%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA074^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 07:46:01 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA074^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:37:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.18/0.27 % (3699099)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (3699105)% WARNING: option uhcvi not known.
% 0.18/0.27 % (3699105)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=413201245:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (3699105)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (3699105)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (3699104)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1758641801_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (3699105) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3699099-3699105"...
% 0.18/0.27 % (3699106)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4283210282:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (3699107)dis+10_1_sil=32000:sp=arity:random_seed=2707872001:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (3699108)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2261659751:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (3699108)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (3699105)...printing done.
% 0.18/0.27 % (3699105)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% 0.18/0.27 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.18/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.27 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.27 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.18/0.27 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.18/0.27 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.18/0.27 thf(func_def_7, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.27 thf(func_def_8, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.27 thf(func_def_9, type, sK2: ('type/realax/real' > $o)).
% 0.18/0.27 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.18/0.27 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.18/0.27 thf(f1,axiom,(
% 0.18/0.27 ! [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' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.18/0.27 thf(f2,conjecture,(
% 0.18/0.27 ! [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' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_')).
% 0.18/0.27 thf(f3,negated_conjecture,(
% 0.18/0.27 ~ ! [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' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 0.18/0.27 inference(negated_conjecture,[status(cth)],[f2])).
% 0.18/0.27 thf(f4,plain,(
% 0.18/0.27 ! [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' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X3)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))),
% 0.18/0.27 inference(rectify,[],[f1])).
% 0.18/0.27 thf(f5,plain,(
% 0.18/0.27 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ((('const/realax/real_le' @ X4 @ X3)) = $true)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true)) & ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true))))),
% 0.18/0.27 inference(fool_elimination,[],[f4])).
% 0.18/0.27 thf(f6,plain,(
% 0.18/0.27 ~ ! [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' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 0.18/0.27 inference(rectify,[],[f3])).
% 0.18/0.27 thf(f7,plain,(
% 0.18/0.27 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true))),
% 0.18/0.27 inference(fool_elimination,[],[f6])).
% 0.18/0.27 thf(f8,plain,(
% 0.18/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.18/0.27 inference(ennf_transformation,[],[f5])).
% 0.18/0.27 thf(f9,plain,(
% 0.18/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.18/0.27 inference(flattening,[],[f8])).
% 0.18/0.27 thf(f10,plain,(
% 0.18/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != $true) & (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.18/0.27 inference(ennf_transformation,[],[f7])).
% 0.18/0.27 thf(f11,plain,(
% 0.18/0.27 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != $true) & ! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.18/0.27 inference(flattening,[],[f10])).
% 0.18/0.27 thf(f12,plain,(
% 0.18/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X5 @ X4))) & ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.18/0.27 inference(rectify,[],[f9])).
% 0.18/0.27 thf(f13,plain,(
% 0.18/0.27 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))))) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f12])).
% 0.18/0.27 thf(f14,plain,(
% 0.18/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X2 @ sK3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11])).
% 0.18/0.27 thf(f17,plain,(
% 0.18/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f13])).
% 0.18/0.27 thf(f18,plain,(
% 0.18/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f13])).
% 0.18/0.27 thf(f19,plain,(
% 0.18/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f13])).
% 0.18/0.27 thf(f20,plain,(
% 0.18/0.27 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f13])).
% 0.18/0.27 thf(f21,plain,(
% 0.18/0.27 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.18/0.27 inference(cnf_transformation,[],[f14])).
% 0.18/0.27 thf(f22,plain,(
% 0.18/0.27 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) | ($true = (('const/realax/real_le' @ X2 @ sK3)))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f14])).
% 0.18/0.27 thf(f23,plain,(
% 0.18/0.27 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))),
% 0.18/0.27 inference(cnf_transformation,[],[f14])).
% 0.18/0.27 thf(f25,definition,(
% 0.18/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.27 thf(f64,plain,(
% 0.18/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1) @ X2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.18/0.27 inference(constrained_superposition,[],[f20,f25])).
% 0.18/0.27 thf(f65,plain,(
% 0.18/0.27 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1) @ X2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ X1) @ X0)))) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f64])).
% 0.18/0.27 thf(f75,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.18/0.27 inference(constrained_superposition,[],[f22,f17])).
% 0.18/0.27 thf(f79,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f75])).
% 0.18/0.27 thf(f83,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) )),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f79,f21])).
% 0.18/0.27 thf(f86,definition,(
% 0.18/0.27 spl5_5 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.18/0.27 thf(f87,plain,(
% 0.18/0.27 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl5_5),
% 0.18/0.27 inference(avatar_component_clause,[],[f86])).
% 0.18/0.27 thf(f89,definition,(
% 0.18/0.27 spl5_6 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.18/0.27 thf(f90,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl5_6),
% 0.18/0.27 inference(avatar_component_clause,[],[f89])).
% 0.18/0.27 thf(f91,plain,(
% 0.18/0.27 spl5_5 | spl5_6),
% 0.18/0.27 inference(avatar_split_clause,[],[f83,f89,f86])).
% 0.18/0.27 thf(f93,definition,(
% 0.18/0.27 spl5_7 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.18/0.27 thf(f94,plain,(
% 0.18/0.27 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1)))) ) | ~spl5_7),
% 0.18/0.27 inference(avatar_component_clause,[],[f93])).
% 0.18/0.27 thf(f96,definition,(
% 0.18/0.27 spl5_8 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.18/0.27 thf(f97,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | ~spl5_8),
% 0.18/0.27 inference(avatar_component_clause,[],[f96])).
% 0.18/0.27 thf(f122,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | ~spl5_5),
% 0.18/0.27 inference(constrained_superposition,[],[f22,f87])).
% 0.18/0.27 thf(f125,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)))) ) | ~spl5_5),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f122])).
% 0.18/0.27 thf(f128,plain,(
% 0.18/0.27 spl5_8 | ~spl5_5),
% 0.18/0.27 inference(avatar_split_clause,[],[f125,f86,f96])).
% 0.18/0.27 thf(f129,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))) ) | ~spl5_6),
% 0.18/0.27 inference(constrained_superposition,[],[f19,f90])).
% 0.18/0.27 thf(f130,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_6),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f129])).
% 0.18/0.27 thf(f131,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_6),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f130])).
% 0.18/0.27 thf(f132,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_6),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f131,f23])).
% 0.18/0.27 thf(f133,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl5_6),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f132,f21])).
% 0.18/0.27 thf(f134,plain,(
% 0.18/0.27 spl5_5 | ~spl5_6),
% 0.18/0.27 inference(avatar_split_clause,[],[f133,f89,f86])).
% 0.18/0.27 thf(f144,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.18/0.27 inference(constrained_superposition,[],[f18,f97])).
% 0.18/0.27 thf(f149,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f144])).
% 0.18/0.27 thf(f152,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl5_8),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f149,f21])).
% 0.18/0.27 thf(f153,plain,(
% 0.18/0.27 spl5_7 | ~spl5_8),
% 0.18/0.27 inference(avatar_split_clause,[],[f152,f96,f93])).
% 0.18/0.27 thf(f164,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl5_7),
% 0.18/0.27 inference(constrained_superposition,[],[f22,f94])).
% 0.18/0.27 thf(f167,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl5_7),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f164])).
% 0.18/0.27 thf(f186,definition,(
% 0.18/0.27 spl5_10 <=> ! [X1 : 'type/realax/real'] : ($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition])).
% 0.18/0.27 thf(f187,plain,(
% 0.18/0.27 ( ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X1 @ sK2) @ X1)))) ) | ~spl5_10),
% 0.18/0.27 inference(avatar_component_clause,[],[f186])).
% 0.18/0.27 thf(f193,plain,(
% 0.18/0.27 ($true = $false) | (~spl5_8 | ~spl5_10)),
% 0.18/0.27 inference(constrained_superposition,[],[f187,f97])).
% 0.18/0.27 thf(f202,plain,(
% 0.18/0.27 $false | (~spl5_8 | ~spl5_10)),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f193])).
% 0.18/0.27 thf(f203,plain,(
% 0.18/0.27 ~spl5_8 | ~spl5_10),
% 0.18/0.27 inference(avatar_contradiction_clause,[],[f202])).
% 0.18/0.27 thf(f224,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))) ) | ~spl5_6),
% 0.18/0.27 inference(constrained_superposition,[],[f65,f90])).
% 0.18/0.27 thf(f229,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl5_6),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f224])).
% 0.18/0.27 thf(f230,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl5_6),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f229])).
% 0.18/0.27 thf(f231,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl5_6),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f230,f23])).
% 0.18/0.27 thf(f232,plain,(
% 0.18/0.27 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))) ) | ~spl5_6),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f231,f21])).
% 0.18/0.27 thf(f233,plain,(
% 0.18/0.27 spl5_10 | ~spl5_6),
% 0.18/0.27 inference(avatar_split_clause,[],[f232,f89,f186])).
% 0.18/0.27 thf(f234,plain,(
% 0.18/0.27 spl5_6 | ~spl5_7),
% 0.18/0.27 inference(avatar_split_clause,[],[f167,f93,f89])).
% 0.18/0.27 cnf(s3, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f91])).
% 0.18/0.27 cnf(s9, plain, ~spl5_5 | spl5_8, inference(sat_conversion,[],[f128])).
% 0.18/0.27 cnf(s12, plain, spl5_5 | ~spl5_6, inference(sat_conversion,[],[f134])).
% 0.18/0.27 cnf(s20, plain, spl5_7 | ~spl5_8, inference(sat_conversion,[],[f153])).
% 0.18/0.27 cnf(s24, plain, ~spl5_8 | ~spl5_10, inference(sat_conversion,[],[f203])).
% 0.18/0.27 cnf(s25, plain, ~spl5_6 | spl5_10, inference(sat_conversion,[],[f233])).
% 0.18/0.27 cnf(s26, plain, spl5_6 | ~spl5_7, inference(sat_conversion,[],[f234])).
% 0.18/0.27 cnf(s29, plain, spl5_5, inference(rat,[],[s3,s12])).
% 0.18/0.27 cnf(s30, plain, spl5_8, inference(rat,[],[s9,s29])).
% 0.18/0.27 cnf(s31, plain, ~spl5_10, inference(rat,[],[s24,s30])).
% 0.18/0.27 cnf(s32, plain, spl5_7, inference(rat,[],[s20,s30])).
% 0.18/0.27 cnf(s33, plain, ~spl5_6, inference(rat,[],[s25,s31])).
% 0.18/0.27 cnf(s35, plain, $false, inference(rat,[],[s26,s32,s33])).
% 0.18/0.27 thf(f235,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(avatar_sat_refutation,[],[s35])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (3699105)------------------------------
% 0.18/0.27 % (3699105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3699105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3699105)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3699105)Termination reason: Refutation
% 0.18/0.27 % (3699105)Time elapsed: 0.008 s
% 0.18/0.27 % (3699105)Peak memory usage: 13 MB
% 0.18/0.27 % (3699105)Instructions burned: 21 (million)
% 0.18/0.27 % (3699099)Success in time 0.037 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------