printing done.
0.32/0.63	% (849655)CaDiCaL version: 2.1.3
0.32/0.63	% (849655)Termination reason: Instruction limit
0.32/0.63	% (849655)Termination phase: Saturation
0.32/0.63	% (849655)Time elapsed: 0.001 s
0.32/0.63	% (849655)Peak memory usage: 12 MB
0.32/0.63	% (849655)Instructions burned: 3 (million)
0.32/0.63	% (849647)Refutation found. Thanks to Tanya!
0.32/0.63	% SZS status Theorem for theBenchmark
0.32/0.63	% SZS output start Proof for theBenchmark
0.32/0.63	thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
0.32/0.63	thf(func_def_0, type, fun_image: (($i > $i) > ($i > $o) > $i > $o)).
0.32/0.63	thf(func_def_2, type, fun_composition: (($i > $i) > ($i > $i) > $i > $i)).
0.32/0.63	thf(func_def_3, type, fun_inv_image: (($i > $i) > ($i > $o) > $i > $o)).
0.32/0.63	thf(func_def_4, type, fun_injective: (($i > $i) > $o)).
0.32/0.63	thf(func_def_5, type, fun_surjective: (($i > $i) > $o)).
0.32/0.63	thf(func_def_6, type, fun_bijective: (($i > $i) > $o)).
0.32/0.63	thf(func_def_7, type, fun_decreasing: (($i > $i) > ($i > $i > $o) > $o)).
0.32/0.63	thf(func_def_8, type, fun_increasing: (($i > $i) > ($i > $i > $o) > $o)).
0.32/0.63	thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.32/0.63	thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
0.32/0.63	thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
0.32/0.63	thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
0.32/0.63	thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
0.32/0.63	thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.32/0.63	thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.32/0.63	thf(func_def_16, type, vAND: ($o > $o > $o)).
0.32/0.63	thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
0.32/0.63	thf(func_def_18, type, vIMP: ($o > $o > $o)).
0.32/0.63	thf(func_def_21, type, sK0: ($i > $i)).
0.32/0.63	thf(func_def_22, type, sK1: ($i > $i)).
0.32/0.63	thf(func_def_23, type, sK2: ($i > $i)).
0.32/0.63	thf(func_def_24, type, vNOT: ($o > $o)).
0.32/0.63	thf(func_def_25, type, sK3: ($i > $i)).
0.32/0.63	thf(func_def_26, type, sK4: ($i > $i)).
0.32/0.63	thf(f2,axiom,(
0.32/0.63	  (fun_composition = (^[X0 : ($i > $i), X1 : ($i > $i), X2 : $i] : ((X1 @ (X0 @ X2)))))),
0.32/0.63	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_composition)).
0.32/0.63	thf(f4,axiom,(
0.32/0.63	  (fun_injective = (^[X0 : ($i > $i)] : (! [X1 : $i,X2 : $i] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)))))),
0.32/0.63	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_injective)).
0.32/0.63	thf(f5,axiom,(
0.32/0.63	  (fun_surjective = (^[X0 : ($i > $i)] : (! [X1 : $i] : ? [X2 : $i] : (X1 = ((X0 @ X2))))))),
0.32/0.63	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_surjective)).
0.32/0.63	thf(f6,axiom,(
0.32/0.63	  (fun_bijective = (^[X0 : ($i > $i)] : ((fun_surjective @ X0) & (fun_injective @ X0))))),
0.32/0.63	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_bijective)).
0.32/0.63	thf(f9,conjecture,(
0.32/0.63	  ! [X2 : ($i > $i),X0 : ($i > $i),X1 : ($i > $i)] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) & (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1))) => (fun_bijective @ X2))),
0.32/0.63	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
0.32/0.63	thf(f10,negated_conjecture,(
0.32/0.63	  ~ ! [X2 : ($i > $i),X0 : ($i > $i),X1 : ($i > $i)] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) & (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1))) => (fun_bijective @ X2))),
0.32/0.63	  inference(negated_conjecture,[status(cth)],[f9])).
0.32/0.63	thf(f11,plain,(
0.32/0.63	  (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
0.32/0.63	  inference(fool_elimination,[],[f5])).
0.32/0.63	thf(f12,plain,(
0.32/0.63	  (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
0.32/0.63	  inference(fool_elimination,[],[f2])).
0.32/0.63	thf(f17,plain,(
0.32/0.63	  ~ ! [X0 : ($i > $i),X1 : ($i > $i),X2 : ($i > $i)] : (((fun_injective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)) & (fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) & (fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2))) => (fun_bijective @ X0))),
0.32/0.63	  inference(rectify,[],[f10])).
0.32/0.63	thf(f18,plain,(
0.32/0.63	  ~ ! [X0 : ($i > $i),X2 : ($i > $i),X1 : ($i > $i)] : ((($true = ((fun_injective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)))) & ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)))) & (((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1))) = $true)) => (((fun_bijective @ X0)) = $true))),
0.32/0.63	  inference(fool_elimination,[],[f17])).
0.32/0.63	thf(f19,plain,(
0.32/0.63	  (fun_bijective = (^[X0 : ($i > $i)] : ((fun_surjective @ X0) & (fun_injective @ X0))))),
0.32/0.63	  inference(rectify,[],[f6])).
0.32/0.63	thf(f20,plain,(
0.32/0.63	  (fun_bijective = (^[Y0 : $i > $i]: ((fun_injective @ Y0) & (fun_surjective @ Y0))))),
0.32/0.63	  inference(fool_elimination,[],[f19])).
0.32/0.63	thf(f25,plain,(
0.32/0.63	  (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
0.32/0.63	  inference(fool_elimination,[],[f4])).
0.32/0.63	thf(f26,plain,(
0.32/0.63	  ? [X0 : ($i > $i),X2 : ($i > $i),X1 : ($i > $i)] : ((((fun_bijective @ X0)) != $true) & (($true = ((fun_injective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)))) & ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)))) & (((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1))) = $true)))),
0.32/0.63	  inference(ennf_transformation,[],[f18])).
0.32/0.63	thf(f27,plain,(
0.32/0.63	  ? [X2 : ($i > $i),X0 : ($i > $i),X1 : ($i > $i)] : ((((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1))) = $true) & (((fun_bijective @ X0)) != $true) & ($true = ((fun_injective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0)))) & ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)))))),
0.32/0.63	  inference(flattening,[],[f26])).
0.32/0.63	thf(f28,plain,(
0.32/0.63	  ? [X0 : ($i > $i),X1 : ($i > $i),X2 : ($i > $i)] : (($true = ((fun_surjective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)))) & ($true != ((fun_bijective @ X1))) & ($true = ((fun_injective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)))) & (((fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) = $true))),
0.32/0.63	  inference(rectify,[],[f27])).
0.32/0.63	thf(f29,plain,(
0.32/0.63	  ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ sK0 @ sK1) @ sK2)))) & ($true != ((fun_bijective @ sK1))) & ($true = ((fun_injective @ (fun_composition @ (fun_composition @ sK2 @ sK0) @ sK1)))) & ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK2) @ sK0))))),
0.32/0.63	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f28])).
0.32/0.63	thf(f30,plain,(
0.32/0.63	  (fun_bijective = (^[Y0 : $i > $i]: ((fun_injective @ Y0) & (fun_surjective @ Y0))))),
0.32/0.63	  inference(cnf_transformation,[],[f20])).
0.32/0.63	thf(f31,plain,(
0.32/0.63	  (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
0.32/0.63	  inference(cnf_transformation,[],[f11])).
0.32/0.63	thf(f33,plain,(
0.32/0.63	  (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
0.32/0.63	  inference(cnf_transformation,[],[f25])).
0.32/0.63	thf(f37,plain,(
0.32/0.63	  ($true = ((fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK2) @ sK0))))),
0.32/0.63	  inference(cnf_transformation,[],[f29])).
0.32/0.63	thf(f38,plain,(
0.32/0.63	  ($true = ((fun_injective @ (fun_composition @ (fun_composition @ sK2 @ sK0) @ sK1))))),
0.32/0.63	  inference(cnf_transformation,[],[f29])).
0.32/0.63	thf(f39,plain,(
0.32/0.63	  ($true != ((fun_bijective @ sK1)))),
0.32/0.63	  inference(cnf_transformation,[],[f29])).
0.32/0.63	thf(f41,plain,(
0.32/0.63	  (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
0.32/0.63	  inference(cnf_transformation,[],[f12])).
0.32/0.63	thf(f44,plain,(
0.32/0.63	  (fun_bijective = (^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0))))),
0.32/0.63	  inference(definition_unfolding,[],[f30,f33,f31])).
0.32/0.63	thf(f46,plain,(
0.32/0.63	  ($true != (((^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0))) @ sK1)))),
0.32/0.63	  inference(definition_unfolding,[],[f39,f44])).
0.32/0.63	thf(f47,plain,(
0.32/0.63	  ($true = (((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK2 @ sK0) @ sK1))))),
0.32/0.63	  inference(definition_unfolding,[],[f38,f33,f41,f41])).
0.32/0.63	thf(f48,plain,(
0.32/0.63	  ($true = (((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK1 @ sK2) @ sK0))))),
0.32/0.63	  inference(definition_unfolding,[],[f37,f31,f41,f41])).
0.32/0.63	thf(f55,plain,(
0.32/0.63	  ($true = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ (sK2 @ (sK1 @ Y1))) = Y0)))))))),
0.32/0.63	  inference(beta-eta_normalization,[],[f48])).
0.32/0.63	thf(f56,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ (sK2 @ (sK1 @ Y1))) = Y0)))) @ X1)))) )),
0.32/0.63	  inference(pi_proxy_clausification,[],[f55])).
0.32/0.63	thf(f57,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ (sK2 @ (sK1 @ Y0))) = X1)))))) )),
0.32/0.63	  inference(beta-eta_normalization,[],[f56])).
0.32/0.63	thf(f58,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ (sK2 @ (sK1 @ Y0))) = X1)) @ (sK4 @ X1))))) )),
0.32/0.63	  inference(sigma_proxy_clausification,[],[f57])).
0.32/0.63	thf(f59,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = (((sK0 @ (sK2 @ (sK1 @ (sK4 @ X1)))) = X1)))) )),
0.32/0.63	  inference(beta-eta_normalization,[],[f58])).
0.32/0.63	thf(f60,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((((sK0 @ (sK2 @ (sK1 @ (sK4 @ X1))))) = X1)) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f59])).
0.32/0.63	thf(f61,plain,(
0.32/0.63	  ($true != (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ Y0) = (sK1 @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0))))))))),
0.32/0.63	  inference(beta-eta_normalization,[],[f46])).
0.32/0.63	thf(f62,plain,(
0.32/0.63	  (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ Y0) = (sK1 @ Y1)) => (Y1 = Y0))))))) = $false)),
0.32/0.63	  inference(and_proxy_clausification,[],[f61])).
0.32/0.63	thf(f63,plain,(
0.32/0.63	  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ Y0) = (sK1 @ Y1)) => (Y1 = Y0))))))) = $false) | ($false = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0)))) @ sK5)))),
0.32/0.63	  inference(sigma_proxy_clausification,[],[f62])).
0.32/0.63	thf(f64,plain,(
0.32/0.63	  ($false = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0)))) @ sK5))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ Y0) = (sK1 @ Y1)) => (Y1 = Y0))))) @ sK6)) = $false)),
0.32/0.63	  inference(sigma_proxy_clausification,[],[f63])).
0.32/0.63	thf(f65,plain,(
0.32/0.63	  (((!! @ $i @ (^[Y0 : $i]: (((sK1 @ sK6) = (sK1 @ Y0)) => (Y0 = sK6))))) = $false) | (((?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) = sK5)))) = $false)),
0.32/0.63	  inference(beta-eta_normalization,[],[f64])).
0.32/0.63	thf(f66,plain,(
0.32/0.63	  ((((^[Y0 : $i]: (((sK1 @ sK6) = (sK1 @ Y0)) => (Y0 = sK6))) @ sK7)) = $false) | (((?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) = sK5)))) = $false)),
0.32/0.63	  inference(sigma_proxy_clausification,[],[f65])).
0.32/0.63	thf(f67,plain,(
0.32/0.63	  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) = sK5)) @ X1)) = $false) | ((((^[Y0 : $i]: (((sK1 @ sK6) = (sK1 @ Y0)) => (Y0 = sK6))) @ sK7)) = $false)) )),
0.32/0.63	  inference(pi_proxy_clausification,[],[f66])).
0.32/0.63	thf(f68,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((((((sK1 @ sK6) = (sK1 @ sK7)) => (sK7 = sK6))) = $false) | ((((sK1 @ X1) = sK5)) = $false)) )),
0.32/0.63	  inference(beta-eta_normalization,[],[f67])).
0.32/0.63	thf(f69,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((((sK7 = sK6)) = $false) | ((((sK1 @ X1) = sK5)) = $false)) )),
0.32/0.63	  inference(imp_proxy_clausification,[],[f68])).
0.32/0.63	thf(f70,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = (((sK1 @ sK6) = (sK1 @ sK7)))) | ((((sK1 @ X1) = sK5)) = $false)) )),
0.32/0.63	  inference(imp_proxy_clausification,[],[f68])).
0.32/0.63	thf(f71,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((((sK1 @ sK7)) = ((sK1 @ sK6))) | ((((sK1 @ X1) = sK5)) = $false)) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f70])).
0.32/0.63	thf(f72,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((((sK1 @ sK7)) = ((sK1 @ sK6))) | (sK5 != ((sK1 @ X1)))) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f71])).
0.32/0.63	thf(f73,plain,(
0.32/0.63	  ( ! [X1 : $i] : (((((sK1 @ X1) = sK5)) = $false) | (sK6 != sK7)) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f69])).
0.32/0.63	thf(f74,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((sK6 != sK7) | (sK5 != ((sK1 @ X1)))) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f73])).
0.32/0.63	thf(f75,plain,(
0.32/0.63	  ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ (sK0 @ (sK2 @ Y0))) = (sK1 @ (sK0 @ (sK2 @ Y1)))) => (Y1 = Y0))))))))),
0.32/0.63	  inference(beta-eta_normalization,[],[f47])).
0.32/0.63	thf(f76,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 @ (sK0 @ (sK2 @ Y0))) = (sK1 @ (sK0 @ (sK2 @ Y1)))) => (Y1 = Y0))))) @ X1)))) )),
0.32/0.63	  inference(pi_proxy_clausification,[],[f75])).
0.32/0.63	thf(f77,plain,(
0.32/0.63	  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (((sK1 @ (sK0 @ (sK2 @ X1))) = (sK1 @ (sK0 @ (sK2 @ Y0)))) => (Y0 = X1))))))) )),
0.32/0.63	  inference(beta-eta_normalization,[],[f76])).
0.32/0.63	thf(f78,plain,(
0.32/0.63	  ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (((sK1 @ (sK0 @ (sK2 @ X1))) = (sK1 @ (sK0 @ (sK2 @ Y0)))) => (Y0 = X1))) @ X2)))) )),
0.32/0.63	  inference(pi_proxy_clausification,[],[f77])).
0.32/0.63	thf(f79,plain,(
0.32/0.63	  ( ! [X2 : $i,X1 : $i] : (($true = ((((sK1 @ (sK0 @ (sK2 @ X1))) = (sK1 @ (sK0 @ (sK2 @ X2)))) => (X2 = X1))))) )),
0.32/0.63	  inference(beta-eta_normalization,[],[f78])).
0.32/0.63	thf(f80,plain,(
0.32/0.63	  ( ! [X2 : $i,X1 : $i] : (($true = ((X2 = X1))) | ((((sK1 @ (sK0 @ (sK2 @ X1))) = (sK1 @ (sK0 @ (sK2 @ X2))))) = $false)) )),
0.32/0.63	  inference(imp_proxy_clausification,[],[f79])).
0.32/0.63	thf(f81,plain,(
0.32/0.63	  ( ! [X2 : $i,X1 : $i] : (((((sK1 @ (sK0 @ (sK2 @ X1))) = (sK1 @ (sK0 @ (sK2 @ X2))))) = $false) | (X1 = X2)) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f80])).
0.32/0.63	thf(f82,plain,(
0.32/0.63	  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ (sK0 @ (sK2 @ X2)))) != ((sK1 @ (sK0 @ (sK2 @ X1))))) | (X1 = X2)) )),
0.32/0.63	  inference(equality_proxy_clausification,[],[f81])).
0.32/0.63	thf(f84,definition,(
0.32/0.63	  spl8_1 <=> ! [X1 : $i] : (sK5 != ((sK1 @ X1)))),
0.32/0.63	  introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
0.32/0.63	thf(f85,plain,(
0.32/0.63	  ( ! [X1 : $i] : ((sK5 != ((sK1 @ X1)))) ) | ~spl8_1),
0.32/0.63	  inference(avatar_component_clause,[],[f84])).
0.32/0.63	thf(f87,definition,(
0.32/0.63	  spl8_2 <=> (((sK1 @ sK7)) = ((sK1 @ sK6)))),
0.32/0.63	  introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
0.32/0.63	thf(f89,plain,(
0.32/0.63	  (((sK1 @ sK7)) = ((sK1 @ sK6))) | ~spl8_2),
0.32/0.63	  inference(avatar_component_clause,[],[f87])).
0.32/0.63	thf(f90,plain,(
0.32/0.63	  spl8_1 | spl8_2),
0.32/0.63	  inference(avatar_split_clause,[],[f72,f87,f84])).
0.32/0.63	thf(f92,definition,(
0.32/0.63	  spl8_3 <=> (sK6 = sK7)),
0.32/0.63	  introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
0.32/0.63	thf(f94,plain,(
0.32/0.63	  (sK6 != sK7) | spl8_3),
0.32/0.63	  inference(avatar_component_clause,[],[f92])).
0.32/0.63	thf(f95,plain,(
0.32/0.63	  ~spl8_3 | spl8_1),
0.32/0.63	  inference(avatar_split_clause,[],[f74,f84,f92])).
0.32/0.63	thf(f99,plain,(
0.32/0.63	  ( ! [X0 : $i,X1 : $i] : ((((sK1 @ X0)) != ((sK1 @ (sK0 @ (sK2 @ X1))))) | (((sK1 @ (sK4 @ X0))) = X1)) )),
0.32/0.64	  inference(constrained_superposition,[],[f82,f60])).
0.32/0.64	thf(f102,plain,(
0.32/0.64	  ( ! [X0 : $i,X1 : $i] : ((((sK1 @ X0)) != ((sK1 @ X1))) | (((sK1 @ (sK4 @ X0))) = ((sK1 @ (sK4 @ X1))))) )),
0.32/0.64	  inference(constrained_superposition,[],[f99,f60])).
0.32/0.64	thf(f103,plain,(
0.32/0.64	  ( ! [X0 : $i] : ((((sK1 @ (sK4 @ (sK0 @ (sK2 @ X0))))) = X0)) )),
0.32/0.64	  inference(equality_resolution,[],[f99])).
0.32/0.64	thf(f113,plain,(
0.32/0.64	  ( ! [X0 : $i] : ((((sK1 @ X0)) != ((sK1 @ sK6))) | (((sK1 @ (sK4 @ sK7))) = ((sK1 @ (sK4 @ X0))))) ) | ~spl8_2),
0.32/0.64	  inference(constrained_superposition,[],[f102,f89])).
0.32/0.64	thf(f127,plain,(
0.32/0.64	  (((sK1 @ (sK4 @ sK7))) = ((sK1 @ (sK4 @ sK6)))) | ~spl8_2),
0.32/0.64	  inference(equality_resolution,[],[f113])).
0.32/0.64	thf(f135,plain,(
0.32/0.64	  (((sK0 @ (sK2 @ (sK1 @ (sK4 @ sK6))))) = sK7) | ~spl8_2),
0.32/0.64	  inference(constrained_superposition,[],[f60,f127])).
0.32/0.64	thf(f136,plain,(
0.32/0.64	  (sK6 = sK7) | ~spl8_2),
0.32/0.64	  inference(forward_demodulation,[],[f135,f60])).
0.32/0.64	thf(f137,plain,(
0.32/0.64	  $false | (~spl8_2 | spl8_3)),
0.32/0.64	  inference(forward_subsumption_resolution,[],[f136,f94])).
0.32/0.64	thf(f138,plain,(
0.32/0.64	  ~spl8_2 | spl8_3),
0.32/0.64	  inference(avatar_contradiction_clause,[],[f137])).
0.32/0.64	thf(f140,plain,(
0.32/0.64	  ( ! [X0 : $i] : ((sK5 != X0)) ) | ~spl8_1),
0.32/0.64	  inference(constrained_superposition,[],[f85,f103])).
0.32/0.64	thf(f144,plain,(
0.32/0.64	  (sK5 != sK5) | ~spl8_1),
0.32/0.64	  inference(imitation,[],[f140])).
0.32/0.64	thf(f147,plain,(
0.32/0.64	  $false | ~spl8_1),
0.32/0.64	  inference(trivial_inequality_removal,[],[f144])).
0.32/0.64	thf(f148,plain,(
0.32/0.64	  ~spl8_1),
0.32/0.64	  inference(avatar_contradiction_clause,[],[f147])).
0.32/0.64	cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f90])).
0.32/0.64	cnf(s2, plain, spl8_1 | ~spl8_3, inference(sat_conversion,[],[f95])).
0.32/0.64	cnf(s3, plain, ~spl8_2 | spl8_3, inference(sat_conversion,[],[f138])).
0.32/0.64	cnf(s5, plain, ~spl8_1, inference(sat_conversion,[],[f148])).
0.32/0.64	cnf(s6, plain, ~spl8_3, inference(rat,[],[s2,s5])).
0.32/0.64	cnf(s7, plain, ~spl8_2, inference(rat,[],[s3,s6])).
0.32/0.64	cnf(s8, plain, $false, inference(rat,[],[s1,s7,s5])).
0.32/0.64	thf(f149,plain,(
0.32/0.64	  $false),
0.32/0.64	  inference(avatar_sat_refutation,[],[s8])).
0.32/0.64	% SZS output end Proof for theBenchmark
0.32/0.64	% (849647)------------------------------
0.32/0.64	% (849647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.32/0.64	% (849647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.32/0.64	% (849647)CaDiCaL version: 2.1.3
0.32/0.64	% (849647)Termination reason: Refutation
0.32/0.64	% (849647)Time elapsed: 0.014 s
0.32/0.64	% (849647)Peak memory usage: 13 MB
0.32/0.64	% (849647)Instructions burned: 15 (million)
0.32/0.64	% (849642)Success in time 0.057 s
0.32/0.64	% Vampire exiting
0.32/0.64	EOF