%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU762^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:33:19 AM UTC 2026
% Result : Theorem 0.23s 0.37s
% Output : Refutation 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU762^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n019.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:23:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.37 % (851398)Will run a generic schedule for satisfiability detection.
% 0.23/0.37 % (851404)% WARNING: option uhcvi not known.
% 0.23/0.37 % (851404)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1753625099:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.37 % (851403)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3990739330_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.37 % (851405)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=14398691:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.37 % (851404)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.37 % (851404)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.37 % Exception at run slice level
% 0.23/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.37 % (851406)dis+10_1_sil=32000:sp=arity:random_seed=3640349115:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.37 % (851413)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4039398858:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.23/0.37 % Exception at run slice level
% 0.23/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.37 % (851409)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1057642523:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.37 % (851407)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1476736027:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.37 % (851408)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4067047612:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.37 % (851407)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.37 % (851416)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3813628789:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.37 % (851406) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-851398-851406"...
% 0.23/0.37 % (851404) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-851398-851404"...
% 0.23/0.37 % (851406)...printing done.
% 0.23/0.37 % (851406)Refutation found. Thanks to Tanya!
% 0.23/0.37 % SZS status Theorem for theBenchmark
% 0.23/0.37 % SZS output start Proof for theBenchmark
% 0.23/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.37 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.37 thf(func_def_1, type, powerset: ($i > $i)).
% 0.23/0.37 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.23/0.37 thf(func_def_3, type, binintersect: ($i > $i > $i)).
% 0.23/0.37 thf(func_def_4, type, binintersectT_lem: $o).
% 0.23/0.37 thf(func_def_6, type, woz13rule1: $o).
% 0.23/0.37 thf(func_def_7, type, woz13rule2: $o).
% 0.23/0.37 thf(func_def_8, type, woz13rule3: $o).
% 0.23/0.37 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.37 thf(func_def_10, type, vIMP: ($o > $o > $o)).
% 0.23/0.37 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.37 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.37 thf(func_def_13, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.37 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.37 thf(func_def_15, type, db3: !>[X0: $tType]:(X0)).
% 0.23/0.37 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.23/0.37 thf(f1,axiom,(
% 0.23/0.37 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.23/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 0.23/0.37 thf(f2,axiom,(
% 0.23/0.37 (woz13rule1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.23/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1)).
% 0.23/0.37 thf(f3,axiom,(
% 0.23/0.37 (woz13rule2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.23/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2)).
% 0.23/0.37 thf(f4,axiom,(
% 0.23/0.37 (woz13rule3 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))),
% 0.23/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3)).
% 0.23/0.37 thf(f5,conjecture,(
% 0.23/0.37 binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4)))))))))))),
% 0.23/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule4)).
% 0.23/0.37 thf(f6,negated_conjecture,(
% 0.23/0.37 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 0.23/0.37 inference(negated_conjecture,[status(cth)],[f5])).
% 0.23/0.37 thf(f7,plain,(
% 0.23/0.37 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.23/0.37 inference(rectify,[],[f1])).
% 0.23/0.37 thf(f8,plain,(
% 0.23/0.37 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 0.23/0.37 inference(fool_elimination,[],[f7])).
% 0.23/0.37 thf(f9,plain,(
% 0.23/0.37 (woz13rule1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.23/0.37 inference(rectify,[],[f2])).
% 0.23/0.37 thf(f10,plain,(
% 0.23/0.37 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 0.23/0.37 inference(fool_elimination,[],[f9])).
% 0.23/0.37 thf(f11,plain,(
% 0.23/0.37 (woz13rule2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.23/0.37 inference(rectify,[],[f3])).
% 0.23/0.37 thf(f12,plain,(
% 0.23/0.37 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 0.23/0.37 inference(fool_elimination,[],[f11])).
% 0.23/0.37 thf(f13,plain,(
% 0.23/0.37 (woz13rule3 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))),
% 0.23/0.37 inference(rectify,[],[f4])).
% 0.23/0.37 thf(f14,plain,(
% 0.23/0.37 (woz13rule3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y2) => ((subset @ Y0 @ Y3) => (subset @ Y0 @ (binintersect @ Y2 @ Y3)))))))))))))))))),
% 0.23/0.37 inference(fool_elimination,[],[f13])).
% 0.23/0.37 thf(f15,plain,(
% 0.23/0.37 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 0.23/0.37 inference(rectify,[],[f6])).
% 0.23/0.37 thf(f16,plain,(
% 0.23/0.37 ~((binintersectT_lem = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X0))) = $true) => ! [X4 : $i] : ((((in @ X4 @ (powerset @ X0))) = $true) => ((((subset @ X1 @ X3)) = $true) => ((((subset @ X2 @ X4)) = $true) => (((subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))) = $true)))))))))))),
% 0.23/0.37 inference(fool_elimination,[],[f15])).
% 0.23/0.37 thf(f17,plain,(
% 0.23/0.37 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((((subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))) != $true) & (((subset @ X2 @ X4)) = $true)) & (((subset @ X1 @ X3)) = $true)) & (((in @ X4 @ (powerset @ X0))) = $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (binintersectT_lem = $true)),
% 0.23/0.37 inference(ennf_transformation,[],[f16])).
% 0.23/0.37 thf(f18,plain,(
% 0.23/0.37 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))) != $true) & (((subset @ X2 @ X4)) = $true) & (((subset @ X1 @ X3)) = $true) & (((in @ X4 @ (powerset @ X0))) = $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (binintersectT_lem = $true)),
% 0.23/0.37 inference(flattening,[],[f17])).
% 0.23/0.37 thf(f19,plain,(
% 0.23/0.37 ((((($true != ((subset @ (binintersect @ sK1 @ sK2) @ (binintersect @ sK3 @ sK4)))) & ($true = ((subset @ sK2 @ sK4))) & ($true = ((subset @ sK1 @ sK3))) & ($true = ((in @ sK4 @ (powerset @ sK0))))) & ($true = ((in @ sK3 @ (powerset @ sK0))))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (binintersectT_lem = $true)),
% 0.23/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f18])).
% 0.23/0.37 thf(f20,plain,(
% 0.23/0.37 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 0.23/0.37 inference(cnf_transformation,[],[f8])).
% 0.23/0.37 thf(f21,plain,(
% 0.23/0.37 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 0.23/0.37 inference(cnf_transformation,[],[f10])).
% 0.23/0.37 thf(f22,plain,(
% 0.23/0.37 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 0.23/0.37 inference(cnf_transformation,[],[f12])).
% 0.23/0.37 thf(f23,plain,(
% 0.23/0.37 (woz13rule3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y2) => ((subset @ Y0 @ Y3) => (subset @ Y0 @ (binintersect @ Y2 @ Y3)))))))))))))))))),
% 0.23/0.37 inference(cnf_transformation,[],[f14])).
% 0.23/0.37 thf(f24,plain,(
% 0.23/0.37 (binintersectT_lem = $true)),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f25,plain,(
% 0.23/0.37 (woz13rule1 = $true)),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f26,plain,(
% 0.23/0.37 (woz13rule2 = $true)),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f27,plain,(
% 0.23/0.37 (woz13rule3 = $true)),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f28,plain,(
% 0.23/0.37 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f29,plain,(
% 0.23/0.37 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f30,plain,(
% 0.23/0.37 ($true = ((in @ sK3 @ (powerset @ sK0))))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f31,plain,(
% 0.23/0.37 ($true = ((in @ sK4 @ (powerset @ sK0))))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f32,plain,(
% 0.23/0.37 ($true = ((subset @ sK1 @ sK3)))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f33,plain,(
% 0.23/0.37 ($true = ((subset @ sK2 @ sK4)))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f34,plain,(
% 0.23/0.37 ($true != ((subset @ (binintersect @ sK1 @ sK2) @ (binintersect @ sK3 @ sK4))))),
% 0.23/0.37 inference(cnf_transformation,[],[f19])).
% 0.23/0.37 thf(f36,definition,(
% 0.23/0.37 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.23/0.37 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.23/0.37 thf(f37,plain,(
% 0.23/0.37 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))) = $true)),
% 0.23/0.37 inference(definition_unfolding,[],[f20,f24])).
% 0.23/0.37 thf(f38,plain,(
% 0.23/0.37 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))) = $true)),
% 0.23/0.37 inference(definition_unfolding,[],[f21,f25])).
% 0.23/0.37 thf(f39,plain,(
% 0.23/0.37 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))) = $true)),
% 0.23/0.37 inference(definition_unfolding,[],[f22,f26])).
% 0.23/0.37 thf(f40,plain,(
% 0.23/0.37 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y2) => ((subset @ Y0 @ Y3) => (subset @ Y0 @ (binintersect @ Y2 @ Y3)))))))))))))))) = $true)),
% 0.23/0.37 inference(definition_unfolding,[],[f23,f27])).
% 0.23/0.37 thf(f41,plain,(
% 0.23/0.37 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y2) => ((subset @ Y0 @ Y3) => (subset @ Y0 @ (binintersect @ Y2 @ Y3)))))))))))))) @ X1)))) )),
% 0.23/0.37 inference(pi_proxy_clausification,[],[f40])).
% 0.23/0.37 thf(f42,plain,(
% 0.23/0.37 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ X1 @ Y1) => ((subset @ X1 @ Y2) => (subset @ X1 @ (binintersect @ Y1 @ Y2)))))))))))))))) )),
% 0.23/0.37 inference(beta-eta_normalization,[],[f41])).
% 0.23/0.37 thf(f43,plain,(
% 0.23/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ X1 @ Y1) => ((subset @ X1 @ Y2) => (subset @ X1 @ (binintersect @ Y1 @ Y2)))))))))))) @ X2)))) )),
% 0.23/0.37 inference(pi_proxy_clausification,[],[f42])).
% 0.23/0.37 thf(f44,plain,(
% 0.23/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => ((subset @ X1 @ Y1) => (subset @ X1 @ (binintersect @ Y0 @ Y1)))))))))))))) )),
% 0.23/0.37 inference(beta-eta_normalization,[],[f43])).
% 0.23/0.37 thf(f45,plain,(
% 0.23/0.37 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => ((subset @ X1 @ Y1) => (subset @ X1 @ (binintersect @ Y0 @ Y1))))))))))))) )),
% 0.23/0.37 inference(imp_proxy_clausification,[],[f44])).
% 0.23/0.37 thf(f46,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => ((subset @ X1 @ Y1) => (subset @ X1 @ (binintersect @ Y0 @ Y1))))))))) @ X3)))) )),
% 0.23/0.37 inference(pi_proxy_clausification,[],[f45])).
% 0.23/0.37 thf(f47,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ X3) => ((subset @ X1 @ Y0) => (subset @ X1 @ (binintersect @ X3 @ Y0))))))))))) )),
% 0.23/0.37 inference(beta-eta_normalization,[],[f46])).
% 0.23/0.37 thf(f48,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ X3) => ((subset @ X1 @ Y0) => (subset @ X1 @ (binintersect @ X3 @ Y0)))))))))) )),
% 0.23/0.37 inference(imp_proxy_clausification,[],[f47])).
% 0.23/0.37 thf(f49,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ X3) => ((subset @ X1 @ Y0) => (subset @ X1 @ (binintersect @ X3 @ Y0)))))) @ X4)))) )),
% 0.23/0.37 inference(pi_proxy_clausification,[],[f48])).
% 0.23/0.37 thf(f50,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ (powerset @ X2)) => ((subset @ X1 @ X3) => ((subset @ X1 @ X4) => (subset @ X1 @ (binintersect @ X3 @ X4)))))))) )),
% 0.23/0.37 inference(beta-eta_normalization,[],[f49])).
% 0.23/0.37 thf(f51,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((subset @ X1 @ X3) => ((subset @ X1 @ X4) => (subset @ X1 @ (binintersect @ X3 @ X4))))))) )),
% 0.23/0.37 inference(imp_proxy_clausification,[],[f50])).
% 0.23/0.37 thf(f52,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | (((subset @ X1 @ X3)) = $false) | ($true = (((subset @ X1 @ X4) => (subset @ X1 @ (binintersect @ X3 @ X4)))))) )),
% 0.23/0.37 inference(imp_proxy_clausification,[],[f51])).
% 0.23/0.37 thf(f53,plain,(
% 0.23/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((subset @ X1 @ (binintersect @ X3 @ X4)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((subset @ X1 @ X4))) | (((subset @ X1 @ X3)) = $false)) )),
% 0.23/0.37 inference(imp_proxy_clausification,[],[f52])).
% 0.23/0.37 thf(f54,plain,(
% 0.23/0.37 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))) @ X1)))) )),
% 0.23/0.37 inference(pi_proxy_clausification,[],[f39])).
% 0.23/0.37 thf(f55,plain,(
% 0.23/0.37 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => (subset @ (binintersect @ X1 @ Y1) @ Y2)))))))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f54])).
% 0.36/0.37 thf(f56,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => (subset @ (binintersect @ X1 @ Y1) @ Y2)))))))))) @ X2)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f55])).
% 0.36/0.37 thf(f57,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ Y0 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1)))))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f56])).
% 0.36/0.37 thf(f58,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ Y0 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1))))))))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f57])).
% 0.36/0.37 thf(f59,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ Y0 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1))))))) @ X3)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f58])).
% 0.36/0.37 thf(f60,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X3 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f59])).
% 0.36/0.37 thf(f61,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X3 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0)))))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f60])).
% 0.36/0.37 thf(f62,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X3 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0)))) @ X4)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f61])).
% 0.36/0.37 thf(f63,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ (powerset @ X2)) => ((subset @ X3 @ X4) => (subset @ (binintersect @ X1 @ X3) @ X4)))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f62])).
% 0.36/0.37 thf(f64,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((subset @ X3 @ X4) => (subset @ (binintersect @ X1 @ X3) @ X4))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f63])).
% 0.36/0.37 thf(f65,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((subset @ (binintersect @ X1 @ X3) @ X4))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((subset @ X3 @ X4)))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f64])).
% 0.36/0.37 thf(f66,plain,(
% 0.36/0.37 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))) @ X1)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f38])).
% 0.36/0.37 thf(f67,plain,(
% 0.36/0.37 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ X1 @ Y2) => (subset @ (binintersect @ X1 @ Y1) @ Y2)))))))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f66])).
% 0.36/0.37 thf(f68,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ X1 @ Y2) => (subset @ (binintersect @ X1 @ Y1) @ Y2)))))))))) @ X2)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f67])).
% 0.36/0.37 thf(f69,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1)))))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f68])).
% 0.36/0.37 thf(f70,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1))))))))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f69])).
% 0.36/0.37 thf(f71,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => ((subset @ X1 @ Y1) => (subset @ (binintersect @ X1 @ Y0) @ Y1))))))) @ X3)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f70])).
% 0.36/0.37 thf(f72,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f71])).
% 0.36/0.37 thf(f73,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0)))))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f72])).
% 0.36/0.37 thf(f74,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((subset @ X1 @ Y0) => (subset @ (binintersect @ X1 @ X3) @ Y0)))) @ X4)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f73])).
% 0.36/0.37 thf(f75,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ (powerset @ X2)) => ((subset @ X1 @ X4) => (subset @ (binintersect @ X1 @ X3) @ X4)))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f74])).
% 0.36/0.37 thf(f76,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((subset @ X1 @ X4) => (subset @ (binintersect @ X1 @ X3) @ X4))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f75])).
% 0.36/0.37 thf(f77,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((subset @ (binintersect @ X1 @ X3) @ X4))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((subset @ X1 @ X4)))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f76])).
% 0.36/0.37 thf(f78,plain,(
% 0.36/0.37 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))) @ X1)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f37])).
% 0.36/0.37 thf(f79,plain,(
% 0.36/0.37 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (binintersect @ X1 @ Y1) @ (powerset @ Y0))))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f78])).
% 0.36/0.37 thf(f80,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (binintersect @ X1 @ Y1) @ (powerset @ Y0))))))) @ X2)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f79])).
% 0.36/0.37 thf(f81,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ Y0) @ (powerset @ X2))))))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f80])).
% 0.36/0.37 thf(f82,plain,(
% 0.36/0.37 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ Y0) @ (powerset @ X2)))))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f81])).
% 0.36/0.37 thf(f83,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ Y0) @ (powerset @ X2)))) @ X3)))) )),
% 0.36/0.37 inference(pi_proxy_clausification,[],[f82])).
% 0.36/0.37 thf(f84,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ X3) @ (powerset @ X2)))))) )),
% 0.36/0.37 inference(beta-eta_normalization,[],[f83])).
% 0.36/0.37 thf(f85,plain,(
% 0.36/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (binintersect @ X1 @ X3) @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2))))) )),
% 0.36/0.37 inference(imp_proxy_clausification,[],[f84])).
% 0.36/0.37 thf(f88,plain,(
% 0.36/0.37 ($true != $true) | (((subset @ (binintersect @ sK1 @ sK2) @ (binintersect @ sK3 @ sK4))) = $false)),
% 0.36/0.37 inference(constrained_superposition,[],[f34,f36])).
% 0.36/0.37 thf(f90,plain,(
% 0.36/0.37 (((subset @ (binintersect @ sK1 @ sK2) @ (binintersect @ sK3 @ sK4))) = $false)),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f88])).
% 0.36/0.37 thf(f200,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ X0)))) | ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK4))) | ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK3)))) )),
% 0.36/0.37 inference(constrained_superposition,[],[f53,f90])).
% 0.36/0.37 thf(f237,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ X0)))) | ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK4))) | ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK3)))) )),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f200])).
% 0.36/0.37 thf(f239,definition,(
% 0.36/0.37 spl5_3 <=> ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK3)))),
% 0.36/0.37 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.36/0.37 thf(f241,plain,(
% 0.36/0.37 ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK3))) | ~spl5_3),
% 0.36/0.37 inference(avatar_component_clause,[],[f239])).
% 0.36/0.37 thf(f243,definition,(
% 0.36/0.37 spl5_4 <=> ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK4)))),
% 0.36/0.37 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.36/0.37 thf(f245,plain,(
% 0.36/0.37 ($false = ((subset @ (binintersect @ sK1 @ sK2) @ sK4))) | ~spl5_4),
% 0.36/0.37 inference(avatar_component_clause,[],[f243])).
% 0.36/0.37 thf(f247,definition,(
% 0.36/0.37 spl5_5 <=> ! [X0 : $i] : (($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0)))))),
% 0.36/0.37 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.36/0.37 thf(f248,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0))))) ) | ~spl5_5),
% 0.36/0.37 inference(avatar_component_clause,[],[f247])).
% 0.36/0.37 thf(f251,plain,(
% 0.36/0.37 spl5_3 | spl5_4 | spl5_5),
% 0.36/0.37 inference(avatar_split_clause,[],[f237,f247,f243,f239])).
% 0.36/0.37 thf(f291,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | (((subset @ sK1 @ sK3)) = $false)) ) | ~spl5_3),
% 0.36/0.37 inference(constrained_superposition,[],[f77,f241])).
% 0.36/0.37 thf(f294,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | (((subset @ sK1 @ sK3)) = $false)) ) | ~spl5_3),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f291])).
% 0.36/0.37 thf(f298,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_3),
% 0.36/0.37 inference(forward_demodulation,[],[f294,f32])).
% 0.36/0.37 thf(f299,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_3),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f298])).
% 0.36/0.37 thf(f357,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_3),
% 0.36/0.37 inference(constrained_superposition,[],[f30,f299])).
% 0.36/0.37 thf(f358,plain,(
% 0.36/0.37 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_3),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f357])).
% 0.36/0.37 thf(f361,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_3),
% 0.36/0.37 inference(forward_demodulation,[],[f358,f29])).
% 0.36/0.37 thf(f362,plain,(
% 0.36/0.37 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_3),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f361])).
% 0.36/0.37 thf(f365,plain,(
% 0.36/0.37 ($true = $false) | ~spl5_3),
% 0.36/0.37 inference(constrained_superposition,[],[f362,f28])).
% 0.36/0.37 thf(f371,plain,(
% 0.36/0.37 $false | ~spl5_3),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f365])).
% 0.36/0.37 thf(f372,plain,(
% 0.36/0.37 ~spl5_3),
% 0.36/0.37 inference(avatar_contradiction_clause,[],[f371])).
% 0.36/0.37 thf(f384,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | ($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0))))) ) | ~spl5_5),
% 0.36/0.37 inference(constrained_superposition,[],[f85,f248])).
% 0.36/0.37 thf(f385,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0))))) ) | ~spl5_5),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f384])).
% 0.36/0.37 thf(f406,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(constrained_superposition,[],[f31,f385])).
% 0.36/0.37 thf(f407,plain,(
% 0.36/0.37 (((in @ sK1 @ (powerset @ sK0))) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f406])).
% 0.36/0.37 thf(f410,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(forward_demodulation,[],[f407,f28])).
% 0.36/0.37 thf(f411,plain,(
% 0.36/0.37 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f410])).
% 0.36/0.37 thf(f414,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(forward_demodulation,[],[f411,f29])).
% 0.36/0.37 thf(f415,plain,(
% 0.36/0.37 (((in @ sK3 @ (powerset @ sK0))) = $false) | ~spl5_5),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f414])).
% 0.36/0.37 thf(f418,plain,(
% 0.36/0.37 ($true = $false) | ~spl5_5),
% 0.36/0.37 inference(constrained_superposition,[],[f415,f30])).
% 0.36/0.37 thf(f424,plain,(
% 0.36/0.37 $false | ~spl5_5),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f418])).
% 0.36/0.37 thf(f425,plain,(
% 0.36/0.37 ~spl5_5),
% 0.36/0.37 inference(avatar_contradiction_clause,[],[f424])).
% 0.36/0.37 thf(f430,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | (((subset @ sK2 @ sK4)) = $false)) ) | ~spl5_4),
% 0.36/0.37 inference(constrained_superposition,[],[f65,f245])).
% 0.36/0.37 thf(f431,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0)))) | (((subset @ sK2 @ sK4)) = $false)) ) | ~spl5_4),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f430])).
% 0.36/0.37 thf(f436,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_4),
% 0.36/0.37 inference(forward_demodulation,[],[f431,f33])).
% 0.36/0.37 thf(f437,plain,(
% 0.36/0.37 ( ! [X0 : $i] : (($false = ((in @ sK4 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_4),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f436])).
% 0.36/0.37 thf(f442,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_4),
% 0.36/0.37 inference(constrained_superposition,[],[f31,f437])).
% 0.36/0.37 thf(f443,plain,(
% 0.36/0.37 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_4),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f442])).
% 0.36/0.37 thf(f446,plain,(
% 0.36/0.37 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_4),
% 0.36/0.37 inference(forward_demodulation,[],[f443,f29])).
% 0.36/0.37 thf(f447,plain,(
% 0.36/0.37 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_4),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f446])).
% 0.36/0.37 thf(f466,plain,(
% 0.36/0.37 ($true = $false) | ~spl5_4),
% 0.36/0.37 inference(constrained_superposition,[],[f447,f28])).
% 0.36/0.37 thf(f472,plain,(
% 0.36/0.37 $false | ~spl5_4),
% 0.36/0.37 inference(trivial_inequality_removal,[],[f466])).
% 0.36/0.37 thf(f473,plain,(
% 0.36/0.37 ~spl5_4),
% 0.36/0.37 inference(avatar_contradiction_clause,[],[f472])).
% 0.36/0.37 cnf(s6, plain, spl5_3 | spl5_4 | spl5_5, inference(sat_conversion,[],[f251])).
% 0.36/0.37 cnf(s17, plain, ~spl5_3, inference(sat_conversion,[],[f372])).
% 0.36/0.37 cnf(s19, plain, ~spl5_5, inference(sat_conversion,[],[f425])).
% 0.36/0.37 cnf(s21, plain, ~spl5_4, inference(sat_conversion,[],[f473])).
% 0.36/0.37 cnf(s23, plain, $false, inference(rat,[],[s6,s19,s21,s17])).
% 0.36/0.37 thf(f474,plain,(
% 0.36/0.37 $false),
% 0.36/0.37 inference(avatar_sat_refutation,[],[s23])).
% 0.36/0.37 % SZS output end Proof for theBenchmark
% 0.36/0.37 % (851406)------------------------------
% 0.36/0.37 % (851406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.37 % (851406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.37 % (851406)CaDiCaL version: 2.1.3
% 0.36/0.37 % (851406)Termination reason: Refutation
% 0.36/0.37 % (851406)Time elapsed: 0.060 s
% 0.36/0.37 % (851406)Peak memory usage: 12 MB
% 0.36/0.37 % (851406)Instructions burned: 70 (million)
% 0.36/0.37 % (851398)Success in time 0.111 s
% 0.36/0.37 % Vampire exiting
%------------------------------------------------------------------------------