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
0.11/0.37	% Computer : n029.cluster.edu
0.11/0.37	% Model    : x86_64 x86_64
0.11/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.37	% Memory   : 8046.5625MB
0.11/0.37	% OS       : Linux 6.8.0-71-generic
0.11/0.37	% CPULimit : 1440
0.11/0.37	% WCLimit  : 180
0.11/0.37	% DateTime : Mon Jul 27 12:05:32 UTC 2026
0.11/0.37	% CPUTime  : 
0.11/0.37	Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.15/0.41	Running higher-order theorem proving
0.15/0.43	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
0.21/0.49	% (2807660)Detected a higher-order problem, will run a greedy HOL sequence.
0.21/0.49	% (2807668)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3527146552:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi)
0.21/0.49	% (2807668)Refutation not found, incomplete strategy
0.21/0.49	% (2807668)------------------------------
0.21/0.49	% (2807668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.21/0.49	% (2807668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.21/0.49	% (2807668)CaDiCaL version: 2.1.3
0.21/0.49	% (2807668)Termination reason: Refutation not found, incomplete strategy
0.21/0.49	% (2807668)Time elapsed: 0.001 s
0.21/0.49	% (2807668)Peak memory usage: 12 MB
0.21/0.49	% (2807668)Instructions burned: 3 (million)
0.21/0.49	% (2807668)------------------------------
0.21/0.49	% (2807668)------------------------------
0.21/0.49	% (2807666)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2074781111:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.21/0.49	% (2807667)lrs+10_16_si=on:nwc=1.5:random_seed=1304916370:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi)
0.21/0.49	% (2807666) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2807660-2807666"...
0.21/0.49	% (2807667) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2807660-2807667"...
0.21/0.49	% (2807674)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1102359043:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi)
0.21/0.49	% (2807669)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=3999470105: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)
0.21/0.49	% (2807666)...printing done.
0.21/0.49	% (2807667)...printing done.
0.21/0.49	% (2807674)Instruction limit reached! 
0.21/0.49	% (2807674)------------------------------
0.21/0.49	% (2807674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.21/0.49	% (2807674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.21/0.49	% (2807674)CaDiCaL version: 2.1.3
0.21/0.49	% (2807674)Termination reason: Instruction limit
0.21/0.49	% (2807674)Termination phase: Saturation
0.21/0.49	% (2807674)Time elapsed: 0.002 s
0.21/0.49	% (2807674)Peak memory usage: 12 MB
0.21/0.49	% (2807674)Instructions burned: 5 (million)
0.21/0.49	% (2807666)Refutation found. Thanks to Tanya!
0.21/0.49	% SZS status Theorem for theBenchmark
0.21/0.49	% SZS output start Proof for theBenchmark
0.21/0.49	thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
0.21/0.49	thf(func_def_0, type, in: ($i > ($i > $o) > $o)).
0.21/0.49	thf(func_def_2, type, is_a: ($i > ($i > $o) > $o)).
0.21/0.49	thf(func_def_3, type, emptyset: ($i > $o)).
0.21/0.49	thf(func_def_4, type, unord_pair: ($i > $i > $i > $o)).
0.21/0.49	thf(func_def_5, type, singleton: ($i > $i > $o)).
0.21/0.49	thf(func_def_6, type, union: (($i > $o) > ($i > $o) > $i > $o)).
0.21/0.49	thf(func_def_7, type, excl_union: (($i > $o) > ($i > $o) > $i > $o)).
0.21/0.49	thf(func_def_8, type, intersection: (($i > $o) > ($i > $o) > $i > $o)).
0.21/0.49	thf(func_def_9, type, setminus: (($i > $o) > ($i > $o) > $i > $o)).
0.21/0.49	thf(func_def_10, type, complement: (($i > $o) > $i > $o)).
0.21/0.49	thf(func_def_11, type, disjoint: (($i > $o) > ($i > $o) > $o)).
0.21/0.49	thf(func_def_12, type, subset: (($i > $o) > ($i > $o) > $o)).
0.21/0.49	thf(func_def_13, type, meets: (($i > $o) > ($i > $o) > $o)).
0.21/0.49	thf(func_def_14, type, misses: (($i > $o) > ($i > $o) > $o)).
0.21/0.49	thf(func_def_15, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.21/0.49	thf(func_def_16, type, vIMP: ($o > $o > $o)).
0.21/0.49	thf(func_def_17, type, db2: !>[X0: $tType]:(X0)).
0.21/0.49	thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
0.21/0.49	thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
0.21/0.49	thf(func_def_20, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.21/0.49	thf(func_def_23, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
0.21/0.49	thf(func_def_24, type, vAND: ($o > $o > $o)).
0.21/0.49	thf(func_def_25, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.21/0.49	thf(func_def_26, type, vNOT: ($o > $o)).
0.21/0.49	thf(func_def_27, type, vOR: ($o > $o > $o)).
0.21/0.49	thf(func_def_28, type, sK0: ($i > $o)).
0.21/0.49	thf(func_def_29, type, sK1: ($i > $o)).
0.21/0.49	thf(func_def_30, type, sK2: ($i > $o)).
0.21/0.49	thf(f6,axiom,(
0.21/0.49	  (union = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
0.21/0.49	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union)).
0.21/0.49	thf(f8,axiom,(
0.21/0.49	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = intersection)),
0.21/0.49	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',intersection)).
0.21/0.49	thf(f9,axiom,(
0.21/0.49	  (setminus = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & ~(X1 @ X2))))),
0.21/0.49	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',setminus)).
0.21/0.49	thf(f15,conjecture,(
0.21/0.49	  ! [X1 : ($i > $o),X0 : ($i > $o),X2 : ($i > $o)] : (((setminus @ X0 @ (setminus @ X1 @ X2))) = ((union @ (setminus @ X0 @ X1) @ (intersection @ X0 @ X2))))),
0.21/0.49	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
0.21/0.49	thf(f16,negated_conjecture,(
0.21/0.49	  ~ ! [X1 : ($i > $o),X0 : ($i > $o),X2 : ($i > $o)] : (((setminus @ X0 @ (setminus @ X1 @ X2))) = ((union @ (setminus @ X0 @ X1) @ (intersection @ X0 @ X2))))),
0.21/0.49	  inference(negated_conjecture,[status(cth)],[f15])).
0.21/0.49	thf(f24,plain,(
0.21/0.49	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = intersection)),
0.21/0.49	  inference(rectify,[],[f8])).
0.21/0.49	thf(f25,plain,(
0.21/0.49	  (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
0.21/0.49	  inference(fool_elimination,[],[f24])).
0.21/0.49	thf(f26,plain,(
0.21/0.49	  (setminus = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & ~(X1 @ X2))))),
0.21/0.49	  inference(rectify,[],[f9])).
0.21/0.49	thf(f27,plain,(
0.21/0.49	  (setminus = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) & (Y0 @ Y2))))))))),
0.21/0.49	  inference(fool_elimination,[],[f26])).
0.21/0.49	thf(f29,plain,(
0.21/0.49	  (union = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
0.21/0.49	  inference(rectify,[],[f6])).
0.21/0.49	thf(f30,plain,(
0.21/0.49	  (union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.21/0.49	  inference(fool_elimination,[],[f29])).
0.21/0.49	thf(f39,plain,(
0.21/0.49	  ~ ! [X1 : ($i > $o),X0 : ($i > $o),X2 : ($i > $o)] : (((union @ (setminus @ X1 @ X0) @ (intersection @ X1 @ X2))) = ((setminus @ X1 @ (setminus @ X0 @ X2))))),
0.21/0.49	  inference(rectify,[],[f16])).
0.21/0.49	thf(f40,plain,(
0.21/0.49	  ? [X2 : ($i > $o),X1 : ($i > $o),X0 : ($i > $o)] : (((union @ (setminus @ X1 @ X0) @ (intersection @ X1 @ X2))) != ((setminus @ X1 @ (setminus @ X0 @ X2))))),
0.21/0.49	  inference(ennf_transformation,[],[f39])).
0.21/0.49	thf(f41,plain,(
0.21/0.49	  ? [X0 : ($i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (((setminus @ X1 @ (setminus @ X2 @ X0))) != ((union @ (setminus @ X1 @ X2) @ (intersection @ X1 @ X0))))),
0.21/0.49	  inference(rectify,[],[f40])).
0.21/0.49	thf(f42,plain,(
0.21/0.49	  (((setminus @ sK1 @ (setminus @ sK2 @ sK0))) != ((union @ (setminus @ sK1 @ sK2) @ (intersection @ sK1 @ sK0))))),
0.21/0.49	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41])).
0.21/0.49	thf(f44,plain,(
0.21/0.49	  (union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.21/0.49	  inference(cnf_transformation,[],[f30])).
0.21/0.49	thf(f46,plain,(
0.21/0.49	  (((setminus @ sK1 @ (setminus @ sK2 @ sK0))) != ((union @ (setminus @ sK1 @ sK2) @ (intersection @ sK1 @ sK0))))),
0.21/0.49	  inference(cnf_transformation,[],[f42])).
0.21/0.49	thf(f48,plain,(
0.21/0.49	  (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
0.21/0.49	  inference(cnf_transformation,[],[f25])).
0.21/0.49	thf(f49,plain,(
0.21/0.49	  (setminus = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) & (Y0 @ Y2))))))))),
0.21/0.49	  inference(cnf_transformation,[],[f27])).
0.21/0.49	thf(f61,plain,(
0.21/0.49	  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) & (Y0 @ Y2))))))) @ sK1 @ sK2) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ sK1 @ sK0))) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) & (Y0 @ Y2))))))) @ sK1 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) & (Y0 @ Y2))))))) @ sK2 @ sK0))))),
0.21/0.49	  inference(definition_unfolding,[],[f46,f49,f49,f44,f49,f48])).
0.21/0.49	thf(f62,plain,(
0.21/0.49	  ((^[Y0 : $i]: ((~ ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) != (^[Y0 : $i]: (((sK0 @ Y0) & (sK1 @ Y0)) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))))),
0.21/0.49	  inference(beta-eta_normalization,[],[f61])).
0.21/0.49	thf(f63,plain,(
0.21/0.49	  ((((^[Y0 : $i]: (((sK0 @ Y0) & (sK1 @ Y0)) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) @ sK3)) != (((^[Y0 : $i]: ((~ ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) @ sK3)))),
0.21/0.49	  inference(negative_extensionality,[],[f62])).
0.21/0.49	thf(f64,plain,(
0.21/0.49	  ($true = (((^[Y0 : $i]: ((~ ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) @ sK3))) | ($true = (((^[Y0 : $i]: (((sK0 @ Y0) & (sK1 @ Y0)) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) @ sK3)))),
0.21/0.49	  inference(xor_proxy_clausification,[],[f63])).
0.21/0.49	thf(f65,plain,(
0.21/0.49	  ((((^[Y0 : $i]: (((sK0 @ Y0) & (sK1 @ Y0)) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) @ sK3)) = $false) | ((((^[Y0 : $i]: ((~ ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) @ sK3)) = $false)),
0.21/0.49	  inference(xor_proxy_clausification,[],[f63])).
0.21/0.49	thf(f66,plain,(
0.21/0.49	  (((((sK0 @ sK3) & (sK1 @ sK3)) | ((~ (sK2 @ sK3)) & (sK1 @ sK3)))) = $false) | ((((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))) & (sK1 @ sK3))) = $false)),
0.21/0.49	  inference(beta-eta_normalization,[],[f65])).
0.21/0.49	thf(f67,plain,(
0.21/0.49	  ((((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))) & (sK1 @ sK3))) = $false) | ((((~ (sK2 @ sK3)) & (sK1 @ sK3))) = $false)),
0.21/0.49	  inference(or_proxy_clausification,[],[f66])).
0.21/0.49	thf(f68,plain,(
0.21/0.49	  ((((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))) & (sK1 @ sK3))) = $false) | ((((sK0 @ sK3) & (sK1 @ sK3))) = $false)),
0.21/0.49	  inference(or_proxy_clausification,[],[f66])).
0.21/0.49	thf(f69,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | ($false = ((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))))) | ((((sK0 @ sK3) & (sK1 @ sK3))) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f68])).
0.21/0.49	thf(f70,plain,(
0.21/0.49	  ((((sK0 @ sK3) & (sK1 @ sK3))) = $false) | ($true = (((~ (sK0 @ sK3)) & (sK2 @ sK3)))) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f69])).
0.21/0.49	thf(f71,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | ($true = (((~ (sK0 @ sK3)) & (sK2 @ sK3)))) | (((sK0 @ sK3)) = $false) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f70])).
0.21/0.49	thf(f73,plain,(
0.21/0.49	  ($true = ((~ (sK0 @ sK3)))) | (((sK1 @ sK3)) = $false) | (((sK1 @ sK3)) = $false) | (((sK0 @ sK3)) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f71])).
0.21/0.49	thf(f74,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | (((sK0 @ sK3)) = $false) | (((sK1 @ sK3)) = $false) | (((sK0 @ sK3)) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f73])).
0.21/0.49	thf(f75,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | (((sK0 @ sK3)) = $false)),
0.21/0.49	  inference(duplicate_literal_removal,[],[f74])).
0.21/0.49	thf(f77,plain,(
0.21/0.49	  ($false = ((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))))) | ((((~ (sK2 @ sK3)) & (sK1 @ sK3))) = $false) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f67])).
0.21/0.49	thf(f78,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | ($true = (((~ (sK0 @ sK3)) & (sK2 @ sK3)))) | ((((~ (sK2 @ sK3)) & (sK1 @ sK3))) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f77])).
0.21/0.49	thf(f79,plain,(
0.21/0.49	  ($true = ((sK2 @ sK3))) | ((((~ (sK2 @ sK3)) & (sK1 @ sK3))) = $false) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f78])).
0.21/0.49	thf(f85,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | (((sK1 @ sK3)) = $false) | ($true = ((sK2 @ sK3))) | ($false = ((~ (sK2 @ sK3))))),
0.21/0.49	  inference(and_proxy_clausification,[],[f79])).
0.21/0.49	thf(f86,plain,(
0.21/0.49	  ($true = ((sK2 @ sK3))) | ($true = ((sK2 @ sK3))) | (((sK1 @ sK3)) = $false) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f85])).
0.21/0.49	thf(f87,plain,(
0.21/0.49	  ($true = ((sK2 @ sK3))) | (((sK1 @ sK3)) = $false)),
0.21/0.49	  inference(duplicate_literal_removal,[],[f86])).
0.21/0.49	thf(f88,plain,(
0.21/0.49	  ($true = (((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))) & (sK1 @ sK3)))) | ($true = ((((sK0 @ sK3) & (sK1 @ sK3)) | ((~ (sK2 @ sK3)) & (sK1 @ sK3)))))),
0.21/0.49	  inference(beta-eta_normalization,[],[f64])).
0.21/0.49	thf(f89,plain,(
0.21/0.49	  ($true = ((((sK0 @ sK3) & (sK1 @ sK3)) | ((~ (sK2 @ sK3)) & (sK1 @ sK3))))) | (((sK1 @ sK3)) = $true)),
0.21/0.49	  inference(and_proxy_clausification,[],[f88])).
0.21/0.49	thf(f90,plain,(
0.21/0.49	  ($true = ((~ ((~ (sK0 @ sK3)) & (sK2 @ sK3))))) | ($true = ((((sK0 @ sK3) & (sK1 @ sK3)) | ((~ (sK2 @ sK3)) & (sK1 @ sK3)))))),
0.21/0.49	  inference(and_proxy_clausification,[],[f88])).
0.21/0.49	thf(f91,plain,(
0.21/0.49	  ($true = ((((sK0 @ sK3) & (sK1 @ sK3)) | ((~ (sK2 @ sK3)) & (sK1 @ sK3))))) | ($false = (((~ (sK0 @ sK3)) & (sK2 @ sK3))))),
0.21/0.49	  inference(not_proxy_clausification,[],[f90])).
0.21/0.49	thf(f92,plain,(
0.21/0.49	  ($true = (((sK0 @ sK3) & (sK1 @ sK3)))) | ($false = (((~ (sK0 @ sK3)) & (sK2 @ sK3)))) | ($true = (((~ (sK2 @ sK3)) & (sK1 @ sK3))))),
0.21/0.49	  inference(or_proxy_clausification,[],[f91])).
0.21/0.49	thf(f94,plain,(
0.21/0.49	  ($false = (((~ (sK0 @ sK3)) & (sK2 @ sK3)))) | ($true = (((~ (sK2 @ sK3)) & (sK1 @ sK3)))) | ($true = ((sK0 @ sK3)))),
0.21/0.49	  inference(and_proxy_clausification,[],[f92])).
0.21/0.49	thf(f95,plain,(
0.21/0.49	  ($true = (((~ (sK2 @ sK3)) & (sK1 @ sK3)))) | (((~ (sK0 @ sK3))) = $false) | (((sK2 @ sK3)) = $false) | ($true = ((sK0 @ sK3)))),
0.21/0.49	  inference(and_proxy_clausification,[],[f94])).
0.21/0.49	thf(f97,plain,(
0.21/0.49	  (((sK2 @ sK3)) = $false) | ($true = ((~ (sK2 @ sK3)))) | ($true = ((sK0 @ sK3))) | (((~ (sK0 @ sK3))) = $false)),
0.21/0.49	  inference(and_proxy_clausification,[],[f95])).
0.21/0.49	thf(f98,plain,(
0.21/0.49	  (((~ (sK0 @ sK3))) = $false) | (((sK2 @ sK3)) = $false) | ($true = ((sK0 @ sK3))) | (((sK2 @ sK3)) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f97])).
0.21/0.49	thf(f99,plain,(
0.21/0.49	  ($true = ((sK0 @ sK3))) | (((sK2 @ sK3)) = $false) | ($true = ((sK0 @ sK3))) | (((sK2 @ sK3)) = $false)),
0.21/0.49	  inference(not_proxy_clausification,[],[f98])).
0.21/0.49	thf(f100,plain,(
0.21/0.49	  ($true = ((sK0 @ sK3))) | (((sK2 @ sK3)) = $false)),
0.21/0.49	  inference(duplicate_literal_removal,[],[f99])).
0.21/0.49	thf(f110,plain,(
0.21/0.49	  ($true = (((sK0 @ sK3) & (sK1 @ sK3)))) | ($true = (((~ (sK2 @ sK3)) & (sK1 @ sK3)))) | (((sK1 @ sK3)) = $true)),
0.21/0.49	  inference(or_proxy_clausification,[],[f89])).
0.21/0.49	thf(f111,plain,(
0.21/0.49	  ($true = (((~ (sK2 @ sK3)) & (sK1 @ sK3)))) | (((sK1 @ sK3)) = $true) | (((sK1 @ sK3)) = $true)),
0.21/0.49	  inference(and_proxy_clausification,[],[f110])).
0.21/0.49	thf(f117,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $true) | (((sK1 @ sK3)) = $true) | (((sK1 @ sK3)) = $true)),
0.21/0.49	  inference(and_proxy_clausification,[],[f111])).
0.21/0.49	thf(f121,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $true)),
0.21/0.49	  inference(duplicate_literal_removal,[],[f117])).
0.21/0.49	thf(f123,definition,(
0.21/0.49	  spl4_1 <=> (((sK0 @ sK3)) = $false)),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
0.21/0.49	thf(f125,plain,(
0.21/0.49	  (((sK0 @ sK3)) = $false) | ~spl4_1),
0.21/0.49	  inference(avatar_component_clause,[],[f123])).
0.21/0.49	thf(f127,definition,(
0.21/0.49	  spl4_2 <=> (((sK1 @ sK3)) = $false)),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
0.21/0.49	thf(f129,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $false) | ~spl4_2),
0.21/0.49	  inference(avatar_component_clause,[],[f127])).
0.21/0.49	thf(f130,plain,(
0.21/0.49	  spl4_1 | spl4_2),
0.21/0.49	  inference(avatar_split_clause,[],[f75,f127,f123])).
0.21/0.49	thf(f132,definition,(
0.21/0.49	  spl4_3 <=> ($true = ((sK2 @ sK3)))),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
0.21/0.49	thf(f134,plain,(
0.21/0.49	  ($true = ((sK2 @ sK3))) | ~spl4_3),
0.21/0.49	  inference(avatar_component_clause,[],[f132])).
0.21/0.49	thf(f137,plain,(
0.21/0.49	  spl4_3 | spl4_2),
0.21/0.49	  inference(avatar_split_clause,[],[f87,f127,f132])).
0.21/0.49	thf(f139,definition,(
0.21/0.49	  spl4_4 <=> (((sK2 @ sK3)) = $false)),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
0.21/0.49	thf(f141,plain,(
0.21/0.49	  (((sK2 @ sK3)) = $false) | ~spl4_4),
0.21/0.49	  inference(avatar_component_clause,[],[f139])).
0.21/0.49	thf(f143,definition,(
0.21/0.49	  spl4_5 <=> ($true = ((sK0 @ sK3)))),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
0.21/0.49	thf(f145,plain,(
0.21/0.49	  ($true = ((sK0 @ sK3))) | ~spl4_5),
0.21/0.49	  inference(avatar_component_clause,[],[f143])).
0.21/0.49	thf(f146,plain,(
0.21/0.49	  spl4_4 | spl4_5),
0.21/0.49	  inference(avatar_split_clause,[],[f100,f143,f139])).
0.21/0.49	thf(f148,definition,(
0.21/0.49	  spl4_6 <=> (((sK1 @ sK3)) = $true)),
0.21/0.49	  introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
0.21/0.49	thf(f150,plain,(
0.21/0.49	  (((sK1 @ sK3)) = $true) | ~spl4_6),
0.21/0.49	  inference(avatar_component_clause,[],[f148])).
0.21/0.49	thf(f157,plain,(
0.21/0.49	  spl4_6),
0.21/0.49	  inference(avatar_split_clause,[],[f121,f148])).
0.21/0.49	thf(f158,plain,(
0.21/0.49	  ($true = $false) | (~spl4_2 | ~spl4_6)),
0.21/0.49	  inference(forward_demodulation,[],[f150,f129])).
0.21/0.49	thf(f159,plain,(
0.21/0.49	  $false | (~spl4_2 | ~spl4_6)),
0.21/0.49	  inference(trivial_inequality_removal,[],[f158])).
0.21/0.49	thf(f160,plain,(
0.21/0.49	  ~spl4_2 | ~spl4_6),
0.21/0.49	  inference(avatar_contradiction_clause,[],[f159])).
0.21/0.49	thf(f162,plain,(
0.21/0.49	  ($true = $false) | (~spl4_3 | ~spl4_4)),
0.21/0.49	  inference(forward_demodulation,[],[f134,f141])).
0.21/0.49	thf(f163,plain,(
0.21/0.49	  $false | (~spl4_3 | ~spl4_4)),
0.21/0.49	  inference(trivial_inequality_removal,[],[f162])).
0.21/0.49	thf(f164,plain,(
0.21/0.49	  ~spl4_3 | ~spl4_4),
0.21/0.49	  inference(avatar_contradiction_clause,[],[f163])).
0.21/0.49	thf(f165,plain,(
0.21/0.49	  ($true = $false) | (~spl4_1 | ~spl4_5)),
0.21/0.49	  inference(forward_demodulation,[],[f145,f125])).
0.21/0.49	thf(f166,plain,(
0.21/0.49	  $false | (~spl4_1 | ~spl4_5)),
0.21/0.49	  inference(trivial_inequality_removal,[],[f165])).
0.21/0.49	thf(f167,plain,(
0.21/0.49	  ~spl4_1 | ~spl4_5),
0.21/0.49	  inference(avatar_contradiction_clause,[],[f166])).
0.21/0.49	cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f130])).
0.21/0.49	cnf(s4, plain, spl4_2 | spl4_3, inference(sat_conversion,[],[f137])).
0.21/0.49	cnf(s5, plain, spl4_4 | spl4_5, inference(sat_conversion,[],[f146])).
0.21/0.49	cnf(s12, plain, spl4_6, inference(sat_conversion,[],[f157])).
0.21/0.49	cnf(s13, plain, ~spl4_2 | ~spl4_6, inference(sat_conversion,[],[f160])).
0.21/0.49	cnf(s14, plain, ~spl4_3 | ~spl4_4, inference(sat_conversion,[],[f164])).
0.21/0.49	cnf(s15, plain, ~spl4_1 | ~spl4_5, inference(sat_conversion,[],[f167])).
0.21/0.49	cnf(s16, plain, ~spl4_2, inference(rat,[],[s13,s12])).
0.21/0.49	cnf(s17, plain, spl4_3, inference(rat,[],[s4,s16])).
0.21/0.49	cnf(s18, plain, ~spl4_4, inference(rat,[],[s14,s17])).
0.21/0.49	cnf(s19, plain, spl4_5, inference(rat,[],[s5,s18])).
0.21/0.49	cnf(s20, plain, ~spl4_1, inference(rat,[],[s15,s19])).
0.21/0.49	cnf(s21, plain, $false, inference(rat,[],[s1,s16,s20])).
0.21/0.49	thf(f168,plain,(
0.21/0.49	  $false),
0.21/0.49	  inference(avatar_sat_refutation,[],[s21])).
0.21/0.49	% SZS output end Proof for theBenchmark
0.21/0.49	% (2807666)------------------------------
0.21/0.49	% (2807666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.21/0.49	% (2807666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.21/0.49	% (2807666)CaDiCaL version: 2.1.3
0.21/0.49	% (2807666)Termination reason: Refutation
0.21/0.49	% (2807666)Time elapsed: 0.005 s
0.21/0.49	% (2807666)Peak memory usage: 13 MB
0.21/0.49	% (2807666)Instructions burned: 8 (million)
0.21/0.49	% (2807660)Success in time 0.047 s
0.21/0.49	% Vampire exiting
0.21/0.49	EOF