%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV124^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:37:51 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV124^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n006.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue Sep 29 15:11:55 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running higher-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.37 % (848660)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (848665)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1289436924:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.37 % (848665) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-848660-848665"...
% 0.24/0.37 % (848665)...printing done.
% 0.24/0.37 % (848671)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.37 % (848671)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.37 % (848665)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Theorem for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% 0.24/0.37 thf(type_def_5, type, a: $tType).
% 0.24/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.37 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.24/0.37 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.24/0.37 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.24/0.37 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.37 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.37 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.24/0.37 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.37 thf(func_def_10, type, sK0: a).
% 0.24/0.37 thf(func_def_11, type, sK1: ((a > a > $o) > $o)).
% 0.24/0.37 thf(func_def_12, type, sK2: ((a > a > $o) > $o)).
% 0.24/0.37 thf(func_def_13, type, sK3: a).
% 0.24/0.37 thf(func_def_14, type, sK4: (a > a > $o)).
% 0.24/0.37 thf(func_def_15, type, sK5: ((a > a > $o) > a)).
% 0.24/0.37 thf(func_def_16, type, sK6: ((a > a > $o) > a)).
% 0.24/0.37 thf(func_def_17, type, sK7: ((a > a > $o) > a > a > $o)).
% 0.24/0.37 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.24/0.37 thf(func_def_19, type, sK8: ((a > a > $o) > a > a > a > a > $o)).
% 0.24/0.37 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.24/0.37 thf(f1,conjecture,(
% 0.24/0.37 ! [X0 : ((a > a > $o) > $o),X2 : a,X3 : a,X1 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : ((! [X6 : a,X5 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : (((^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : ((! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 0.24/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM254_A_pme)).
% 0.24/0.37 thf(f2,negated_conjecture,(
% 0.24/0.37 ~ ! [X0 : ((a > a > $o) > $o),X2 : a,X3 : a,X1 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : ((! [X6 : a,X5 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : (((^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : ((! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 0.24/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.37 thf(f3,plain,(
% 0.24/0.37 ~ ! [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X3 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X1 @ X2)) => ! [X8 : (a > a > $o)] : ((! [X9 : a,X10 : a] : (? [X11 : (a > a > $o)] : ((X11 @ X10 @ X9) & ? [X12 : (a > a > $o)] : (((^[X13 : a, X14 : a] : (! [X15 : (a > a > $o)] : ((! [X16 : a,X17 : a] : ((X12 @ X16 @ X17) => (X15 @ X16 @ X17)) & (X0 @ X15)) => (X15 @ X13 @ X14)))) = X11) & (X3 @ X12))) => (X8 @ X10 @ X9)) & (X0 @ X8)) => (X8 @ X1 @ X2)))),
% 0.24/0.37 inference(rectify,[],[f2])).
% 0.24/0.37 thf(f4,plain,(
% 0.24/0.37 ~ ! [X0 : ((a > a > $o) > $o),X1 : a,X3 : ((a > a > $o) > $o),X2 : a] : (! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ($true = ((X3 @ X7)))) => (((X4 @ X5 @ X6)) = $true)) & (((X0 @ X4)) = $true)) => (((X4 @ X1 @ X2)) = $true)) => ! [X8 : (a > a > $o)] : ((! [X9 : a,X10 : a] : (? [X11 : (a > a > $o)] : (? [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) = X11) & ($true = ((X3 @ X12)))) & ($true = ((X11 @ X10 @ X9)))) => ($true = ((X8 @ X10 @ X9)))) & ($true = ((X0 @ X8)))) => ($true = ((X8 @ X1 @ X2)))))),
% 0.24/0.37 inference(fool_elimination,[],[f3])).
% 0.24/0.37 thf(f5,plain,(
% 0.24/0.37 ? [X0 : ((a > a > $o) > $o),X1 : a,X3 : ((a > a > $o) > $o),X2 : a] : (? [X8 : (a > a > $o)] : (($true != ((X8 @ X1 @ X2))) & (! [X9 : a,X10 : a] : (($true = ((X8 @ X10 @ X9))) | ! [X11 : (a > a > $o)] : (($true != ((X11 @ X10 @ X9))) | ! [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X11) | ($true != ((X3 @ X12)))))) & ($true = ((X0 @ X8))))) & ! [X4 : (a > a > $o)] : ((((X4 @ X1 @ X2)) = $true) | (? [X6 : a,X5 : a] : ((((X4 @ X5 @ X6)) != $true) & ? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ($true = ((X3 @ X7))))) | (((X0 @ X4)) != $true))))),
% 0.24/0.37 inference(ennf_transformation,[],[f4])).
% 0.24/0.37 thf(f6,plain,(
% 0.24/0.37 ? [X1 : a,X3 : ((a > a > $o) > $o),X0 : ((a > a > $o) > $o),X2 : a] : (? [X8 : (a > a > $o)] : (($true = ((X0 @ X8))) & ! [X9 : a,X10 : a] : (($true = ((X8 @ X10 @ X9))) | ! [X11 : (a > a > $o)] : (($true != ((X11 @ X10 @ X9))) | ! [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X11) | ($true != ((X3 @ X12)))))) & ($true != ((X8 @ X1 @ X2)))) & ! [X4 : (a > a > $o)] : (? [X6 : a,X5 : a] : ((((X4 @ X5 @ X6)) != $true) & ? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ($true = ((X3 @ X7))))) | (((X0 @ X4)) != $true) | (((X4 @ X1 @ X2)) = $true)))),
% 0.24/0.37 inference(flattening,[],[f5])).
% 0.24/0.37 thf(f7,plain,(
% 0.24/0.37 ? [X0 : a,X1 : ((a > a > $o) > $o),X2 : ((a > a > $o) > $o),X3 : a] : (? [X4 : (a > a > $o)] : (($true = ((X2 @ X4))) & ! [X5 : a,X6 : a] : (($true = ((X4 @ X6 @ X5))) | ! [X7 : (a > a > $o)] : (($true != ((X7 @ X6 @ X5))) | ! [X8 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X7) | (((X1 @ X8)) != $true)))) & ($true != ((X4 @ X0 @ X3)))) & ! [X9 : (a > a > $o)] : (? [X10 : a,X11 : a] : (($true != ((X9 @ X11 @ X10))) & ? [X12 : (a > a > $o)] : ((((X12 @ X11 @ X10)) = $true) & ($true = ((X1 @ X12))))) | (((X2 @ X9)) != $true) | ($true = ((X9 @ X0 @ X3)))))),
% 0.24/0.37 inference(rectify,[],[f6])).
% 0.24/0.37 thf(f8,plain,(
% 0.24/0.37 (($true = ((sK2 @ sK4))) & ! [X5 : a,X6 : a] : (($true = ((sK4 @ X6 @ X5))) | ! [X7 : (a > a > $o)] : (($true != ((X7 @ X6 @ X5))) | ! [X8 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X7) | ($true != ((sK1 @ X8)))))) & ($true != ((sK4 @ sK0 @ sK3)))) & ! [X9 : (a > a > $o)] : ((($true != ((X9 @ (sK6 @ X9) @ (sK5 @ X9)))) & (($true = ((sK7 @ X9 @ (sK6 @ X9) @ (sK5 @ X9)))) & ($true = ((sK1 @ (sK7 @ X9)))))) | ($true != ((sK2 @ X9))) | ($true = ((X9 @ sK0 @ sK3))))),
% 0.24/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X12,sK7 @ X9),skolemize(X12,sK7 @ X9),skolemize(X12,sK7 @ X9)],[f7])).
% 0.24/0.37 thf(f9,plain,(
% 0.24/0.37 ( ! [X9 : (a > a > $o)] : (($true != ((sK2 @ X9))) | ($true = ((sK1 @ (sK7 @ X9)))) | ($true = ((X9 @ sK0 @ sK3)))) )),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f10,plain,(
% 0.24/0.37 ( ! [X9 : (a > a > $o)] : (($true != ((sK2 @ X9))) | ($true = ((sK7 @ X9 @ (sK6 @ X9) @ (sK5 @ X9)))) | ($true = ((X9 @ sK0 @ sK3)))) )),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f11,plain,(
% 0.24/0.37 ( ! [X9 : (a > a > $o)] : (($true != ((X9 @ (sK6 @ X9) @ (sK5 @ X9)))) | ($true = ((X9 @ sK0 @ sK3))) | ($true != ((sK2 @ X9)))) )),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f12,plain,(
% 0.24/0.37 ($true != ((sK4 @ sK0 @ sK3)))),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f13,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X7 : (a > a > $o),X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ($true != ((X7 @ X6 @ X5))) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X7) | ($true != ((sK1 @ X8)))) )),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f14,plain,(
% 0.24/0.37 ($true = ((sK2 @ sK4)))),
% 0.24/0.37 inference(cnf_transformation,[],[f8])).
% 0.24/0.37 thf(f17,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ($true != (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) @ X6 @ X5))) | ($true != ((sK1 @ X8)))) )),
% 0.24/0.37 inference(equality_resolution,[],[f13])).
% 0.24/0.37 thf(f18,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ($true != ((sK1 @ X8))) | ($true != ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X6 @ X5))))))) )),
% 0.24/0.37 inference(beta-eta_normalization,[],[f17])).
% 0.24/0.37 thf(f19,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ((((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X6 @ X5))) @ (sK8 @ X8 @ X5 @ X6))) = $false) | ($true != ((sK1 @ X8)))) )),
% 0.24/0.37 inference(sigma_proxy_clausification,[],[f18])).
% 0.24/0.37 thf(f20,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true != ((sK1 @ X8))) | ($true = ((sK4 @ X6 @ X5))) | (((((sK2 @ (sK8 @ X8 @ X5 @ X6)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0))))))) => (sK8 @ X8 @ X5 @ X6 @ X6 @ X5))) = $false)) )),
% 0.24/0.37 inference(beta-eta_normalization,[],[f19])).
% 0.24/0.37 thf(f21,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true != ((sK1 @ X8))) | (((sK8 @ X8 @ X5 @ X6 @ X6 @ X5)) = $false) | ($true = ((sK4 @ X6 @ X5)))) )),
% 0.24/0.37 inference(imp_proxy_clausification,[],[f20])).
% 0.24/0.37 thf(f22,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true != ((sK1 @ X8))) | ((((sK2 @ (sK8 @ X8 @ X5 @ X6)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0)))))))) = $true) | ($true = ((sK4 @ X6 @ X5)))) )),
% 0.24/0.37 inference(imp_proxy_clausification,[],[f20])).
% 0.24/0.37 thf(f23,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true != ((sK1 @ X8))) | ($true = ((sK4 @ X6 @ X5))) | ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0))))))))) )),
% 0.24/0.37 inference(and_proxy_clausification,[],[f22])).
% 0.24/0.37 thf(f25,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ($true = (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0))))) @ X9))) | ($true != ((sK1 @ X8)))) )),
% 0.24/0.37 inference(pi_proxy_clausification,[],[f23])).
% 0.24/0.37 thf(f26,plain,(
% 0.24/0.37 ( ! [X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : ((((!! @ a @ (^[Y0 : a]: ((X8 @ Y0 @ X9) => (sK8 @ X8 @ X5 @ X6 @ Y0 @ X9))))) = $true) | ($true = ((sK4 @ X6 @ X5))) | ($true != ((sK1 @ X8)))) )),
% 0.24/0.37 inference(beta-eta_normalization,[],[f25])).
% 0.24/0.37 thf(f27,plain,(
% 0.24/0.37 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X6 @ X5))) | ($true != ((sK1 @ X8))) | ($true = (((^[Y0 : a]: ((X8 @ Y0 @ X9) => (sK8 @ X8 @ X5 @ X6 @ Y0 @ X9))) @ X10)))) )),
% 0.24/0.37 inference(pi_proxy_clausification,[],[f26])).
% 0.24/0.37 thf(f28,plain,(
% 0.24/0.37 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true != ((sK1 @ X8))) | ($true = (((X8 @ X10 @ X9) => (sK8 @ X8 @ X5 @ X6 @ X10 @ X9)))) | ($true = ((sK4 @ X6 @ X5)))) )),
% 0.24/0.37 inference(beta-eta_normalization,[],[f27])).
% 0.24/0.37 thf(f29,plain,(
% 0.24/0.37 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true != ((sK1 @ X8))) | (((X8 @ X10 @ X9)) = $false) | ($true = ((sK4 @ X6 @ X5))) | ($true = ((sK8 @ X8 @ X5 @ X6 @ X10 @ X9)))) )),
% 0.24/0.37 inference(imp_proxy_clausification,[],[f28])).
% 0.24/0.37 thf(f30,plain,(
% 0.24/0.37 ($true = ((sK4 @ sK0 @ sK3))) | ($true != $true) | ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.24/0.37 inference(constrained_superposition,[],[f9,f14])).
% 0.24/0.37 thf(f31,plain,(
% 0.24/0.37 ($true = ((sK4 @ sK0 @ sK3))) | ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f30])).
% 0.24/0.37 thf(f32,plain,(
% 0.24/0.37 ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.24/0.37 inference(forward_subsumption_resolution,[],[f31,f12])).
% 0.24/0.37 thf(f75,plain,(
% 0.24/0.37 ($true = ((sK7 @ sK4 @ (sK6 @ sK4) @ (sK5 @ sK4)))) | ($true = ((sK4 @ sK0 @ sK3))) | ($true != $true)),
% 0.24/0.37 inference(constrained_superposition,[],[f10,f14])).
% 0.24/0.37 thf(f76,plain,(
% 0.24/0.37 ($true = ((sK7 @ sK4 @ (sK6 @ sK4) @ (sK5 @ sK4)))) | ($true = ((sK4 @ sK0 @ sK3)))),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f75])).
% 0.24/0.37 thf(f77,plain,(
% 0.24/0.37 ($true = ((sK7 @ sK4 @ (sK6 @ sK4) @ (sK5 @ sK4))))),
% 0.24/0.37 inference(forward_subsumption_resolution,[],[f76,f12])).
% 0.24/0.37 thf(f84,plain,(
% 0.24/0.37 ( ! [X0 : a,X1 : a] : (($true = ((sK4 @ X1 @ X0))) | ($true != $true) | (((sK8 @ (sK7 @ sK4) @ X0 @ X1 @ X1 @ X0)) = $false)) )),
% 0.24/0.37 inference(constrained_superposition,[],[f21,f32])).
% 0.24/0.37 thf(f85,plain,(
% 0.24/0.37 ( ! [X0 : a,X1 : a] : ((((sK8 @ (sK7 @ sK4) @ X0 @ X1 @ X1 @ X0)) = $false) | ($true = ((sK4 @ X1 @ X0)))) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f84])).
% 0.24/0.37 thf(f86,plain,(
% 0.24/0.37 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = ((sK4 @ X2 @ X3))) | ($true = ((sK8 @ (sK7 @ sK4) @ X3 @ X2 @ X0 @ X1))) | ($true != $true) | (((sK7 @ sK4 @ X0 @ X1)) = $false)) )),
% 0.24/0.37 inference(constrained_superposition,[],[f29,f32])).
% 0.24/0.37 thf(f87,plain,(
% 0.24/0.37 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = ((sK8 @ (sK7 @ sK4) @ X3 @ X2 @ X0 @ X1))) | (((sK7 @ sK4 @ X0 @ X1)) = $false) | ($true = ((sK4 @ X2 @ X3)))) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f86])).
% 0.24/0.37 thf(f89,plain,(
% 0.24/0.37 ( ! [X0 : a,X1 : a] : (($true = ((sK4 @ X1 @ X0))) | ($true = ((sK4 @ X1 @ X0))) | ($true = $false) | (((sK7 @ sK4 @ X1 @ X0)) = $false)) )),
% 0.24/0.37 inference(constrained_superposition,[],[f85,f87])).
% 0.24/0.37 thf(f92,plain,(
% 0.24/0.37 ( ! [X0 : a,X1 : a] : ((((sK7 @ sK4 @ X1 @ X0)) = $false) | ($true = $false) | ($true = ((sK4 @ X1 @ X0)))) )),
% 0.24/0.37 inference(duplicate_literal_removal,[],[f89])).
% 0.24/0.37 thf(f93,plain,(
% 0.24/0.37 ( ! [X0 : a,X1 : a] : ((((sK7 @ sK4 @ X1 @ X0)) = $false) | ($true = ((sK4 @ X1 @ X0)))) )),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f92])).
% 0.24/0.37 thf(f99,plain,(
% 0.24/0.37 ($true = ((sK4 @ (sK6 @ sK4) @ (sK5 @ sK4)))) | ($true = $false)),
% 0.24/0.37 inference(constrained_superposition,[],[f77,f93])).
% 0.24/0.37 thf(f100,plain,(
% 0.24/0.37 ($true = ((sK4 @ (sK6 @ sK4) @ (sK5 @ sK4))))),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f99])).
% 0.24/0.37 thf(f102,plain,(
% 0.24/0.37 ($true != $true) | ($true != ((sK2 @ sK4))) | ($true = ((sK4 @ sK0 @ sK3)))),
% 0.24/0.37 inference(constrained_superposition,[],[f11,f100])).
% 0.24/0.37 thf(f103,plain,(
% 0.24/0.37 ($true = ((sK4 @ sK0 @ sK3))) | ($true != ((sK2 @ sK4)))),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f102])).
% 0.24/0.37 thf(f104,plain,(
% 0.24/0.37 ($true != ((sK2 @ sK4)))),
% 0.24/0.37 inference(forward_subsumption_resolution,[],[f103,f12])).
% 0.24/0.37 thf(f105,plain,(
% 0.24/0.37 $false),
% 0.24/0.37 inference(forward_subsumption_resolution,[],[f104,f14])).
% 0.24/0.37 % SZS output end Proof for theBenchmark
% 0.24/0.37 % (848665)------------------------------
% 0.24/0.37 % (848665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (848665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (848665)CaDiCaL version: 2.1.3
% 0.24/0.37 % (848665)Termination reason: Refutation
% 0.24/0.37 % (848665)Time elapsed: 0.007 s
% 0.24/0.37 % (848665)Peak memory usage: 12 MB
% 0.24/0.37 % (848665)Instructions burned: 12 (million)
% 0.24/0.37 % (848660)Success in time 0.031 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------