%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU785^2 : 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 : n018.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 08:33:24 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU785^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:30:56 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.27 % (158940)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (158946)% WARNING: option uhcvi not known.
% 0.19/0.27 % (158946)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4077091367:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (158946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (158946)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (158945)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=705227073_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (158946) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-158940-158946"...
% 0.19/0.27 % (158947)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1664341649:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (158948)dis+10_1_sil=32000:sp=arity:random_seed=3557526325:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (158949)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2061112787:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (158949)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (158946)...printing done.
% 0.19/0.27 % (158946)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.27 thf(func_def_1, type, binunion: ($i > $i > $i)).
% 0.19/0.27 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.19/0.27 thf(func_def_3, type, breln1: ($i > $i > $o)).
% 0.19/0.27 thf(func_def_4, type, breln1unionIL: $o).
% 0.19/0.27 thf(func_def_6, type, breln1unionIR: $o).
% 0.19/0.27 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.19/0.27 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_12, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_13, type, db4: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(func_def_22, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 (breln1unionIL = ! [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) @ X1) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL)).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 (breln1unionIR = ! [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) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIR)).
% 0.19/0.27 thf(f3,conjecture,(
% 0.19/0.27 breln1unionIL => (breln1unionIR => ! [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) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionI)).
% 0.19/0.27 thf(f4,negated_conjecture,(
% 0.19/0.27 ~(breln1unionIL => (breln1unionIR => ! [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) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)))))))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 (breln1unionIL = ! [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) @ X1) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 (breln1unionIL = ((!! @ $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) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))))),
% 0.19/0.27 inference(fool_elimination,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 (breln1unionIR = ! [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) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 (breln1unionIR = ((!! @ $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) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))))),
% 0.19/0.27 inference(fool_elimination,[],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ~(breln1unionIL => (breln1unionIR => ! [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) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)))))))))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ~((breln1unionIL = $true) => ((breln1unionIR = $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) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) = $true)) => (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))) = $true))))))))),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))) != $true) & ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) = $true))) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((breln1 @ X0 @ X2)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)),
% 0.19/0.27 inference(ennf_transformation,[],[f10])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))) != $true) & ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) = $true)) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((breln1 @ X0 @ X2)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (breln1unionIR = $true) & (breln1unionIL = $true)),
% 0.19/0.27 inference(flattening,[],[f11])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ((((($true != ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2)))) & (($true = ((in @ (kpair @ sK3 @ sK4) @ sK2))) | ($true = ((in @ (kpair @ sK3 @ sK4) @ sK1)))) & ($true = ((in @ sK4 @ sK0)))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((breln1 @ sK0 @ sK2)))) & ($true = ((breln1 @ sK0 @ sK1)))) & (breln1unionIR = $true) & (breln1unionIL = $true)),
% 0.19/0.27 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)],[f12])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 (breln1unionIL = ((!! @ $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) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))))),
% 0.19/0.27 inference(cnf_transformation,[],[f6])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 (breln1unionIR = ((!! @ $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) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))))),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 (breln1unionIL = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 (breln1unionIR = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ($true = ((breln1 @ sK0 @ sK1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ($true = ((breln1 @ sK0 @ sK2)))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ($true = ((in @ sK3 @ sK0)))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ($true = ((in @ sK4 @ sK0)))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ($true = ((in @ (kpair @ sK3 @ sK4) @ sK2))) | ($true = ((in @ (kpair @ sK3 @ sK4) @ sK1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ($true != ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2))))),
% 0.19/0.27 inference(cnf_transformation,[],[f13])).
% 0.19/0.27 thf(f25,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 (((!! @ $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) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))) = $true)),
% 0.19/0.27 inference(definition_unfolding,[],[f14,f16])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 (((!! @ $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) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))))) = $true)),
% 0.19/0.27 inference(definition_unfolding,[],[f15,f17])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ( ! [X1 : $i] : (($true = (((^[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) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))) @ X1)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f27])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (binunion @ X1 @ Y1)))))))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f28])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (binunion @ X1 @ Y1)))))))))))))) @ X2)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f29])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0)))))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f30])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0))))))))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f31])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = (((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0))))))))))) @ X3)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f32])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = (((breln1 @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f33])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3)))))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f34])).
% 0.19/0.27 thf(f36,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3)))))))) @ X4)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f35])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = (((in @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X3) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3)))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f36])).
% 0.19/0.27 thf(f38,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X3) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f37])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X3) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3))))) @ X5)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f38])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = (((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f39])).
% 0.19/0.27 thf(f41,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($true = (((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3)))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f40])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3)))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((breln1 @ X2 @ X1))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ X3)))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f41])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 ( ! [X1 : $i] : (($true = (((^[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) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ (binunion @ Y0 @ Y2)))))))))))))))) @ X1)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f26])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ (binunion @ X1 @ Y1)))))))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f43])).
% 0.19/0.27 thf(f45,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ (binunion @ X1 @ Y1)))))))))))))) @ X2)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f44])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0)))))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f45])).
% 0.19/0.27 thf(f47,plain,(
% 0.19/0.27 ( ! [X2 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0))))))))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f46])).
% 0.19/0.27 thf(f48,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = (((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ (binunion @ X1 @ Y0))))))))))) @ X3)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f47])).
% 0.19/0.27 thf(f49,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($true = (((breln1 @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3))))))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f48])).
% 0.19/0.27 thf(f50,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3)))))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f49])).
% 0.19/0.27 thf(f51,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ (binunion @ X1 @ X3)))))))) @ X4)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f50])).
% 0.19/0.27 thf(f52,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($true = (((in @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X1) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3)))))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f51])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X1) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3))))))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f52])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ X1) => (in @ (kpair @ X4 @ Y0) @ (binunion @ X1 @ X3))))) @ X5)))) )),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f53])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($true = (((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X1) => (in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3))))))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f54])).
% 0.19/0.27 thf(f56,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((breln1 @ X2 @ X1))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X5 @ X2))) | ($true = (((in @ (kpair @ X4 @ X5) @ X1) => (in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3)))))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f55])).
% 0.19/0.27 thf(f57,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (kpair @ X4 @ X5) @ (binunion @ X1 @ X3)))) | ($false = ((breln1 @ X2 @ X3))) | ($false = ((breln1 @ X2 @ X1))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ (kpair @ X4 @ X5) @ X1)))) )),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f56])).
% 0.19/0.27 thf(f59,definition,(
% 0.19/0.27 spl5_1 <=> ($true = ((in @ (kpair @ sK3 @ sK4) @ sK1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.27 thf(f61,plain,(
% 0.19/0.27 ($true = ((in @ (kpair @ sK3 @ sK4) @ sK1))) | ~spl5_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f59])).
% 0.19/0.27 thf(f63,definition,(
% 0.19/0.27 spl5_2 <=> ($true = ((in @ (kpair @ sK3 @ sK4) @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.27 thf(f65,plain,(
% 0.19/0.27 ($true = ((in @ (kpair @ sK3 @ sK4) @ sK2))) | ~spl5_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f63])).
% 0.19/0.27 thf(f66,plain,(
% 0.19/0.27 spl5_1 | spl5_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f22,f63,f59])).
% 0.19/0.27 thf(f69,plain,(
% 0.19/0.27 ($true != $true) | (((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2))) = $false)),
% 0.19/0.27 inference(constrained_superposition,[],[f23,f25])).
% 0.19/0.27 thf(f71,plain,(
% 0.19/0.27 (((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2))) = $false)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f69])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($true != $true) | ($false = ((breln1 @ X0 @ sK2))) | ($false = ((breln1 @ X0 @ sK1))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK3 @ X0))) | (((in @ (kpair @ sK3 @ sK4) @ sK2)) = $false)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f23,f42])).
% 0.19/0.27 thf(f93,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($false = ((breln1 @ X0 @ sK2))) | ($false = ((breln1 @ X0 @ sK1))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK3 @ X0))) | (((in @ (kpair @ sK3 @ sK4) @ sK2)) = $false)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f84])).
% 0.19/0.27 thf(f103,definition,(
% 0.19/0.27 spl5_3 <=> (((in @ (kpair @ sK3 @ sK4) @ sK2)) = $false)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.27 thf(f105,plain,(
% 0.19/0.27 (((in @ (kpair @ sK3 @ sK4) @ sK2)) = $false) | ~spl5_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f103])).
% 0.19/0.27 thf(f107,definition,(
% 0.19/0.27 spl5_4 <=> ! [X0 : $i] : (($false = ((breln1 @ X0 @ sK2))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK4 @ X0))) | ($false = ((breln1 @ X0 @ sK1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.19/0.27 thf(f108,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($false = ((breln1 @ X0 @ sK2))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK4 @ X0))) | ($false = ((breln1 @ X0 @ sK1)))) ) | ~spl5_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f107])).
% 0.19/0.27 thf(f109,plain,(
% 0.19/0.27 spl5_3 | spl5_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f93,f107,f103])).
% 0.19/0.27 thf(f153,definition,(
% 0.19/0.27 spl5_5 <=> (((in @ (kpair @ sK3 @ sK4) @ sK1)) = $false)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.19/0.27 thf(f155,plain,(
% 0.19/0.27 (((in @ (kpair @ sK3 @ sK4) @ sK1)) = $false) | ~spl5_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f153])).
% 0.19/0.27 thf(f157,plain,(
% 0.19/0.27 ($true = $false) | (~spl5_2 | ~spl5_3)),
% 0.19/0.27 inference(constrained_superposition,[],[f105,f65])).
% 0.19/0.27 thf(f163,plain,(
% 0.19/0.27 $false | (~spl5_2 | ~spl5_3)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f157])).
% 0.19/0.27 thf(f164,plain,(
% 0.19/0.27 ~spl5_2 | ~spl5_3),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f163])).
% 0.19/0.27 thf(f166,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($true = $false) | ($false = ((breln1 @ X0 @ sK2))) | ($false = ((breln1 @ X0 @ sK1))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK3 @ X0))) | (((in @ (kpair @ sK3 @ sK4) @ sK1)) = $false)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f71,f57])).
% 0.19/0.27 thf(f176,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($false = ((breln1 @ X0 @ sK2))) | ($false = ((breln1 @ X0 @ sK1))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK3 @ X0))) | (((in @ (kpair @ sK3 @ sK4) @ sK1)) = $false)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f166])).
% 0.19/0.27 thf(f178,plain,(
% 0.19/0.27 spl5_5 | spl5_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f176,f107,f153])).
% 0.19/0.27 thf(f181,plain,(
% 0.19/0.27 ($true = $false) | (((in @ sK3 @ sK0)) = $false) | (((in @ sK4 @ sK0)) = $false) | (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(constrained_superposition,[],[f19,f108])).
% 0.19/0.27 thf(f182,plain,(
% 0.19/0.27 (((in @ sK3 @ sK0)) = $false) | (((in @ sK4 @ sK0)) = $false) | (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f181])).
% 0.19/0.27 thf(f185,plain,(
% 0.19/0.27 ($true = $false) | (((in @ sK4 @ sK0)) = $false) | (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(forward_demodulation,[],[f182,f20])).
% 0.19/0.27 thf(f186,plain,(
% 0.19/0.27 (((in @ sK4 @ sK0)) = $false) | (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f185])).
% 0.19/0.27 thf(f189,plain,(
% 0.19/0.27 ($true = $false) | (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(forward_demodulation,[],[f186,f21])).
% 0.19/0.27 thf(f190,plain,(
% 0.19/0.27 (((breln1 @ sK0 @ sK1)) = $false) | ~spl5_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f189])).
% 0.19/0.27 thf(f193,plain,(
% 0.19/0.27 ($true = $false) | ~spl5_4),
% 0.19/0.27 inference(constrained_superposition,[],[f190,f18])).
% 0.19/0.27 thf(f199,plain,(
% 0.19/0.27 $false | ~spl5_4),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f193])).
% 0.19/0.27 thf(f200,plain,(
% 0.19/0.27 ~spl5_4),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f199])).
% 0.19/0.27 thf(f201,plain,(
% 0.19/0.27 ($true = $false) | (~spl5_1 | ~spl5_5)),
% 0.19/0.27 inference(constrained_superposition,[],[f155,f61])).
% 0.19/0.27 thf(f207,plain,(
% 0.19/0.27 $false | (~spl5_1 | ~spl5_5)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f201])).
% 0.19/0.27 thf(f208,plain,(
% 0.19/0.27 ~spl5_1 | ~spl5_5),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f207])).
% 0.19/0.27 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f66])).
% 0.19/0.27 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f109])).
% 0.19/0.27 cnf(s5, plain, ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f164])).
% 0.19/0.27 cnf(s7, plain, spl5_4 | spl5_5, inference(sat_conversion,[],[f178])).
% 0.19/0.27 cnf(s9, plain, ~spl5_4, inference(sat_conversion,[],[f200])).
% 0.19/0.27 cnf(s11, plain, ~spl5_1 | ~spl5_5, inference(sat_conversion,[],[f208])).
% 0.19/0.27 cnf(s12, plain, spl5_5, inference(rat,[],[s7,s9])).
% 0.19/0.27 cnf(s13, plain, ~spl5_1, inference(rat,[],[s11,s12])).
% 0.19/0.27 cnf(s14, plain, spl5_3, inference(rat,[],[s2,s9])).
% 0.19/0.27 cnf(s15, plain, ~spl5_2, inference(rat,[],[s5,s14])).
% 0.19/0.27 cnf(s16, plain, $false, inference(rat,[],[s1,s15,s13])).
% 0.19/0.27 thf(f209,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s16])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (158946)------------------------------
% 0.19/0.27 % (158946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (158946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (158946)CaDiCaL version: 2.1.3
% 0.19/0.27 % (158946)Termination reason: Refutation
% 0.19/0.27 % (158946)Time elapsed: 0.009 s
% 0.19/0.27 % (158946)Peak memory usage: 13 MB
% 0.19/0.27 % (158946)Instructions burned: 32 (million)
% 0.19/0.27 % (158940)Success in time 0.037 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------