%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA086^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 07:46:02 AM UTC 2026
% Result : Theorem 0.09s 0.14s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA086^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 17:40:19 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.14 % (438668)Will run a generic schedule for satisfiability detection.
% 0.09/0.14 % (438674)% WARNING: option uhcvi not known.
% 0.09/0.14 % (438674)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3526751993:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.09/0.14 % (438673)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1445975811_3000 on theBenchmark for (3000ds/0Mi)
% 0.09/0.14 % (438676)dis+10_1_sil=32000:sp=arity:random_seed=4081381121:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.09/0.14 % (438678)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3455965958:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.09/0.14 % (438675)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3984506965:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.09/0.14 % (438677)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3298732874:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.14 % (438674)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.14 % (438679)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4165883054:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.09/0.14 % (438677)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.14 % (438674)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.14 % Exception at run slice level
% 0.09/0.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.14 % (438678) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438668-438678"...
% 0.09/0.14 % (438677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438668-438677"...
% 0.09/0.14 % (438674) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438668-438674"...
% 0.09/0.14 % (438678)...printing done.
% 0.09/0.14 % (438676) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438668-438676"...
% 0.09/0.14 % (438678)Refutation found. Thanks to Tanya!
% 0.09/0.14 % SZS status Theorem for theBenchmark
% 0.09/0.14 % SZS output start Proof for theBenchmark
% 0.09/0.14 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.09/0.14 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.14 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.09/0.14 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.09/0.14 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.09/0.14 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.09/0.14 thf(func_def_7, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.09/0.14 thf(func_def_8, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.09/0.14 thf(func_def_9, type, sK2: ('type/realax/real' > $o)).
% 0.09/0.14 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.09/0.14 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.09/0.14 thf(f1,axiom,(
% 0.09/0.14 ! [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' @ X1 @ X2)) & (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' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.09/0.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.09/0.14 thf(f2,conjecture,(
% 0.09/0.14 ! [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' @ X1 @ X2)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 0.09/0.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_')).
% 0.09/0.14 thf(f3,negated_conjecture,(
% 0.09/0.14 ~ ! [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' @ X1 @ X2)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 0.09/0.14 inference(negated_conjecture,[status(cth)],[f2])).
% 0.09/0.14 thf(f4,plain,(
% 0.09/0.14 ! [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' @ X1 @ X2)) & (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' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 0.09/0.14 inference(rectify,[],[f1])).
% 0.09/0.14 thf(f5,plain,(
% 0.09/0.14 ! [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' @ X1 @ X2)) = $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' @ X3 @ X4)) = $true)) => ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true)) & ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true))))),
% 0.09/0.14 inference(fool_elimination,[],[f4])).
% 0.09/0.14 thf(f6,plain,(
% 0.09/0.14 ~ ! [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' @ X1 @ X2)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 0.09/0.14 inference(rectify,[],[f3])).
% 0.09/0.14 thf(f7,plain,(
% 0.09/0.14 ~ ! [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' @ X1 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true))),
% 0.09/0.14 inference(fool_elimination,[],[f6])).
% 0.09/0.14 thf(f8,plain,(
% 0.09/0.14 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X4)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.09/0.14 inference(ennf_transformation,[],[f5])).
% 0.09/0.14 thf(f9,plain,(
% 0.09/0.14 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X4)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.09/0.14 inference(flattening,[],[f8])).
% 0.09/0.14 thf(f10,plain,(
% 0.09/0.14 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true) & (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.09/0.14 inference(ennf_transformation,[],[f7])).
% 0.09/0.14 thf(f11,plain,(
% 0.09/0.14 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true) & ! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.09/0.14 inference(flattening,[],[f10])).
% 0.09/0.14 thf(f12,plain,(
% 0.09/0.14 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ X5))) & ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.09/0.14 inference(rectify,[],[f9])).
% 0.09/0.14 thf(f13,plain,(
% 0.09/0.14 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))))) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.09/0.14 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f12])).
% 0.09/0.14 thf(f14,plain,(
% 0.09/0.14 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ X2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.09/0.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11])).
% 0.09/0.14 thf(f17,plain,(
% 0.09/0.14 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.09/0.14 inference(cnf_transformation,[],[f13])).
% 0.09/0.14 thf(f18,plain,(
% 0.09/0.14 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.09/0.14 inference(cnf_transformation,[],[f13])).
% 0.09/0.14 thf(f19,plain,(
% 0.09/0.14 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.09/0.14 inference(cnf_transformation,[],[f13])).
% 0.09/0.14 thf(f20,plain,(
% 0.09/0.14 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.09/0.14 inference(cnf_transformation,[],[f13])).
% 0.09/0.15 thf(f21,plain,(
% 0.09/0.15 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.09/0.15 inference(cnf_transformation,[],[f14])).
% 0.09/0.15 thf(f22,plain,(
% 0.09/0.15 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X2)))) )),
% 0.09/0.15 inference(cnf_transformation,[],[f14])).
% 0.09/0.15 thf(f23,plain,(
% 0.09/0.15 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))),
% 0.09/0.15 inference(cnf_transformation,[],[f14])).
% 0.09/0.15 thf(f115,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.09/0.15 inference(constrained_superposition,[],[f22,f17])).
% 0.09/0.15 thf(f125,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f115])).
% 0.09/0.15 thf(f141,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))))) )),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f125,f21])).
% 0.09/0.15 thf(f148,definition,(
% 0.09/0.15 spl5_5 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2)))))),
% 0.09/0.15 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.09/0.15 thf(f149,plain,(
% 0.09/0.15 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_5),
% 0.09/0.15 inference(avatar_component_clause,[],[f148])).
% 0.09/0.15 thf(f151,definition,(
% 0.09/0.15 spl5_6 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))),
% 0.09/0.15 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.09/0.15 thf(f152,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))) ) | ~spl5_6),
% 0.09/0.15 inference(avatar_component_clause,[],[f151])).
% 0.09/0.15 thf(f153,plain,(
% 0.09/0.15 spl5_5 | spl5_6),
% 0.09/0.15 inference(avatar_split_clause,[],[f141,f151,f148])).
% 0.09/0.15 thf(f156,definition,(
% 0.09/0.15 spl5_7 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.09/0.15 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.09/0.15 thf(f157,plain,(
% 0.09/0.15 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl5_7),
% 0.09/0.15 inference(avatar_component_clause,[],[f156])).
% 0.09/0.15 thf(f159,definition,(
% 0.09/0.15 spl5_8 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))))),
% 0.09/0.15 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.09/0.15 thf(f160,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_8),
% 0.09/0.15 inference(avatar_component_clause,[],[f159])).
% 0.09/0.15 thf(f168,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))) ) | ~spl5_7),
% 0.09/0.15 inference(constrained_superposition,[],[f22,f157])).
% 0.09/0.15 thf(f175,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK1 @ X0 @ sK2))))) ) | ~spl5_7),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f168])).
% 0.09/0.15 thf(f181,plain,(
% 0.09/0.15 spl5_6 | ~spl5_7),
% 0.09/0.15 inference(avatar_split_clause,[],[f175,f156,f151])).
% 0.09/0.15 thf(f184,definition,(
% 0.09/0.15 spl5_9 <=> ! [X1 : 'type/realax/real'] : ($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2))))),
% 0.09/0.15 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.09/0.15 thf(f185,plain,(
% 0.09/0.15 ( ! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK2))))) ) | ~spl5_9),
% 0.09/0.15 inference(avatar_component_clause,[],[f184])).
% 0.09/0.15 thf(f195,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_8),
% 0.09/0.15 inference(constrained_superposition,[],[f19,f160])).
% 0.09/0.15 thf(f196,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true != (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_8),
% 0.09/0.15 inference(constrained_superposition,[],[f20,f160])).
% 0.09/0.15 thf(f197,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true != (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(duplicate_literal_removal,[],[f196])).
% 0.09/0.15 thf(f198,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true != (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f197])).
% 0.09/0.15 thf(f199,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(duplicate_literal_removal,[],[f195])).
% 0.09/0.15 thf(f200,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f199])).
% 0.09/0.15 thf(f201,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f198,f23])).
% 0.09/0.15 thf(f202,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_8),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f200,f23])).
% 0.09/0.15 thf(f203,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK2))))) ) | ~spl5_8),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f201,f21])).
% 0.09/0.15 thf(f204,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl5_8),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f202,f21])).
% 0.09/0.15 thf(f205,plain,(
% 0.09/0.15 spl5_9 | ~spl5_8),
% 0.09/0.15 inference(avatar_split_clause,[],[f203,f159,f184])).
% 0.09/0.15 thf(f206,plain,(
% 0.09/0.15 spl5_7 | ~spl5_8),
% 0.09/0.15 inference(avatar_split_clause,[],[f204,f159,f156])).
% 0.09/0.15 thf(f213,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_6),
% 0.09/0.15 inference(constrained_superposition,[],[f18,f152])).
% 0.09/0.15 thf(f214,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_6),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f213])).
% 0.09/0.15 thf(f236,plain,(
% 0.09/0.15 ($true != $true) | (~spl5_6 | ~spl5_9)),
% 0.09/0.15 inference(constrained_superposition,[],[f185,f152])).
% 0.09/0.15 thf(f239,plain,(
% 0.09/0.15 $false | (~spl5_6 | ~spl5_9)),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f236])).
% 0.09/0.15 thf(f240,plain,(
% 0.09/0.15 ~spl5_6 | ~spl5_9),
% 0.09/0.15 inference(avatar_contradiction_clause,[],[f239])).
% 0.09/0.15 thf(f245,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_5),
% 0.09/0.15 inference(constrained_superposition,[],[f22,f149])).
% 0.09/0.15 thf(f252,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_5),
% 0.09/0.15 inference(trivial_inequality_removal,[],[f245])).
% 0.09/0.15 thf(f258,plain,(
% 0.09/0.15 spl5_8 | ~spl5_5),
% 0.09/0.15 inference(avatar_split_clause,[],[f252,f148,f159])).
% 0.09/0.15 thf(f266,plain,(
% 0.09/0.15 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) ) | ~spl5_6),
% 0.09/0.15 inference(forward_subsumption_resolution,[],[f214,f21])).
% 0.09/0.15 thf(f267,plain,(
% 0.09/0.15 spl5_5 | ~spl5_6),
% 0.09/0.15 inference(avatar_split_clause,[],[f266,f151,f148])).
% 0.09/0.15 cnf(s3, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f153])).
% 0.09/0.15 cnf(s9, plain, spl5_6 | ~spl5_7, inference(sat_conversion,[],[f181])).
% 0.09/0.15 cnf(s15, plain, ~spl5_8 | spl5_9, inference(sat_conversion,[],[f205])).
% 0.09/0.15 cnf(s16, plain, spl5_7 | ~spl5_8, inference(sat_conversion,[],[f206])).
% 0.09/0.15 cnf(s17, plain, ~spl5_6 | ~spl5_9, inference(sat_conversion,[],[f240])).
% 0.09/0.15 cnf(s19, plain, ~spl5_5 | spl5_8, inference(sat_conversion,[],[f258])).
% 0.09/0.15 cnf(s25, plain, spl5_5 | ~spl5_6, inference(sat_conversion,[],[f267])).
% 0.09/0.15 cnf(s26, plain, spl5_5, inference(rat,[],[s3,s25])).
% 0.09/0.15 cnf(s27, plain, spl5_8, inference(rat,[],[s19,s26])).
% 0.09/0.15 cnf(s28, plain, spl5_7, inference(rat,[],[s16,s27])).
% 0.09/0.15 cnf(s29, plain, spl5_9, inference(rat,[],[s15,s27])).
% 0.09/0.15 cnf(s30, plain, spl5_6, inference(rat,[],[s9,s28])).
% 0.09/0.15 cnf(s32, plain, $false, inference(rat,[],[s17,s29,s30])).
% 0.09/0.15 thf(f268,plain,(
% 0.09/0.15 $false),
% 0.09/0.15 inference(avatar_sat_refutation,[],[s32])).
% 0.09/0.15 % SZS output end Proof for theBenchmark
% 0.09/0.15 % (438678)------------------------------
% 0.09/0.15 % (438678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.15 % (438678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.15 % (438678)CaDiCaL version: 2.1.3
% 0.09/0.15 % (438678)Termination reason: Refutation
% 0.09/0.15 % (438678)Time elapsed: 0.007 s
% 0.09/0.15 % (438678)Peak memory usage: 12 MB
% 0.09/0.15 % (438678)Instructions burned: 22 (million)
% 0.09/0.15 % (438668)Success in time 0.02 s
% 0.09/0.15 % Vampire exiting
%------------------------------------------------------------------------------