%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA077^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 07:45:52 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA077^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:40:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (2979535)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2979543)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2779610124:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.27 % (2979543) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979535-2979543"...
% 0.20/0.27 % (2979546)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (2979546)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
% 0.20/0.27 % (2979543)...printing done.
% 0.20/0.27 % (2979543)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.27 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.27 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.27 thf(func_def_3, type, 'const/realax/real_neg': ('type/realax/real' > 'type/realax/real')).
% 0.20/0.27 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.27 thf(func_def_5, type, 'const/realax/real_abs': ('type/realax/real' > 'type/realax/real')).
% 0.20/0.27 thf(func_def_9, type, sK0: ('type/realax/real' > 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.27 thf(func_def_10, type, sK1: ('type/realax/real' > $o)).
% 0.20/0.27 thf(func_def_11, type, sK2: 'type/realax/real').
% 0.20/0.27 thf(func_def_13, type, sK4: 'type/realax/real').
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) & ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_')).
% 0.20/0.27 thf(f2,axiom,(
% 0.20/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1) = (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_')).
% 0.20/0.27 thf(f3,conjecture,(
% 0.20/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_ABS_SUP_LE_')).
% 0.20/0.27 thf(f4,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1) = (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true)) <=> ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true))),
% 0.20/0.27 inference(fool_elimination,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) & ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)))),
% 0.20/0.27 inference(rectify,[],[f1])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => (((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)))),
% 0.20/0.27 inference(fool_elimination,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) = $true))),
% 0.20/0.27 inference(fool_elimination,[],[f9])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) != $true) & (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.20/0.27 inference(ennf_transformation,[],[f10])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) != $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.20/0.27 inference(flattening,[],[f11])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) | (? [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.20/0.27 inference(ennf_transformation,[],[f8])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)))),
% 0.20/0.27 inference(flattening,[],[f13])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0))))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f14])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1)))) & ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2)) != $true) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f12])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true)) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) != $true)) & (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) != $true))))),
% 0.20/0.27 inference(nnf_transformation,[],[f6])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ! [X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true)) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) != $true)) & (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) != $true)))),
% 0.20/0.27 inference(flattening,[],[f17])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((($true = (('const/realax/real_le' @ X1 @ X0))) & ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ X1)))) | ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ X1) @ X0)))) & (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X1) @ X0))) | ($true != (('const/realax/real_le' @ X1 @ X0))) | ($true != (('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ X1)))))),
% 0.20/0.27 inference(rectify,[],[f18])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f22,plain,(
% 0.20/0.27 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0))))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f24,plain,(
% 0.20/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2)) != $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X1) @ X0))) | ($true != (('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ X1))) | ($true != (('const/realax/real_le' @ X1 @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f19])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ X1))) | ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ X1) @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f19])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ X1) @ X0))) | ($true = (('const/realax/real_le' @ X1 @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f19])).
% 0.20/0.27 thf(f32,definition,(
% 0.20/0.27 spl3_1 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK1)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.20/0.27 thf(f34,plain,(
% 0.20/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK1) | spl3_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f32])).
% 0.20/0.27 thf(f35,plain,(
% 0.20/0.27 ~spl3_1),
% 0.20/0.27 inference(avatar_split_clause,[],[f24,f32])).
% 0.20/0.27 thf(f37,definition,(
% 0.20/0.27 spl3_2 <=> ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2)) = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.20/0.27 thf(f39,plain,(
% 0.20/0.27 ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2)) != $true) | spl3_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f37])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 ~spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f25,f37])).
% 0.20/0.27 thf(f62,plain,(
% 0.20/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) != $true) | spl3_2),
% 0.20/0.27 inference(superposition,[],[f39,f27])).
% 0.20/0.27 thf(f64,plain,(
% 0.20/0.27 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) != $true) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | spl3_2),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.27 thf(f66,definition,(
% 0.20/0.27 spl3_7 <=> ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.20/0.27 thf(f70,definition,(
% 0.20/0.27 spl3_8 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.20/0.27 thf(f72,plain,(
% 0.20/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | spl3_8),
% 0.20/0.27 inference(avatar_component_clause,[],[f70])).
% 0.20/0.27 thf(f73,plain,(
% 0.20/0.27 ~spl3_7 | ~spl3_8 | spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f64,f37,f70,f66])).
% 0.20/0.27 thf(f74,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2)))) )),
% 0.20/0.27 inference(superposition,[],[f26,f20])).
% 0.20/0.27 thf(f75,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f74])).
% 0.20/0.27 thf(f76,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) ) | spl3_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f75,f34])).
% 0.20/0.27 thf(f77,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true)) )),
% 0.20/0.27 inference(superposition,[],[f26,f21])).
% 0.20/0.27 thf(f78,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f77])).
% 0.20/0.27 thf(f79,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | spl3_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f78,f34])).
% 0.20/0.27 thf(f82,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) ) | spl3_1),
% 0.20/0.27 inference(superposition,[],[f29,f76])).
% 0.20/0.27 thf(f83,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) ) | spl3_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f82])).
% 0.20/0.27 thf(f85,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | spl3_1),
% 0.20/0.27 inference(superposition,[],[f22,f83])).
% 0.20/0.27 thf(f87,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | spl3_1),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f85])).
% 0.20/0.27 thf(f88,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) ) | spl3_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f87])).
% 0.20/0.27 thf(f90,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | spl3_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f88,f34])).
% 0.20/0.27 thf(f92,definition,(
% 0.20/0.27 spl3_9 <=> ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.20/0.27 thf(f93,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl3_9),
% 0.20/0.27 inference(avatar_component_clause,[],[f92])).
% 0.20/0.27 thf(f95,plain,(
% 0.20/0.27 spl3_9 | spl3_1),
% 0.20/0.27 inference(avatar_split_clause,[],[f90,f32,f92])).
% 0.20/0.27 thf(f96,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true)) ) | spl3_1),
% 0.20/0.27 inference(superposition,[],[f29,f79])).
% 0.20/0.27 thf(f97,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | spl3_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f96])).
% 0.20/0.27 thf(f98,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2)))) ) | spl3_1),
% 0.20/0.27 inference(superposition,[],[f23,f97])).
% 0.20/0.27 thf(f100,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | spl3_1),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f98])).
% 0.20/0.27 thf(f101,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | spl3_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f100])).
% 0.20/0.27 thf(f103,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2)))) ) | spl3_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f101,f34])).
% 0.20/0.27 thf(f106,definition,(
% 0.20/0.27 spl3_10 <=> ! [X0 : 'type/realax/real'] : ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.20/0.27 thf(f107,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) ) | ~spl3_10),
% 0.20/0.27 inference(avatar_component_clause,[],[f106])).
% 0.20/0.27 thf(f108,plain,(
% 0.20/0.27 spl3_8 | spl3_10 | spl3_1),
% 0.20/0.27 inference(avatar_split_clause,[],[f103,f32,f106,f70])).
% 0.20/0.27 thf(f110,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ sK2 @ ('const/realax/real_neg' @ X0) @ sK1)) @ X0))) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ ('const/sets/sup' @ sK1))) = $true) | ($true != $true)) ) | ~spl3_9),
% 0.20/0.27 inference(superposition,[],[f93,f28])).
% 0.20/0.27 thf(f112,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ sK2 @ ('const/realax/real_neg' @ X0) @ sK1)) @ X0))) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X0) @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl3_9),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f110])).
% 0.20/0.27 thf(f116,plain,(
% 0.20/0.27 ($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) = $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) = $true) | (spl3_1 | ~spl3_9)),
% 0.20/0.27 inference(superposition,[],[f112,f76])).
% 0.20/0.27 thf(f118,plain,(
% 0.20/0.27 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) = $true) | ($true != $true) | (spl3_1 | ~spl3_9)),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f116])).
% 0.20/0.27 thf(f119,plain,(
% 0.20/0.27 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))) = $true) | (spl3_1 | ~spl3_9)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f118])).
% 0.20/0.27 thf(f123,plain,(
% 0.20/0.27 spl3_7 | spl3_1 | ~spl3_9),
% 0.20/0.27 inference(avatar_split_clause,[],[f119,f92,f32,f66])).
% 0.20/0.27 thf(f128,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ sK2 @ ('const/realax/real_neg' @ X0) @ sK1)) @ X0))) | ($true != $true)) ) | ~spl3_10),
% 0.20/0.27 inference(superposition,[],[f107,f28])).
% 0.20/0.27 thf(f131,plain,(
% 0.20/0.27 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ sK2 @ ('const/realax/real_neg' @ X0) @ sK1)) @ X0)))) ) | ~spl3_10),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f128])).
% 0.20/0.27 thf(f133,plain,(
% 0.20/0.27 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != $true) | (spl3_1 | ~spl3_10)),
% 0.20/0.27 inference(superposition,[],[f131,f79])).
% 0.20/0.27 thf(f136,plain,(
% 0.20/0.27 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | (spl3_1 | ~spl3_10)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f133])).
% 0.20/0.27 thf(f138,plain,(
% 0.20/0.27 $false | (spl3_1 | spl3_8 | ~spl3_10)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f136,f72])).
% 0.20/0.27 thf(f139,plain,(
% 0.20/0.27 spl3_1 | spl3_8 | ~spl3_10),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f138])).
% 0.20/0.27 cnf(s1, plain, ~spl3_1, inference(sat_conversion,[],[f35])).
% 0.20/0.27 cnf(s2, plain, ~spl3_2, inference(sat_conversion,[],[f40])).
% 0.20/0.27 cnf(s5, plain, spl3_2 | ~spl3_7 | ~spl3_8, inference(sat_conversion,[],[f73])).
% 0.20/0.27 cnf(s7, plain, spl3_1 | spl3_9, inference(sat_conversion,[],[f95])).
% 0.20/0.27 cnf(s8, plain, spl3_1 | spl3_8 | spl3_10, inference(sat_conversion,[],[f108])).
% 0.20/0.27 cnf(s11, plain, spl3_1 | spl3_7 | ~spl3_9, inference(sat_conversion,[],[f123])).
% 0.20/0.27 cnf(s13, plain, spl3_1 | spl3_8 | ~spl3_10, inference(sat_conversion,[],[f139])).
% 0.20/0.27 cnf(s14, plain, spl3_9, inference(rat,[],[s7,s1])).
% 0.20/0.27 cnf(s15, plain, spl3_7, inference(rat,[],[s11,s1,s14])).
% 0.20/0.27 cnf(s16, plain, ~spl3_8, inference(rat,[],[s5,s2,s15])).
% 0.20/0.27 cnf(s17, plain, ~spl3_10, inference(rat,[],[s13,s1,s16])).
% 0.20/0.27 cnf(s18, plain, $false, inference(rat,[],[s8,s1,s17,s16])).
% 0.20/0.27 thf(f140,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s18])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (2979543)------------------------------
% 0.20/0.27 % (2979543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2979543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2979543)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2979543)Termination reason: Refutation
% 0.20/0.27 % (2979543)Time elapsed: 0.005 s
% 0.20/0.27 % (2979543)Peak memory usage: 13 MB
% 0.20/0.27 % (2979543)Instructions burned: 15 (million)
% 0.20/0.27 % (2979535)Success in time 0.03 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------