%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:15:29 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:54:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.09/0.25 % (1945034)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1945047)dis+10_1_sil=32000:sp=arity:random_seed=1757896406:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (1945044)% WARNING: option uhcvi not known.
% 0.09/0.25 % (1945047) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1945034-1945047"...
% 0.09/0.25 % (1945047)...printing done.
% 0.09/0.25 % (1945047)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, mworld: $tType).
% 0.09/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.09/0.25 thf(func_def_1, type, mactual: mworld).
% 0.09/0.25 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.09/0.25 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_11, type, eiw_di: ($i > mworld > $o)).
% 0.09/0.25 thf(func_def_12, type, mforall_di: (($i > mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_13, type, mexists_di: (($i > mworld > $o) > mworld > $o)).
% 0.09/0.25 thf(func_def_14, type, big_q: ($i > mworld > $o)).
% 0.09/0.25 thf(func_def_15, type, big_p: ($i > mworld > $o)).
% 0.09/0.25 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.25 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.09/0.25 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_20, type, vAND: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_21, type, db2: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_22, type, vOR: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_23, type, vIMP: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_24, type, vIFF: ($o > $o > $o)).
% 0.09/0.25 thf(func_def_25, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.25 thf(func_def_26, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.25 thf(func_def_29, type, sK0: (mworld > $i)).
% 0.09/0.25 thf(func_def_30, type, db3: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_31, type, db4: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_32, type, db5: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_33, type, sK1: ($i > mworld)).
% 0.09/0.25 thf(func_def_34, type, sK2: ($i > $i)).
% 0.09/0.25 thf(func_def_35, type, sK3: ($i > mworld)).
% 0.09/0.25 thf(func_def_36, type, sK4: ($i > mworld)).
% 0.09/0.25 thf(func_def_37, type, sK5: ($i > mworld)).
% 0.09/0.25 thf(f1,axiom,(
% 0.09/0.25 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.09/0.25 thf(f4,axiom,(
% 0.09/0.25 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def)).
% 0.09/0.25 thf(f5,axiom,(
% 0.09/0.25 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 0.09/0.25 thf(f7,axiom,(
% 0.09/0.25 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.09/0.25 thf(f9,axiom,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal)).
% 0.09/0.25 thf(f10,axiom,(
% 0.09/0.25 ! [X0 : mworld] : ? [X1 : $i] : (eiw_di @ X1 @ X0)),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty)).
% 0.09/0.25 thf(f11,axiom,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((mrel @ X0 @ X1) & (eiw_di @ X2 @ X0)) => (eiw_di @ X2 @ X1))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul)).
% 0.09/0.25 thf(f12,axiom,(
% 0.09/0.25 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.09/0.25 thf(f13,axiom,(
% 0.09/0.25 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 0.09/0.25 thf(f14,conjecture,(
% 0.09/0.25 (mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mforall_di @ (^[X1 : $i] : ((mbox @ (mimplies @ (mbox @ (big_p @ X0)) @ (mor @ (mbox @ (big_q @ X0)) @ (mbox @ (big_p @ X1)))))))))))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2137)).
% 0.09/0.25 thf(f15,negated_conjecture,(
% 0.09/0.25 ~(mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mforall_di @ (^[X1 : $i] : ((mbox @ (mimplies @ (mbox @ (big_p @ X0)) @ (mor @ (mbox @ (big_q @ X0)) @ (mbox @ (big_p @ X1)))))))))))))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f14])).
% 0.09/0.25 thf(f16,plain,(
% 0.09/0.25 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.09/0.25 inference(fool_elimination,[],[f1])).
% 0.09/0.25 thf(f21,plain,(
% 0.09/0.25 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))),
% 0.09/0.25 inference(rectify,[],[f4])).
% 0.09/0.25 thf(f22,plain,(
% 0.09/0.25 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f21])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.09/0.25 inference(rectify,[],[f5])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f23])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.09/0.25 inference(rectify,[],[f7])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f27])).
% 0.09/0.25 thf(f31,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 0.09/0.25 inference(rectify,[],[f9])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld] : (((mrel @ X0 @ X1)) = $true)),
% 0.09/0.25 inference(fool_elimination,[],[f31])).
% 0.09/0.25 thf(f33,plain,(
% 0.09/0.25 ! [X0 : mworld] : ? [X1 : $i] : (eiw_di @ X1 @ X0)),
% 0.09/0.25 inference(rectify,[],[f10])).
% 0.09/0.25 thf(f34,plain,(
% 0.09/0.25 ! [X0 : mworld] : ? [X1 : $i] : (((eiw_di @ X1 @ X0)) = $true)),
% 0.09/0.25 inference(fool_elimination,[],[f33])).
% 0.09/0.25 thf(f35,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((mrel @ X0 @ X1) & (eiw_di @ X2 @ X0)) => (eiw_di @ X2 @ X1))),
% 0.09/0.25 inference(rectify,[],[f11])).
% 0.09/0.25 thf(f36,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((((mrel @ X0 @ X1)) = $true) & (((eiw_di @ X2 @ X0)) = $true)) => (((eiw_di @ X2 @ X1)) = $true))),
% 0.09/0.25 inference(fool_elimination,[],[f35])).
% 0.09/0.25 thf(f37,plain,(
% 0.09/0.25 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.09/0.25 inference(rectify,[],[f12])).
% 0.09/0.25 thf(f38,plain,(
% 0.09/0.25 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f37])).
% 0.09/0.25 thf(f39,plain,(
% 0.09/0.25 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 0.09/0.25 inference(rectify,[],[f13])).
% 0.09/0.25 thf(f40,plain,(
% 0.09/0.25 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f39])).
% 0.09/0.25 thf(f41,plain,(
% 0.09/0.25 ~(mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mforall_di @ (^[X1 : $i] : ((mbox @ (mimplies @ (mbox @ (big_p @ X0)) @ (mor @ (mbox @ (big_q @ X0)) @ (mbox @ (big_p @ X1)))))))))))))),
% 0.09/0.25 inference(rectify,[],[f15])).
% 0.09/0.25 thf(f42,plain,(
% 0.09/0.25 ~ ($true = ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1)))))))))))))),
% 0.09/0.25 inference(fool_elimination,[],[f41])).
% 0.09/0.25 thf(f43,plain,(
% 0.09/0.25 ($true != ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1)))))))))))))),
% 0.09/0.25 inference(flattening,[],[f42])).
% 0.09/0.25 thf(f44,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((eiw_di @ X2 @ X1)) = $true) | ((((mrel @ X0 @ X1)) != $true) | (((eiw_di @ X2 @ X0)) != $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f36])).
% 0.09/0.25 thf(f45,plain,(
% 0.09/0.25 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((eiw_di @ X2 @ X1)) = $true) | (((mrel @ X0 @ X1)) != $true) | (((eiw_di @ X2 @ X0)) != $true))),
% 0.09/0.25 inference(flattening,[],[f44])).
% 0.09/0.25 thf(f46,plain,(
% 0.09/0.25 ! [X0 : mworld] : ($true = ((eiw_di @ (sK0 @ X0) @ X0)))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f34])).
% 0.09/0.25 thf(f47,plain,(
% 0.09/0.25 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.09/0.25 inference(cnf_transformation,[],[f16])).
% 0.09/0.25 thf(f50,plain,(
% 0.09/0.25 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f22])).
% 0.09/0.25 thf(f51,plain,(
% 0.09/0.25 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f24])).
% 0.09/0.25 thf(f53,plain,(
% 0.09/0.25 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f28])).
% 0.09/0.25 thf(f55,plain,(
% 0.09/0.25 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X1)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f32])).
% 0.09/0.25 thf(f56,plain,(
% 0.09/0.25 ( ! [X0 : mworld] : (($true = ((eiw_di @ (sK0 @ X0) @ X0)))) )),
% 0.09/0.25 inference(cnf_transformation,[],[f46])).
% 0.09/0.25 thf(f57,plain,(
% 0.09/0.25 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : ((((eiw_di @ X2 @ X1)) = $true) | (((mrel @ X0 @ X1)) != $true) | (((eiw_di @ X2 @ X0)) != $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f45])).
% 0.09/0.25 thf(f58,plain,(
% 0.09/0.25 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f38])).
% 0.09/0.25 thf(f59,plain,(
% 0.09/0.25 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f40])).
% 0.09/0.25 thf(f60,plain,(
% 0.09/0.25 ($true != ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1)))))))))))))),
% 0.09/0.25 inference(cnf_transformation,[],[f43])).
% 0.09/0.25 thf(f63,plain,(
% 0.09/0.25 ($true != (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_p @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_q @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_p @ Y1)))))))))))))),
% 0.09/0.25 inference(definition_unfolding,[],[f60,f47,f59,f53,f58,f53,f51,f53,f50,f53,f53])).
% 0.09/0.25 thf(f64,plain,(
% 0.09/0.25 ($true != ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y0 @ Y4)))) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_q @ Y0 @ Y4)))) | (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y2 @ Y4))))))))))))))))))))),
% 0.09/0.25 inference(beta-eta_normalization,[],[f63])).
% 0.09/0.25 thf(f65,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y0 @ Y4)))) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_q @ Y0 @ Y4)))) | (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y2 @ Y4))))))))))))))))) @ X1)))) )),
% 0.09/0.25 inference(pi_proxy_clausification,[],[f64])).
% 0.09/0.25 thf(f66,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((eiw_di @ X1 @ mactual) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3))))))))))))))))))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f65])).
% 0.09/0.25 thf(f67,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3))))))))))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(and_proxy_clausification,[],[f66])).
% 0.09/0.25 thf(f68,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3)))))))))))))) @ (sK1 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(sigma_proxy_clausification,[],[f67])).
% 0.09/0.25 thf(f69,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((mrel @ mactual @ (sK1 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK1 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK1 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2))))))))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f68])).
% 0.09/0.25 thf(f70,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK1 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK1 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2)))))))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f69])).
% 0.09/0.25 thf(f72,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK1 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK1 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2))))))))))) @ (sK2 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(sigma_proxy_clausification,[],[f70])).
% 0.09/0.25 thf(f73,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((eiw_di @ (sK2 @ X1) @ (sK1 @ X1)) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK1 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK2 @ X1) @ Y1)))))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f72])).
% 0.09/0.25 thf(f74,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK1 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK2 @ X1) @ Y1))))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f73])).
% 0.09/0.25 thf(f75,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($true = ((eiw_di @ (sK2 @ X1) @ (sK1 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f73])).
% 0.09/0.25 thf(f76,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((^[Y0 : mworld]: ((mrel @ (sK1 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK2 @ X1) @ Y1)))))))) @ (sK3 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(sigma_proxy_clausification,[],[f74])).
% 0.09/0.25 thf(f77,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((mrel @ (sK1 @ X1) @ (sK3 @ X1)) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ X1 @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ (sK2 @ X1) @ Y0))))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f76])).
% 0.09/0.25 thf(f78,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ X1 @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ (sK2 @ X1) @ Y0)))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f77])).
% 0.09/0.25 thf(f80,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ (sK2 @ X1) @ Y0))))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f78])).
% 0.09/0.25 thf(f81,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ X1 @ Y0)))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f78])).
% 0.09/0.25 thf(f82,plain,(
% 0.09/0.25 ( ! [X2 : mworld,X1 : $i] : (($true = (((^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ X1 @ Y0))) @ X2))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(pi_proxy_clausification,[],[f81])).
% 0.09/0.25 thf(f83,plain,(
% 0.09/0.25 ( ! [X2 : mworld,X1 : $i] : (($true = (((mrel @ (sK3 @ X1) @ X2) => (big_p @ X1 @ X2)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f82])).
% 0.09/0.25 thf(f84,plain,(
% 0.09/0.25 ( ! [X2 : mworld,X1 : $i] : (($false = ((mrel @ (sK3 @ X1) @ X2))) | ($false = ((eiw_di @ X1 @ mactual))) | ($true = ((big_p @ X1 @ X2)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f83])).
% 0.09/0.25 thf(f85,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ (sK2 @ X1) @ Y0)))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(or_proxy_clausification,[],[f80])).
% 0.09/0.25 thf(f91,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => (big_p @ (sK2 @ X1) @ Y0))) @ (sK5 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(sigma_proxy_clausification,[],[f85])).
% 0.09/0.25 thf(f92,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = (((mrel @ (sK3 @ X1) @ (sK5 @ X1)) => (big_p @ (sK2 @ X1) @ (sK5 @ X1))))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(beta-eta_normalization,[],[f91])).
% 0.09/0.25 thf(f93,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($false = ((big_p @ (sK2 @ X1) @ (sK5 @ X1)))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(imp_proxy_clausification,[],[f92])).
% 0.09/0.25 thf(f104,plain,(
% 0.09/0.25 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : ((((eiw_di @ X2 @ X0)) != $true) | (((eiw_di @ X2 @ X1)) = $true)) )),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f57,f55])).
% 0.09/0.25 thf(f106,plain,(
% 0.09/0.25 ( ! [X0 : mworld,X1 : mworld] : (($true != $true) | ($true = ((eiw_di @ (sK0 @ X0) @ X1)))) )),
% 0.09/0.25 inference(constrained_superposition,[],[f104,f56])).
% 0.09/0.25 thf(f107,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : mworld] : (($true != $true) | ($true = ((eiw_di @ (sK2 @ X0) @ X1))) | ($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(constrained_superposition,[],[f104,f75])).
% 0.09/0.25 thf(f108,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : mworld] : (($true = ((eiw_di @ (sK2 @ X0) @ X1))) | ($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f107])).
% 0.09/0.25 thf(f109,plain,(
% 0.09/0.25 ( ! [X0 : mworld,X1 : mworld] : (($true = ((eiw_di @ (sK0 @ X0) @ X1)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f106])).
% 0.09/0.25 thf(f143,plain,(
% 0.09/0.25 ( ! [X2 : mworld,X1 : $i] : (($true = $false) | ($false = ((eiw_di @ X1 @ mactual))) | ($true = ((big_p @ X1 @ X2)))) )),
% 0.09/0.25 inference(forward_demodulation,[],[f84,f55])).
% 0.09/0.25 thf(f144,plain,(
% 0.09/0.25 ( ! [X2 : mworld,X1 : $i] : (($true = ((big_p @ X1 @ X2))) | ($false = ((eiw_di @ X1 @ mactual)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f143])).
% 0.09/0.25 thf(f146,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true = $false) | ($false = ((eiw_di @ X0 @ mactual))) | ($false = ((eiw_di @ (sK2 @ X0) @ mactual)))) )),
% 0.09/0.25 inference(constrained_superposition,[],[f93,f144])).
% 0.09/0.25 thf(f147,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($false = ((eiw_di @ (sK2 @ X0) @ mactual))) | ($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f146])).
% 0.09/0.25 thf(f154,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true = $false) | ($false = ((eiw_di @ X0 @ mactual))) | ($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(constrained_superposition,[],[f108,f147])).
% 0.09/0.25 thf(f155,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true = $false) | ($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(duplicate_literal_removal,[],[f154])).
% 0.09/0.25 thf(f156,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($false = ((eiw_di @ X0 @ mactual)))) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f155])).
% 0.09/0.25 thf(f171,plain,(
% 0.09/0.25 ($true = $false)),
% 0.09/0.25 inference(constrained_superposition,[],[f109,f156])).
% 0.09/0.25 thf(f172,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f171])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (1945047)------------------------------
% 0.09/0.25 % (1945047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1945047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1945047)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1945047)Termination reason: Refutation
% 0.09/0.25 % (1945047)Time elapsed: 0.006 s
% 0.09/0.25 % (1945047)Peak memory usage: 12 MB
% 0.09/0.25 % (1945047)Instructions burned: 18 (million)
% 0.09/0.25 % (1945034)Success in time 0.022 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------