%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU781^2 : 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 : n020.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 08:33:23 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU781^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n020.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 14:29:04 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.19/0.28 % (1130732)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (1130738)% WARNING: option uhcvi not known.
% 0.19/0.28 % (1130738)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4211144480:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (1130738)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (1130738)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (1130737)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=493335953_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (1130738) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1130732-1130738"...
% 0.19/0.28 % (1130738)...printing done.
% 0.19/0.28 % (1130738)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.19/0.28 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.19/0.28 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.19/0.28 thf(func_def_6, type, breln1: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_7, type, breln1compset: ($i > $i > $i > $i)).
% 0.19/0.28 thf(func_def_8, type, breln1compE: $o).
% 0.19/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_13, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_14, type, vIMP: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_15, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_16, type, db4: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_17, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_18, type, vAND: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_19, type, db5: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_27, type, sK5: $o).
% 0.19/0.28 thf(func_def_28, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_29, type, sK6: ($i > $i > $i > $i > $i > $i)).
% 0.19/0.28 thf(f1,axiom,(
% 0.19/0.28 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 0.19/0.28 thf(f2,axiom,(
% 0.19/0.28 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1)).
% 0.19/0.28 thf(f3,axiom,(
% 0.19/0.28 (breln1compE = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0))))))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE)).
% 0.19/0.28 thf(f4,conjecture,(
% 0.19/0.28 breln1compE => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ! [X5 : $o] : (! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X3 @ X6) @ X1) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5))))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compEex)).
% 0.19/0.28 thf(f5,negated_conjecture,(
% 0.19/0.28 ~(breln1compE => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ! [X5 : $o] : (! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X3 @ X6) @ X1) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5)))))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.28 thf(f6,plain,(
% 0.19/0.28 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.28 inference(fool_elimination,[],[f1])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.28 inference(fool_elimination,[],[f2])).
% 0.19/0.28 thf(f8,plain,(
% 0.19/0.28 (breln1compE = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0))))))))),
% 0.19/0.28 inference(rectify,[],[f3])).
% 0.19/0.28 thf(f9,plain,(
% 0.19/0.28 (breln1compE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (breln1compset @ Y1 @ Y0 @ Y2)) => (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (in @ (kpair @ Y3 @ Y5) @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2)))))))))))))))))))))),
% 0.19/0.28 inference(fool_elimination,[],[f8])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 ~(breln1compE => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ! [X5 : $o] : (! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X3 @ X6) @ X1) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5)))))))),
% 0.19/0.28 inference(rectify,[],[f5])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 ~((breln1compE = $true) => ! [X0 : $i,X1 : $i] : ((((breln1 @ X0 @ X1)) = $true) => ! [X2 : $i] : ((((breln1 @ X0 @ X2)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) = $true) => ! [X5 : $o] : (! [X6 : $i] : ((((in @ X6 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X6) @ X1)) = $true) => ((((in @ (kpair @ X6 @ X4) @ X2)) = $true) => ($true = X5)))) => ($true = X5))))))))),
% 0.19/0.28 inference(fool_elimination,[],[f10])).
% 0.19/0.28 thf(f12,plain,(
% 0.19/0.28 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((($true = X5) | (((in @ (kpair @ X6 @ X4) @ X2)) != $true)) | (((in @ (kpair @ X3 @ X6) @ X1)) != $true)) | (((in @ X6 @ X0)) != $true))) & (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) = $true)) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((breln1 @ X0 @ X2)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (breln1compE = $true)),
% 0.19/0.28 inference(ennf_transformation,[],[f11])).
% 0.19/0.28 thf(f13,plain,(
% 0.19/0.28 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | (((in @ (kpair @ X6 @ X4) @ X2)) != $true) | (((in @ (kpair @ X3 @ X6) @ X1)) != $true) | (((in @ X6 @ X0)) != $true))) & (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) = $true) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((breln1 @ X0 @ X2)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (breln1compE = $true)),
% 0.19/0.28 inference(flattening,[],[f12])).
% 0.19/0.28 thf(f14,plain,(
% 0.19/0.28 (((((($true != sK5) & ! [X6 : $i] : (($true = sK5) | ($true != ((in @ (kpair @ X6 @ sK4) @ sK2))) | ($true != ((in @ (kpair @ sK3 @ X6) @ sK1))) | ($true != ((in @ X6 @ sK0))))) & ($true = ((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = ((in @ sK4 @ sK0)))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((breln1 @ sK0 @ sK2)))) & ($true = ((breln1 @ sK0 @ sK1)))) & (breln1compE = $true)),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f13])).
% 0.19/0.28 thf(f15,plain,(
% 0.19/0.28 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.28 inference(cnf_transformation,[],[f6])).
% 0.19/0.28 thf(f16,plain,(
% 0.19/0.28 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.28 inference(cnf_transformation,[],[f7])).
% 0.19/0.28 thf(f17,plain,(
% 0.19/0.28 (breln1compE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (breln1compset @ Y1 @ Y0 @ Y2)) => (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (in @ (kpair @ Y3 @ Y5) @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2)))))))))))))))))))))),
% 0.19/0.28 inference(cnf_transformation,[],[f9])).
% 0.19/0.28 thf(f18,plain,(
% 0.19/0.28 (breln1compE = $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f19,plain,(
% 0.19/0.28 ($true = ((breln1 @ sK0 @ sK1)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f20,plain,(
% 0.19/0.28 ($true = ((breln1 @ sK0 @ sK2)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f21,plain,(
% 0.19/0.28 ($true = ((in @ sK3 @ sK0)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f22,plain,(
% 0.19/0.28 ($true = ((in @ sK4 @ sK0)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f23,plain,(
% 0.19/0.28 ($true = ((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f24,plain,(
% 0.19/0.28 ( ! [X6 : $i] : (($true = sK5) | ($true != ((in @ (kpair @ X6 @ sK4) @ sK2))) | ($true != ((in @ (kpair @ sK3 @ X6) @ sK1))) | ($true != ((in @ X6 @ sK0)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f25,plain,(
% 0.19/0.28 ($true != sK5)),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f27,definition,(
% 0.19/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.28 thf(f28,plain,(
% 0.19/0.28 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.28 inference(definition_unfolding,[],[f16,f15])).
% 0.19/0.28 thf(f29,plain,(
% 0.19/0.28 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (breln1compset @ Y1 @ Y0 @ Y2)) => (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (in @ (kpair @ Y3 @ Y5) @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2)))))))))))))))))))))),
% 0.19/0.28 inference(definition_unfolding,[],[f17,f18,f28,f28])).
% 0.19/0.28 thf(f30,plain,(
% 0.19/0.28 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK2)))),
% 0.19/0.28 inference(definition_unfolding,[],[f20,f28])).
% 0.19/0.28 thf(f31,plain,(
% 0.19/0.28 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK1)))),
% 0.19/0.28 inference(definition_unfolding,[],[f19,f28])).
% 0.19/0.28 thf(f32,plain,(
% 0.19/0.28 ($true = ((subset @ sK1 @ (cartprod @ sK0 @ sK0))))),
% 0.19/0.28 inference(beta-eta_normalization,[],[f31])).
% 0.19/0.28 thf(f33,plain,(
% 0.19/0.28 ($true = ((subset @ sK2 @ (cartprod @ sK0 @ sK0))))),
% 0.19/0.28 inference(beta-eta_normalization,[],[f30])).
% 0.19/0.28 thf(f34,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (breln1compset @ Y1 @ Y0 @ Y2)) => (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (in @ (kpair @ Y3 @ Y5) @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2)))))))))))))))))) @ X1)))) )),
% 0.19/0.28 inference(pi_proxy_clausification,[],[f29])).
% 0.19/0.28 thf(f35,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ (breln1compset @ Y0 @ X1 @ Y1)) => (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (in @ (kpair @ Y2 @ Y4) @ X1)) & (in @ (kpair @ Y4 @ Y3) @ Y1)))))))))))))))))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f34])).
% 0.19/0.28 thf(f36,plain,(
% 0.19/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ (breln1compset @ Y0 @ X1 @ Y1)) => (?? @ $i @ (^[Y4 : $i]: (((in @ Y4 @ Y0) & (in @ (kpair @ Y2 @ Y4) @ X1)) & (in @ (kpair @ Y4 @ Y3) @ Y1)))))))))))))))) @ X2)))) )),
% 0.19/0.28 inference(pi_proxy_clausification,[],[f35])).
% 0.19/0.28 thf(f37,plain,(
% 0.19/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((subset @ X1 @ (cartprod @ X2 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ (breln1compset @ X2 @ X1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X2) & (in @ (kpair @ Y1 @ Y3) @ X1)) & (in @ (kpair @ Y3 @ Y2) @ Y0)))))))))))))))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f36])).
% 0.19/0.28 thf(f38,plain,(
% 0.19/0.28 ( ! [X2 : $i,X1 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ (breln1compset @ X2 @ X1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X2) & (in @ (kpair @ Y1 @ Y3) @ X1)) & (in @ (kpair @ Y3 @ Y2) @ Y0))))))))))))))))) )),
% 0.19/0.28 inference(imp_proxy_clausification,[],[f37])).
% 0.19/0.28 thf(f39,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($true = (((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ (breln1compset @ X2 @ X1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: (((in @ Y3 @ X2) & (in @ (kpair @ Y1 @ Y3) @ X1)) & (in @ (kpair @ Y3 @ Y2) @ Y0))))))))))))) @ X3)))) )),
% 0.19/0.28 inference(pi_proxy_clausification,[],[f38])).
% 0.19/0.28 thf(f40,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($true = (((subset @ X3 @ (cartprod @ X2 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X2) & (in @ (kpair @ Y0 @ Y2) @ X1)) & (in @ (kpair @ Y2 @ Y1) @ X3))))))))))))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f39])).
% 0.19/0.28 thf(f41,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X2) & (in @ (kpair @ Y0 @ Y2) @ X1)) & (in @ (kpair @ Y2 @ Y1) @ X3)))))))))))))) )),
% 0.19/0.28 inference(imp_proxy_clausification,[],[f40])).
% 0.19/0.28 thf(f42,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ X2) & (in @ (kpair @ Y0 @ Y2) @ X1)) & (in @ (kpair @ Y2 @ Y1) @ X3)))))))))) @ X4)))) )),
% 0.19/0.28 inference(pi_proxy_clausification,[],[f41])).
% 0.19/0.28 thf(f43,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($true = (((in @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ X2) & (in @ (kpair @ X4 @ Y1) @ X1)) & (in @ (kpair @ Y1 @ Y0) @ X3)))))))))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f42])).
% 0.19/0.28 thf(f44,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ X2) & (in @ (kpair @ X4 @ Y1) @ X1)) & (in @ (kpair @ Y1 @ Y0) @ X3))))))))))) )),
% 0.19/0.28 inference(imp_proxy_clausification,[],[f43])).
% 0.19/0.28 thf(f45,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ X2) & (in @ (kpair @ X4 @ Y1) @ X1)) & (in @ (kpair @ Y1 @ Y0) @ X3))))))) @ X5)))) )),
% 0.19/0.28 inference(pi_proxy_clausification,[],[f44])).
% 0.19/0.28 thf(f46,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = (((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ X2) & (in @ (kpair @ X4 @ Y0) @ X1)) & (in @ (kpair @ Y0 @ X5) @ X3))))))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f45])).
% 0.19/0.28 thf(f47,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($true = (((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)) => (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ X2) & (in @ (kpair @ X4 @ Y0) @ X1)) & (in @ (kpair @ Y0 @ X5) @ X3)))))))) )),
% 0.19/0.28 inference(imp_proxy_clausification,[],[f46])).
% 0.19/0.28 thf(f48,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($true = ((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ X2) & (in @ (kpair @ X4 @ Y0) @ X1)) & (in @ (kpair @ Y0 @ X5) @ X3))))))) )),
% 0.19/0.28 inference(imp_proxy_clausification,[],[f47])).
% 0.19/0.28 thf(f49,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($true = (((^[Y0 : $i]: (((in @ Y0 @ X2) & (in @ (kpair @ X4 @ Y0) @ X1)) & (in @ (kpair @ Y0 @ X5) @ X3))) @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3))))) )),
% 0.19/0.28 inference(sigma_proxy_clausification,[],[f48])).
% 0.19/0.28 thf(f50,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($true = ((((in @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3) @ X2) & (in @ (kpair @ X4 @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3)) @ X1)) & (in @ (kpair @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3) @ X5) @ X3))))) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f49])).
% 0.19/0.28 thf(f51,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (kpair @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3) @ X5) @ X3))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($false = ((in @ X4 @ X2)))) )),
% 0.19/0.28 inference(and_proxy_clausification,[],[f50])).
% 0.19/0.28 thf(f52,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($true = (((in @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3) @ X2) & (in @ (kpair @ X4 @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3)) @ X1))))) )),
% 0.19/0.28 inference(and_proxy_clausification,[],[f50])).
% 0.19/0.28 thf(f53,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (kpair @ X4 @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3)) @ X1))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($false = ((in @ X4 @ X2)))) )),
% 0.19/0.28 inference(and_proxy_clausification,[],[f52])).
% 0.19/0.28 thf(f54,plain,(
% 0.19/0.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (sK6 @ X1 @ X2 @ X5 @ X4 @ X3) @ X2))) | ($false = ((subset @ X3 @ (cartprod @ X2 @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X2 @ X1 @ X3)))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X2))))) )),
% 0.19/0.28 inference(and_proxy_clausification,[],[f52])).
% 0.19/0.28 thf(f56,definition,(
% 0.19/0.28 spl7_1 <=> ! [X6 : $i] : (($true != ((in @ (kpair @ X6 @ sK4) @ sK2))) | ($true != ((in @ X6 @ sK0))) | ($true != ((in @ (kpair @ sK3 @ X6) @ sK1))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.19/0.28 thf(f57,plain,(
% 0.19/0.28 ( ! [X6 : $i] : (($true != ((in @ (kpair @ sK3 @ X6) @ sK1))) | ($true != ((in @ X6 @ sK0))) | ($true != ((in @ (kpair @ X6 @ sK4) @ sK2)))) ) | ~spl7_1),
% 0.19/0.28 inference(avatar_component_clause,[],[f56])).
% 0.19/0.28 thf(f59,definition,(
% 0.19/0.28 spl7_2 <=> ($true = sK5)),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.19/0.28 thf(f62,plain,(
% 0.19/0.28 spl7_1 | spl7_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f24,f59,f56])).
% 0.19/0.28 thf(f63,plain,(
% 0.19/0.28 ~spl7_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f25,f59])).
% 0.19/0.28 thf(f66,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK0))) | ($true != ((in @ (kpair @ X0 @ sK4) @ sK2))) | ($false = ((in @ (kpair @ sK3 @ X0) @ sK1)))) ) | ~spl7_1),
% 0.19/0.28 inference(constrained_superposition,[],[f57,f27])).
% 0.19/0.28 thf(f70,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true != ((in @ (kpair @ X0 @ sK4) @ sK2))) | ($true != ((in @ X0 @ sK0))) | ($false = ((in @ (kpair @ sK3 @ X0) @ sK1)))) ) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f66])).
% 0.19/0.28 thf(f82,plain,(
% 0.19/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ (sK6 @ X0 @ X1 @ sK4 @ X2 @ sK2) @ sK0))) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ X1 @ sK4 @ X2 @ sK2)) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ X1 @ X1)))) | ($false = ((subset @ X0 @ (cartprod @ X1 @ X1)))) | ($false = ((in @ sK4 @ X1))) | ($false = ((in @ (kpair @ X2 @ sK4) @ (breln1compset @ X1 @ X0 @ sK2)))) | ($false = ((in @ X2 @ X1)))) ) | ~spl7_1),
% 0.19/0.28 inference(constrained_superposition,[],[f70,f51])).
% 0.19/0.28 thf(f87,plain,(
% 0.19/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK6 @ X0 @ X1 @ sK4 @ X2 @ sK2) @ sK0))) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ X1 @ sK4 @ X2 @ sK2)) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ X1 @ X1)))) | ($false = ((subset @ X0 @ (cartprod @ X1 @ X1)))) | ($false = ((in @ sK4 @ X1))) | ($false = ((in @ (kpair @ X2 @ sK4) @ (breln1compset @ X1 @ X0 @ sK2)))) | ($false = ((in @ X2 @ X1)))) ) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f82])).
% 0.19/0.28 thf(f140,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((in @ X1 @ sK0))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0))))) ) | ~spl7_1),
% 0.19/0.28 inference(constrained_superposition,[],[f87,f54])).
% 0.19/0.28 thf(f141,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(duplicate_literal_removal,[],[f140])).
% 0.19/0.28 thf(f142,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f141])).
% 0.19/0.28 thf(f144,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f142,f33])).
% 0.19/0.28 thf(f145,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f144])).
% 0.19/0.28 thf(f146,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f145,f22])).
% 0.19/0.28 thf(f147,plain,(
% 0.19/0.28 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (kpair @ sK3 @ (sK6 @ X0 @ sK0 @ sK4 @ X1 @ sK2)) @ sK1))) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ sK0)))) | ($false = ((in @ (kpair @ X1 @ sK4) @ (breln1compset @ sK0 @ X0 @ sK2)))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f146])).
% 0.19/0.28 thf(f168,plain,(
% 0.19/0.28 ($true = $false) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(constrained_superposition,[],[f53,f147])).
% 0.19/0.28 thf(f170,plain,(
% 0.19/0.28 ($true = $false) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(duplicate_literal_removal,[],[f168])).
% 0.19/0.28 thf(f171,plain,(
% 0.19/0.28 ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f170])).
% 0.19/0.28 thf(f175,plain,(
% 0.19/0.28 ($true = $false) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f171,f33])).
% 0.19/0.28 thf(f176,plain,(
% 0.19/0.28 ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f175])).
% 0.19/0.28 thf(f179,plain,(
% 0.19/0.28 ($true = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f176,f32])).
% 0.19/0.28 thf(f180,plain,(
% 0.19/0.28 (((in @ sK4 @ sK0)) = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f179])).
% 0.19/0.28 thf(f183,plain,(
% 0.19/0.28 ($true = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f180,f22])).
% 0.19/0.28 thf(f184,plain,(
% 0.19/0.28 (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | (((in @ sK3 @ sK0)) = $false) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f183])).
% 0.19/0.28 thf(f187,plain,(
% 0.19/0.28 ($true = $false) | (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | ~spl7_1),
% 0.19/0.28 inference(forward_demodulation,[],[f184,f21])).
% 0.19/0.28 thf(f188,plain,(
% 0.19/0.28 (((in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) = $false) | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f187])).
% 0.19/0.28 thf(f203,plain,(
% 0.19/0.28 ($true = $false) | ~spl7_1),
% 0.19/0.28 inference(constrained_superposition,[],[f188,f23])).
% 0.19/0.28 thf(f207,plain,(
% 0.19/0.28 $false | ~spl7_1),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f203])).
% 0.19/0.28 thf(f208,plain,(
% 0.19/0.28 ~spl7_1),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f207])).
% 0.19/0.28 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f62])).
% 0.19/0.28 cnf(s2, plain, ~spl7_2, inference(sat_conversion,[],[f63])).
% 0.19/0.28 cnf(s6, plain, ~spl7_1, inference(sat_conversion,[],[f208])).
% 0.19/0.28 cnf(s7, plain, $false, inference(rat,[],[s1,s2,s6])).
% 0.19/0.28 thf(f210,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(avatar_sat_refutation,[],[s7])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (1130738)------------------------------
% 0.19/0.28 % (1130738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1130738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1130738)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1130738)Termination reason: Refutation
% 0.19/0.28 % (1130738)Time elapsed: 0.012 s
% 0.19/0.28 % (1130738)Peak memory usage: 13 MB
% 0.19/0.28 % (1130738)Instructions burned: 41 (million)
% 0.19/0.28 % (1130732)Success in time 0.044 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------