%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU666^2 : 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 : n017.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 08:32:54 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU666^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:02:03 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.27 % (389724)Will run a generic schedule for satisfiability detection.
% 0.07/0.27 % (389730)% WARNING: option uhcvi not known.
% 0.07/0.27 % (389730)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1506151453:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.27 % (389729)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=886228029_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.27 % (389731)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1949460438:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.27 % (389730)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.27 % (389730)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.27 % Exception at run slice level
% 0.07/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.27 % (389730) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-389724-389730"...
% 0.07/0.27 % (389730)...printing done.
% 0.07/0.27 % (389731) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-389724-389731"...
% 0.07/0.27 % (389730)Refutation found. Thanks to Tanya!
% 0.07/0.27 % SZS status Theorem for theBenchmark
% 0.07/0.27 % SZS output start Proof for theBenchmark
% 0.07/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.07/0.27 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.07/0.27 thf(func_def_2, type, dsetconstrEL: $o).
% 0.07/0.27 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.07/0.27 thf(func_def_5, type, subsetI2: $o).
% 0.07/0.27 thf(func_def_6, type, kpair: ($i > $i > $i)).
% 0.07/0.27 thf(func_def_7, type, cartprod: ($i > $i > $i)).
% 0.07/0.27 thf(func_def_8, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 0.07/0.27 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.27 thf(func_def_10, type, vIMP: ($o > $o > $o)).
% 0.07/0.27 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.07/0.27 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.27 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.27 thf(func_def_15, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.27 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 0.07/0.27 thf(func_def_17, type, db4: !>[X0: $tType]:(X0)).
% 0.07/0.27 thf(func_def_18, type, db3: !>[X0: $tType]:(X0)).
% 0.07/0.27 thf(func_def_19, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.27 thf(func_def_24, type, sK2: ($i > $i > $o)).
% 0.07/0.27 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.07/0.27 thf(func_def_26, type, sK3: ($i > $i > $i)).
% 0.07/0.27 thf(f1,axiom,(
% 0.07/0.27 (dsetconstrEL = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)))),
% 0.07/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.07/0.27 thf(f2,axiom,(
% 0.07/0.27 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.07/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.07/0.27 thf(f3,axiom,(
% 0.07/0.27 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0))))))))),
% 0.07/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr)).
% 0.07/0.27 thf(f4,conjecture,(
% 0.07/0.27 dsetconstrEL => (subsetI2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (subset @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4)))) @ (cartprod @ X0 @ X1)))),
% 0.07/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub)).
% 0.07/0.27 thf(f5,negated_conjecture,(
% 0.07/0.27 ~(dsetconstrEL => (subsetI2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (subset @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4)))) @ (cartprod @ X0 @ X1))))),
% 0.07/0.27 inference(negated_conjecture,[status(cth)],[f4])).
% 0.07/0.27 thf(f6,plain,(
% 0.07/0.27 (dsetconstrEL = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)))),
% 0.07/0.27 inference(rectify,[],[f1])).
% 0.07/0.27 thf(f7,plain,(
% 0.07/0.27 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2))))))))))),
% 0.07/0.27 inference(fool_elimination,[],[f6])).
% 0.07/0.27 thf(f8,plain,(
% 0.07/0.27 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.07/0.27 inference(rectify,[],[f2])).
% 0.07/0.27 thf(f9,plain,(
% 0.07/0.27 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.07/0.27 inference(fool_elimination,[],[f8])).
% 0.07/0.27 thf(f10,plain,(
% 0.07/0.27 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0))))))))),
% 0.07/0.27 inference(rectify,[],[f3])).
% 0.07/0.27 thf(f11,plain,(
% 0.07/0.27 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.07/0.27 inference(fool_elimination,[],[f10])).
% 0.07/0.27 thf(f12,plain,(
% 0.07/0.27 ~(dsetconstrEL => (subsetI2 => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (subset @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4)))) @ (cartprod @ X0 @ X1))))),
% 0.07/0.27 inference(rectify,[],[f5])).
% 0.07/0.27 thf(f13,plain,(
% 0.07/0.27 ~((dsetconstrEL = $true) => ((subsetI2 = $true) => ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : ($true = ((subset @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))) @ (cartprod @ X0 @ X1))))))),
% 0.07/0.27 inference(fool_elimination,[],[f12])).
% 0.07/0.27 thf(f14,plain,(
% 0.07/0.27 (? [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : ($true != ((subset @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))) @ (cartprod @ X0 @ X1)))) & (subsetI2 = $true)) & (dsetconstrEL = $true)),
% 0.07/0.27 inference(ennf_transformation,[],[f13])).
% 0.07/0.27 thf(f15,plain,(
% 0.07/0.27 ? [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : ($true != ((subset @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))) @ (cartprod @ X0 @ X1)))) & (subsetI2 = $true) & (dsetconstrEL = $true)),
% 0.07/0.27 inference(flattening,[],[f14])).
% 0.07/0.27 thf(f16,plain,(
% 0.07/0.27 ($true != ((subset @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))) @ (cartprod @ sK0 @ sK1)))) & (subsetI2 = $true) & (dsetconstrEL = $true)),
% 0.07/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15])).
% 0.07/0.27 thf(f17,plain,(
% 0.07/0.27 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2))))))))))),
% 0.07/0.27 inference(cnf_transformation,[],[f7])).
% 0.07/0.27 thf(f18,plain,(
% 0.07/0.27 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.07/0.27 inference(cnf_transformation,[],[f9])).
% 0.07/0.27 thf(f19,plain,(
% 0.07/0.27 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.07/0.27 inference(cnf_transformation,[],[f11])).
% 0.07/0.27 thf(f20,plain,(
% 0.07/0.27 (dsetconstrEL = $true)),
% 0.07/0.27 inference(cnf_transformation,[],[f16])).
% 0.07/0.27 thf(f21,plain,(
% 0.07/0.27 (subsetI2 = $true)),
% 0.07/0.27 inference(cnf_transformation,[],[f16])).
% 0.07/0.27 thf(f22,plain,(
% 0.07/0.27 ($true != ((subset @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))) @ (cartprod @ sK0 @ sK1))))),
% 0.07/0.27 inference(cnf_transformation,[],[f16])).
% 0.07/0.27 thf(f24,definition,(
% 0.07/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.27 thf(f25,plain,(
% 0.07/0.27 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2))))))))) = $true)),
% 0.07/0.27 inference(definition_unfolding,[],[f17,f20])).
% 0.07/0.27 thf(f26,plain,(
% 0.07/0.27 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))) = $true)),
% 0.07/0.27 inference(definition_unfolding,[],[f18,f21])).
% 0.07/0.27 thf(f27,plain,(
% 0.07/0.27 ($true != ((subset @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))) @ sK0 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))) @ (cartprod @ sK0 @ sK1))))),
% 0.07/0.27 inference(definition_unfolding,[],[f22,f19])).
% 0.07/0.27 thf(f28,plain,(
% 0.07/0.27 ($true != ((subset @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0))))))))) @ (cartprod @ sK0 @ sK1))))),
% 0.07/0.27 inference(beta-eta_normalization,[],[f27])).
% 0.07/0.27 thf(f29,plain,(
% 0.07/0.27 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 0.07/0.27 inference(pi_proxy_clausification,[],[f26])).
% 0.07/0.27 thf(f30,plain,(
% 0.07/0.27 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))))))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f29])).
% 0.07/0.27 thf(f31,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2)))) )),
% 0.07/0.27 inference(pi_proxy_clausification,[],[f30])).
% 0.07/0.27 thf(f32,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1))))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f31])).
% 0.07/0.27 thf(f33,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.07/0.27 inference(imp_proxy_clausification,[],[f32])).
% 0.07/0.27 thf(f34,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.07/0.27 inference(sigma_proxy_clausification,[],[f33])).
% 0.07/0.27 thf(f35,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK3 @ X1 @ X2) @ X2) => (in @ (sK3 @ X1 @ X2) @ X1)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f34])).
% 0.07/0.27 thf(f36,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK3 @ X1 @ X2) @ X1))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.07/0.27 inference(imp_proxy_clausification,[],[f35])).
% 0.07/0.27 thf(f37,plain,(
% 0.07/0.27 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X2) @ X2))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.07/0.27 inference(imp_proxy_clausification,[],[f35])).
% 0.07/0.27 thf(f38,plain,(
% 0.07/0.27 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2))))))) @ X1)))) )),
% 0.07/0.27 inference(pi_proxy_clausification,[],[f25])).
% 0.07/0.27 thf(f39,plain,(
% 0.07/0.27 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (in @ X1 @ Y1))))))))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f38])).
% 0.07/0.27 thf(f40,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (in @ X1 @ Y1))))) @ X2)))) )),
% 0.07/0.27 inference(pi_proxy_clausification,[],[f39])).
% 0.07/0.27 thf(f41,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (in @ X1 @ Y0))))))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f40])).
% 0.07/0.27 thf(f42,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (in @ X1 @ Y0))) @ X3)))) )),
% 0.07/0.27 inference(pi_proxy_clausification,[],[f41])).
% 0.07/0.27 thf(f43,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (dsetconstr @ X3 @ X2)) => (in @ X1 @ X3))))) )),
% 0.07/0.27 inference(beta-eta_normalization,[],[f42])).
% 0.07/0.27 thf(f44,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (dsetconstr @ X3 @ X2)))) | ($true = ((in @ X1 @ X3)))) )),
% 0.07/0.27 inference(imp_proxy_clausification,[],[f43])).
% 0.07/0.27 thf(f56,plain,(
% 0.07/0.27 ($true != $true) | ($false = ((subset @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0))))))))) @ (cartprod @ sK0 @ sK1))))),
% 0.07/0.27 inference(constrained_superposition,[],[f28,f24])).
% 0.07/0.27 thf(f57,plain,(
% 0.07/0.27 ($false = ((subset @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (sK2 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0))))))))) @ (cartprod @ sK0 @ sK1))))),
% 0.07/0.27 inference(trivial_inequality_removal,[],[f56])).
% 0.07/0.27 thf(f60,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true = $false) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | ($true = ((subset @ (dsetconstr @ X1 @ X2) @ X0)))) )),
% 0.07/0.27 inference(constrained_superposition,[],[f44,f37])).
% 0.07/0.27 thf(f64,plain,(
% 0.07/0.27 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | ($true = ((subset @ (dsetconstr @ X1 @ X2) @ X0)))) )),
% 0.07/0.27 inference(trivial_inequality_removal,[],[f60])).
% 0.07/0.27 thf(f74,plain,(
% 0.07/0.27 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = $false) | ($true = ((subset @ (dsetconstr @ X0 @ X1) @ X0))) | ($true = ((subset @ (dsetconstr @ X0 @ X1) @ X0)))) )),
% 0.07/0.27 inference(constrained_superposition,[],[f36,f64])).
% 0.07/0.27 thf(f75,plain,(
% 0.07/0.27 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = $false) | ($true = ((subset @ (dsetconstr @ X0 @ X1) @ X0)))) )),
% 0.07/0.27 inference(duplicate_literal_removal,[],[f74])).
% 0.07/0.27 thf(f76,plain,(
% 0.07/0.27 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = ((subset @ (dsetconstr @ X0 @ X1) @ X0)))) )),
% 0.07/0.27 inference(trivial_inequality_removal,[],[f75])).
% 0.07/0.27 thf(f83,plain,(
% 0.07/0.27 ($true = $false)),
% 0.07/0.27 inference(constrained_superposition,[],[f57,f76])).
% 0.07/0.27 thf(f84,plain,(
% 0.07/0.27 $false),
% 0.07/0.27 inference(trivial_inequality_removal,[],[f83])).
% 0.07/0.27 % SZS output end Proof for theBenchmark
% 0.07/0.27 % (389730)------------------------------
% 0.07/0.27 % (389730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.27 % (389730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.27 % (389730)CaDiCaL version: 2.1.3
% 0.07/0.27 % (389730)Termination reason: Refutation
% 0.07/0.27 % (389730)Time elapsed: 0.007 s
% 0.07/0.27 % (389730)Peak memory usage: 12 MB
% 0.07/0.27 % (389730)Instructions burned: 10 (million)
% 0.07/0.27 % (389724)Success in time 0.049 s
% 0.07/0.27 % Vampire exiting
%------------------------------------------------------------------------------