%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU627^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 08:32:44 AM UTC 2026
% Result : Theorem 0.08s 0.29s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU627^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:59:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.29 % (2902906)Will run a generic schedule for satisfiability detection.
% 0.08/0.29 % (2902925)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3802264483:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.29 % (2902925)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.29 % (2902922)% WARNING: option uhcvi not known.
% 0.08/0.29 % (2902925) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2902906-2902925"...
% 0.08/0.29 % (2902924)dis+10_1_sil=32000:sp=arity:random_seed=3860818378:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.29 % (2902922)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=458383378:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.29 % (2902925)...printing done.
% 0.08/0.29 % (2902922)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.29 % (2902925)Refutation found. Thanks to Tanya!
% 0.08/0.29 % SZS status Theorem for theBenchmark
% 0.08/0.29 % SZS output start Proof for theBenchmark
% 0.08/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.29 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.08/0.29 thf(func_def_3, type, powerset: ($i > $i)).
% 0.08/0.29 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.08/0.29 thf(func_def_5, type, subsetI2: $o).
% 0.08/0.29 thf(func_def_7, type, binunion: ($i > $i > $i)).
% 0.08/0.29 thf(func_def_8, type, singletoninpowunion: $o).
% 0.08/0.29 thf(func_def_9, type, upairset2E: $o).
% 0.08/0.29 thf(func_def_10, type, upairinpowunion: $o).
% 0.08/0.29 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.29 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 0.08/0.29 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.29 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.29 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.29 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.29 thf(func_def_17, type, vOR: ($o > $o > $o)).
% 0.08/0.29 thf(func_def_18, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.29 thf(func_def_19, type, db3: !>[X0: $tType]:(X0)).
% 0.08/0.29 thf(func_def_26, type, vNOT: ($o > $o)).
% 0.08/0.29 thf(func_def_27, type, sK4: ($i > $i > $i)).
% 0.08/0.29 thf(f1,axiom,(
% 0.08/0.29 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.08/0.29 thf(f2,axiom,(
% 0.08/0.29 (singletoninpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion)).
% 0.08/0.29 thf(f3,axiom,(
% 0.08/0.29 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X1) | (X2 = X0))))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)).
% 0.08/0.29 thf(f4,axiom,(
% 0.08/0.29 (upairinpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion)).
% 0.08/0.29 thf(f5,conjecture,(
% 0.08/0.29 subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1)).
% 0.08/0.29 thf(f6,negated_conjecture,(
% 0.08/0.29 ~(subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))))),
% 0.08/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.08/0.29 thf(f7,plain,(
% 0.08/0.29 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.08/0.29 inference(rectify,[],[f1])).
% 0.08/0.29 thf(f8,plain,(
% 0.08/0.29 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.08/0.29 inference(fool_elimination,[],[f7])).
% 0.08/0.29 thf(f9,plain,(
% 0.08/0.29 (singletoninpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))),
% 0.08/0.29 inference(rectify,[],[f2])).
% 0.08/0.29 thf(f10,plain,(
% 0.08/0.29 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))),
% 0.08/0.29 inference(fool_elimination,[],[f9])).
% 0.08/0.29 thf(f11,plain,(
% 0.08/0.29 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X1) | (X2 = X0))))),
% 0.08/0.29 inference(rectify,[],[f3])).
% 0.08/0.29 thf(f12,plain,(
% 0.08/0.29 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))))),
% 0.08/0.29 inference(fool_elimination,[],[f11])).
% 0.08/0.29 thf(f13,plain,(
% 0.08/0.29 (upairinpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 0.08/0.29 inference(rectify,[],[f4])).
% 0.08/0.29 thf(f14,plain,(
% 0.08/0.29 (upairinpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))))),
% 0.08/0.29 inference(fool_elimination,[],[f13])).
% 0.08/0.29 thf(f15,plain,(
% 0.08/0.29 ~(subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))))),
% 0.08/0.29 inference(rectify,[],[f6])).
% 0.08/0.29 thf(f16,plain,(
% 0.08/0.29 ~((subsetI2 = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairinpowunion = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))) = $true)))))))),
% 0.08/0.29 inference(fool_elimination,[],[f15])).
% 0.08/0.29 thf(f17,plain,(
% 0.08/0.29 (((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (upairinpowunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (subsetI2 = $true)),
% 0.08/0.29 inference(ennf_transformation,[],[f16])).
% 0.08/0.29 thf(f18,plain,(
% 0.08/0.29 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (upairinpowunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (subsetI2 = $true)),
% 0.08/0.29 inference(flattening,[],[f17])).
% 0.08/0.29 thf(f19,plain,(
% 0.08/0.29 ((($true != ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))))) & ($true = ((in @ sK3 @ sK1)))) & ($true = ((in @ sK2 @ sK0)))) & (upairinpowunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (subsetI2 = $true)),
% 0.08/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f18])).
% 0.08/0.29 thf(f20,plain,(
% 0.08/0.29 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.08/0.29 inference(cnf_transformation,[],[f8])).
% 0.08/0.29 thf(f21,plain,(
% 0.08/0.29 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))),
% 0.08/0.29 inference(cnf_transformation,[],[f10])).
% 0.08/0.29 thf(f22,plain,(
% 0.08/0.29 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))))),
% 0.08/0.29 inference(cnf_transformation,[],[f12])).
% 0.08/0.29 thf(f23,plain,(
% 0.08/0.29 (upairinpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))))),
% 0.08/0.29 inference(cnf_transformation,[],[f14])).
% 0.08/0.29 thf(f24,plain,(
% 0.08/0.29 (subsetI2 = $true)),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f25,plain,(
% 0.08/0.29 (singletoninpowunion = $true)),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f26,plain,(
% 0.08/0.29 (upairset2E = $true)),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f27,plain,(
% 0.08/0.29 (upairinpowunion = $true)),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f28,plain,(
% 0.08/0.29 ($true = ((in @ sK2 @ sK0)))),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f29,plain,(
% 0.08/0.29 ($true = ((in @ sK3 @ sK1)))),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f30,plain,(
% 0.08/0.29 ($true != ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1)))))),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f32,definition,(
% 0.08/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.29 thf(f33,plain,(
% 0.08/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))) = $true)),
% 0.08/0.29 inference(definition_unfolding,[],[f20,f24])).
% 0.08/0.29 thf(f34,plain,(
% 0.08/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1))))))))))) = $true)),
% 0.08/0.29 inference(definition_unfolding,[],[f21,f25])).
% 0.08/0.29 thf(f35,plain,(
% 0.08/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))) = $true)),
% 0.08/0.29 inference(definition_unfolding,[],[f22,f26])).
% 0.08/0.29 thf(f36,plain,(
% 0.08/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) = $true)),
% 0.08/0.29 inference(definition_unfolding,[],[f23,f27])).
% 0.08/0.29 thf(f37,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))) @ X1)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f36])).
% 0.08/0.29 thf(f38,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0)))))))))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f37])).
% 0.08/0.29 thf(f39,plain,(
% 0.08/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0)))))))))) @ X2)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f38])).
% 0.08/0.29 thf(f40,plain,(
% 0.08/0.29 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ (powerset @ (binunion @ Y0 @ X2)))))))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f39])).
% 0.08/0.29 thf(f41,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ (powerset @ (binunion @ Y0 @ X2)))))))) @ X3)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f40])).
% 0.08/0.29 thf(f42,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X3 @ X2)))))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f41])).
% 0.08/0.29 thf(f43,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X3 @ X2))))))))) )),
% 0.08/0.29 inference(imp_proxy_clausification,[],[f42])).
% 0.08/0.29 thf(f44,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X3 @ X2))))) @ X4)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f43])).
% 0.08/0.29 thf(f45,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X4 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ (powerset @ (binunion @ X3 @ X2))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f44])).
% 0.08/0.29 thf(f46,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ (powerset @ (binunion @ X3 @ X2))))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X1 @ X3)))) )),
% 0.08/0.29 inference(imp_proxy_clausification,[],[f45])).
% 0.08/0.29 thf(f47,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))) @ X1)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f35])).
% 0.08/0.29 thf(f48,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y1 = X1) | (Y0 = X1)))))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f47])).
% 0.08/0.29 thf(f49,plain,(
% 0.08/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y1 = X1) | (Y0 = X1)))))) @ X2)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f48])).
% 0.08/0.29 thf(f50,plain,(
% 0.08/0.29 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset))) => ((Y0 = X1) | (X2 = X1)))))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f49])).
% 0.08/0.29 thf(f51,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset))) => ((Y0 = X1) | (X2 = X1)))) @ X3)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f50])).
% 0.08/0.29 thf(f52,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) => ((X3 = X1) | (X2 = X1)))))) )),
% 0.08/0.29 inference(beta-eta_normalization,[],[f51])).
% 0.08/0.29 thf(f53,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | ($true = (((X3 = X1) | (X2 = X1))))) )),
% 0.08/0.29 inference(imp_proxy_clausification,[],[f52])).
% 0.08/0.29 thf(f54,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | ($true = ((X2 = X1))) | ($true = ((X3 = X1)))) )),
% 0.08/0.29 inference(or_proxy_clausification,[],[f53])).
% 0.08/0.29 thf(f55,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | (X1 = X2) | ($true = ((X3 = X1)))) )),
% 0.08/0.29 inference(equality_proxy_clausification,[],[f54])).
% 0.08/0.29 thf(f56,plain,(
% 0.08/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | (X1 = X2) | (X1 = X3)) )),
% 0.08/0.29 inference(equality_proxy_clausification,[],[f55])).
% 0.08/0.29 thf(f57,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1))))))))) @ X1)))) )),
% 0.08/0.29 inference(pi_proxy_clausification,[],[f34])).
% 0.08/0.29 thf(f58,plain,(
% 0.08/0.29 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ Y1 @ Y0))))))))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f57])).
% 0.08/0.30 thf(f59,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ Y1 @ Y0))))))) @ X2)))) )),
% 0.08/0.30 inference(pi_proxy_clausification,[],[f58])).
% 0.08/0.30 thf(f60,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ Y0 @ X2))))))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f59])).
% 0.08/0.30 thf(f61,plain,(
% 0.08/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ Y0 @ X2))))) @ X3)))) )),
% 0.08/0.30 inference(pi_proxy_clausification,[],[f60])).
% 0.08/0.30 thf(f62,plain,(
% 0.08/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X2))))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f61])).
% 0.08/0.30 thf(f63,plain,(
% 0.08/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X2))))) | ($false = ((in @ X1 @ X3)))) )),
% 0.08/0.30 inference(imp_proxy_clausification,[],[f62])).
% 0.08/0.30 thf(f64,plain,(
% 0.08/0.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 0.08/0.30 inference(pi_proxy_clausification,[],[f33])).
% 0.08/0.30 thf(f65,plain,(
% 0.08/0.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f64])).
% 0.08/0.30 thf(f66,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2)))) )),
% 0.08/0.30 inference(pi_proxy_clausification,[],[f65])).
% 0.08/0.30 thf(f67,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f66])).
% 0.08/0.30 thf(f68,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.08/0.30 inference(imp_proxy_clausification,[],[f67])).
% 0.08/0.30 thf(f69,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK4 @ X1 @ X2)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.08/0.30 inference(sigma_proxy_clausification,[],[f68])).
% 0.08/0.30 thf(f70,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK4 @ X1 @ X2) @ X2) => (in @ (sK4 @ X1 @ X2) @ X1)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f69])).
% 0.08/0.30 thf(f71,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK4 @ X1 @ X2) @ X1))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.08/0.30 inference(imp_proxy_clausification,[],[f70])).
% 0.08/0.30 thf(f72,plain,(
% 0.08/0.30 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X1 @ X2) @ X2))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.08/0.30 inference(imp_proxy_clausification,[],[f70])).
% 0.08/0.30 thf(f75,plain,(
% 0.08/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X2) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X1) | ($true = ((subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ X0)))) )),
% 0.08/0.30 inference(constrained_superposition,[],[f56,f72])).
% 0.08/0.30 thf(f79,plain,(
% 0.08/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ X0))) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X1) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X2)) )),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f75])).
% 0.08/0.30 thf(f94,plain,(
% 0.08/0.30 ($true != $true) | (((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1)))) = $false)),
% 0.08/0.30 inference(constrained_superposition,[],[f30,f32])).
% 0.08/0.30 thf(f95,plain,(
% 0.08/0.30 (((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1)))) = $false)),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f94])).
% 0.08/0.30 thf(f99,plain,(
% 0.08/0.30 ($true = $false) | (((setadjoin @ sK2 @ emptyset)) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | (((setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))),
% 0.08/0.30 inference(constrained_superposition,[],[f79,f95])).
% 0.08/0.30 thf(f104,plain,(
% 0.08/0.30 (((setadjoin @ sK2 @ emptyset)) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | (((setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f99])).
% 0.08/0.30 thf(f106,definition,(
% 0.08/0.30 spl5_1 <=> (((setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))),
% 0.08/0.30 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.08/0.30 thf(f108,plain,(
% 0.08/0.30 (((setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | ~spl5_1),
% 0.08/0.30 inference(avatar_component_clause,[],[f106])).
% 0.08/0.30 thf(f110,definition,(
% 0.08/0.30 spl5_2 <=> (((setadjoin @ sK2 @ emptyset)) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))),
% 0.08/0.30 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.08/0.30 thf(f112,plain,(
% 0.08/0.30 (((setadjoin @ sK2 @ emptyset)) = ((sK4 @ (powerset @ (binunion @ sK0 @ sK1)) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | ~spl5_2),
% 0.08/0.30 inference(avatar_component_clause,[],[f110])).
% 0.08/0.30 thf(f115,plain,(
% 0.08/0.30 spl5_1 | spl5_2),
% 0.08/0.30 inference(avatar_split_clause,[],[f104,f110,f106])).
% 0.08/0.30 thf(f117,plain,(
% 0.08/0.30 ($false = ((in @ (setadjoin @ sK2 @ emptyset) @ (powerset @ (binunion @ sK0 @ sK1))))) | ($true = ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))))) | ~spl5_2),
% 0.08/0.30 inference(constrained_superposition,[],[f71,f112])).
% 0.08/0.30 thf(f118,plain,(
% 0.08/0.30 ($false = ((in @ (setadjoin @ sK2 @ emptyset) @ (powerset @ (binunion @ sK0 @ sK1))))) | ~spl5_2),
% 0.08/0.30 inference(forward_subsumption_resolution,[],[f117,f30])).
% 0.08/0.30 thf(f122,plain,(
% 0.08/0.30 ($true = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl5_2),
% 0.08/0.30 inference(constrained_superposition,[],[f63,f118])).
% 0.08/0.30 thf(f123,plain,(
% 0.08/0.30 (((in @ sK2 @ sK0)) = $false) | ~spl5_2),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f122])).
% 0.08/0.30 thf(f126,plain,(
% 0.08/0.30 ($true = $false) | ~spl5_2),
% 0.08/0.30 inference(constrained_superposition,[],[f123,f28])).
% 0.08/0.30 thf(f132,plain,(
% 0.08/0.30 $false | ~spl5_2),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f126])).
% 0.08/0.30 thf(f133,plain,(
% 0.08/0.30 ~spl5_2),
% 0.08/0.30 inference(avatar_contradiction_clause,[],[f132])).
% 0.08/0.30 thf(f136,plain,(
% 0.08/0.30 ($false = ((in @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))))) | ($true = ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))))) | ~spl5_1),
% 0.08/0.30 inference(constrained_superposition,[],[f71,f108])).
% 0.08/0.30 thf(f137,plain,(
% 0.08/0.30 ($false = ((in @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))))) | ~spl5_1),
% 0.08/0.30 inference(forward_subsumption_resolution,[],[f136,f30])).
% 0.08/0.30 thf(f141,plain,(
% 0.08/0.30 ($true = $false) | (((in @ sK3 @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl5_1),
% 0.08/0.30 inference(constrained_superposition,[],[f46,f137])).
% 0.08/0.30 thf(f142,plain,(
% 0.08/0.30 (((in @ sK3 @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl5_1),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f141])).
% 0.08/0.30 thf(f145,plain,(
% 0.08/0.30 ($true = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl5_1),
% 0.08/0.30 inference(forward_demodulation,[],[f142,f29])).
% 0.08/0.30 thf(f146,plain,(
% 0.08/0.30 (((in @ sK2 @ sK0)) = $false) | ~spl5_1),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f145])).
% 0.08/0.30 thf(f149,plain,(
% 0.08/0.30 ($true = $false) | ~spl5_1),
% 0.08/0.30 inference(constrained_superposition,[],[f146,f28])).
% 0.08/0.30 thf(f155,plain,(
% 0.08/0.30 $false | ~spl5_1),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f149])).
% 0.08/0.30 thf(f156,plain,(
% 0.08/0.30 ~spl5_1),
% 0.08/0.30 inference(avatar_contradiction_clause,[],[f155])).
% 0.08/0.30 cnf(s3, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f115])).
% 0.08/0.30 cnf(s5, plain, ~spl5_2, inference(sat_conversion,[],[f133])).
% 0.08/0.30 cnf(s7, plain, ~spl5_1, inference(sat_conversion,[],[f156])).
% 0.08/0.30 cnf(s8, plain, $false, inference(rat,[],[s3,s5,s7])).
% 0.08/0.30 thf(f157,plain,(
% 0.08/0.30 $false),
% 0.08/0.30 inference(avatar_sat_refutation,[],[s8])).
% 0.08/0.30 % SZS output end Proof for theBenchmark
% 0.08/0.30 % (2902925)------------------------------
% 0.08/0.30 % (2902925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.30 % (2902925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.30 % (2902925)CaDiCaL version: 2.1.3
% 0.08/0.30 % (2902925)Termination reason: Refutation
% 0.08/0.30 % (2902925)Time elapsed: 0.011 s
% 0.08/0.30 % (2902925)Peak memory usage: 12 MB
% 0.08/0.30 % (2902925)Instructions burned: 20 (million)
% 0.08/0.30 % (2902906)Success in time 0.049 s
% 0.08/0.30 % Vampire exiting
%------------------------------------------------------------------------------