%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV493^1 : 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 : n026.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 08:39:35 AM UTC 2026
% Result : Theorem 0.12s 0.29s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV493^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n026.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 15:55:57 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 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
% 0.12/0.29 % (774635)Will run a generic schedule for satisfiability detection.
% 0.12/0.29 % (774641)% WARNING: option uhcvi not known.
% 0.12/0.29 % (774641)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3199302856:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.29 % (774641)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.29 % (774641)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.29 % (774645)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2916652970:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.29 % (774640)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2544548013_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.29 % (774642)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2878894078:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.29 % (774643)dis+10_1_sil=32000:sp=arity:random_seed=646085372:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.29 % (774644)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=604711507:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.29 % (774646)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1330112008:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.29 % (774644)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.29 % Exception at run slice level
% 0.12/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.29 % (774641) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-774635-774641"...
% 0.12/0.29 % (774641)...printing done.
% 0.12/0.29 % (774641)Refutation found. Thanks to Tanya!
% 0.12/0.29 % SZS status Theorem for theBenchmark
% 0.12/0.29 % SZS output start Proof for theBenchmark
% 0.12/0.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.12/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.29 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.12/0.29 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.12/0.29 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.12/0.29 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.12/0.29 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 0.12/0.29 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.12/0.29 thf(func_def_10, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.29 thf(func_def_11, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.29 thf(func_def_12, type, sK2: (('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.29 thf(func_def_13, type, sK3: ('type/realax/real' > $o)).
% 0.12/0.29 thf(func_def_14, type, sK4: 'type/realax/real').
% 0.12/0.29 thf(func_def_16, type, sK6: 'type/realax/real').
% 0.12/0.29 thf(f1,axiom,(
% 0.12/0.29 ! [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))))),
% 0.12/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.12/0.29 thf(f3,axiom,(
% 0.12/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 0.12/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_')).
% 0.12/0.29 thf(f4,axiom,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 0.12/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_LEMMA_')).
% 0.12/0.29 thf(f5,conjecture,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.12/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_')).
% 0.12/0.29 thf(f6,negated_conjecture,(
% 0.12/0.29 ~ ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.12/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.12/0.29 thf(f7,plain,(
% 0.12/0.29 ! [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))))),
% 0.12/0.29 inference(rectify,[],[f1])).
% 0.12/0.29 thf(f8,plain,(
% 0.12/0.29 ! [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))))),
% 0.12/0.29 inference(fool_elimination,[],[f7])).
% 0.12/0.29 thf(f11,plain,(
% 0.12/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 0.12/0.29 inference(rectify,[],[f3])).
% 0.12/0.29 thf(f12,plain,(
% 0.12/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = ((X0 = X1)))),
% 0.12/0.29 inference(fool_elimination,[],[f11])).
% 0.12/0.29 thf(f13,plain,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 0.12/0.29 inference(rectify,[],[f4])).
% 0.12/0.29 thf(f14,plain,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => ? [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/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)))),
% 0.12/0.29 inference(fool_elimination,[],[f13])).
% 0.12/0.29 thf(f15,plain,(
% 0.12/0.29 ~ ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 0.12/0.29 inference(rectify,[],[f6])).
% 0.12/0.29 thf(f16,plain,(
% 0.12/0.29 ~ ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)) => (! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true)) & ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) = $true)))),
% 0.12/0.29 inference(fool_elimination,[],[f15])).
% 0.12/0.29 thf(f17,plain,(
% 0.12/0.29 ! [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)))),
% 0.12/0.29 inference(ennf_transformation,[],[f8])).
% 0.12/0.29 thf(f18,plain,(
% 0.12/0.29 ! [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))),
% 0.12/0.29 inference(flattening,[],[f17])).
% 0.12/0.29 thf(f19,plain,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : (? [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/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)))),
% 0.12/0.29 inference(ennf_transformation,[],[f14])).
% 0.12/0.29 thf(f20,plain,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : (? [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/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 0.12/0.29 inference(flattening,[],[f19])).
% 0.12/0.29 thf(f21,plain,(
% 0.12/0.29 ? [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) != $true)) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true)))),
% 0.12/0.29 inference(ennf_transformation,[],[f16])).
% 0.12/0.29 thf(f22,plain,(
% 0.12/0.29 ? [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) = $true)) | ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) = $true))),
% 0.12/0.29 inference(flattening,[],[f21])).
% 0.12/0.29 thf(f23,plain,(
% 0.12/0.29 ! [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))),
% 0.12/0.29 inference(rectify,[],[f18])).
% 0.12/0.29 thf(f24,plain,(
% 0.12/0.29 ! [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))),
% 0.12/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f23])).
% 0.12/0.29 thf(f25,plain,(
% 0.12/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ X0) @ X2))) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true))),
% 0.12/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.12/0.29 thf(f26,plain,(
% 0.12/0.29 ((($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK4 @ sK3)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK3) @ sK3)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK3) & ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK3)))),
% 0.12/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f22])).
% 0.12/0.29 thf(f27,plain,(
% 0.12/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f28,plain,(
% 0.12/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f29,plain,(
% 0.12/0.29 ( ! [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' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f30,plain,(
% 0.12/0.29 ( ! [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)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f31,plain,(
% 0.12/0.29 ( ! [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)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f32,plain,(
% 0.12/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f24])).
% 0.12/0.29 thf(f34,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = ((X0 = X1)))) )),
% 0.12/0.29 inference(cnf_transformation,[],[f12])).
% 0.12/0.29 thf(f35,plain,(
% 0.12/0.29 ( ! [X0 : ('type/realax/real' > $o)] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X0) @ X0)))) )),
% 0.12/0.29 inference(cnf_transformation,[],[f25])).
% 0.12/0.29 thf(f36,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ($true = (('const/realax/real_le' @ (sK2 @ X0) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0)) != $true)) )),
% 0.12/0.29 inference(cnf_transformation,[],[f25])).
% 0.12/0.29 thf(f37,plain,(
% 0.12/0.29 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK3)))),
% 0.12/0.29 inference(cnf_transformation,[],[f26])).
% 0.12/0.29 thf(f38,plain,(
% 0.12/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK3)),
% 0.12/0.29 inference(cnf_transformation,[],[f26])).
% 0.12/0.29 thf(f39,plain,(
% 0.12/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK4 @ sK3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK3) @ sK3)))),
% 0.12/0.29 inference(cnf_transformation,[],[f26])).
% 0.12/0.29 thf(f40,plain,(
% 0.12/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK3) @ sK3)))),
% 0.12/0.29 inference(cnf_transformation,[],[f26])).
% 0.12/0.29 thf(f42,definition,(
% 0.12/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.12/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.12/0.29 thf(f44,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0))) = $false) | ($true = ((X0 = X1)))) )),
% 0.12/0.29 inference(iff_proxy_clausification,[],[f34])).
% 0.12/0.29 thf(f45,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) = $false) | ($true = ((X0 = X1))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.12/0.29 inference(and_proxy_clausification,[],[f44])).
% 0.12/0.29 thf(f46,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false) | (X0 = X1)) )),
% 0.12/0.29 inference(equality_proxy_clausification,[],[f45])).
% 0.12/0.29 thf(f52,definition,(
% 0.12/0.29 spl5_1 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK3) @ sK3)))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.12/0.29 thf(f56,definition,(
% 0.12/0.29 spl5_2 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK4 @ sK3)))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.12/0.29 thf(f58,plain,(
% 0.12/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK4 @ sK3))) | ~spl5_2),
% 0.12/0.29 inference(avatar_component_clause,[],[f56])).
% 0.12/0.29 thf(f59,plain,(
% 0.12/0.29 ~spl5_1 | spl5_2),
% 0.12/0.29 inference(avatar_split_clause,[],[f39,f56,f52])).
% 0.12/0.29 thf(f61,definition,(
% 0.12/0.29 spl5_3 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK4)))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.12/0.29 thf(f64,plain,(
% 0.12/0.29 ~spl5_1 | ~spl5_3),
% 0.12/0.29 inference(avatar_split_clause,[],[f40,f61,f52])).
% 0.12/0.29 thf(f104,plain,(
% 0.12/0.29 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ sK3) @ sK3)))),
% 0.12/0.29 inference(constrained_superposition,[],[f35,f37])).
% 0.12/0.29 thf(f107,plain,(
% 0.12/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ sK3) @ sK3)))),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f104])).
% 0.12/0.29 thf(f108,plain,(
% 0.12/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ sK3) @ sK3)))),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f107,f38])).
% 0.12/0.29 thf(f111,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ X1))))) )),
% 0.12/0.29 inference(constrained_superposition,[],[f28,f42])).
% 0.12/0.29 thf(f112,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ X1))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f111])).
% 0.12/0.29 thf(f119,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true != (('const/realax/real_le' @ X2 @ (sK0 @ X2 @ X1)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ X1))))) )),
% 0.12/0.29 inference(constrained_superposition,[],[f32,f42])).
% 0.12/0.29 thf(f120,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/realax/real_le' @ X2 @ (sK0 @ X2 @ X1)))) | ($true = (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ X1))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f119])).
% 0.12/0.29 thf(f128,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ X1))))) )),
% 0.12/0.29 inference(constrained_superposition,[],[f31,f42])).
% 0.12/0.29 thf(f129,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f128])).
% 0.12/0.29 thf(f133,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ X1) @ (sK0 @ X0 @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1)) )),
% 0.12/0.29 inference(constrained_superposition,[],[f36,f29])).
% 0.12/0.29 thf(f134,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ X1) @ (sK0 @ X0 @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) )),
% 0.12/0.29 inference(duplicate_literal_removal,[],[f133])).
% 0.12/0.29 thf(f135,plain,(
% 0.12/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/sets/FINITE' @ 'type/realax/real' @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ (sK2 @ X1) @ (sK0 @ X0 @ X1)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f134])).
% 0.12/0.29 thf(f142,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) )),
% 0.12/0.29 inference(constrained_superposition,[],[f27,f108])).
% 0.12/0.29 thf(f145,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f142])).
% 0.12/0.29 thf(f147,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3)))) )),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f145,f38])).
% 0.12/0.29 thf(f150,definition,(
% 0.12/0.29 spl5_8 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3)))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.12/0.29 thf(f151,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3)))) ) | ~spl5_8),
% 0.12/0.29 inference(avatar_component_clause,[],[f150])).
% 0.12/0.29 thf(f153,definition,(
% 0.12/0.29 spl5_9 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.12/0.29 thf(f155,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ~spl5_9),
% 0.12/0.29 inference(avatar_component_clause,[],[f153])).
% 0.12/0.29 thf(f156,plain,(
% 0.12/0.29 spl5_8 | spl5_9),
% 0.12/0.29 inference(avatar_split_clause,[],[f147,f153,f150])).
% 0.12/0.29 thf(f206,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) )),
% 0.12/0.29 inference(constrained_superposition,[],[f112,f108])).
% 0.12/0.29 thf(f220,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f206])).
% 0.12/0.29 thf(f222,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) )),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f220,f38])).
% 0.12/0.29 thf(f224,definition,(
% 0.12/0.29 spl5_10 <=> ! [X1 : 'type/realax/real'] : ($false = (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK3))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition])).
% 0.12/0.29 thf(f225,plain,(
% 0.12/0.29 ( ! [X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X1 @ (sK1 @ X1 @ sK3))))) ) | ~spl5_10),
% 0.12/0.29 inference(avatar_component_clause,[],[f224])).
% 0.12/0.29 thf(f230,plain,(
% 0.12/0.29 spl5_10 | spl5_9),
% 0.12/0.29 inference(avatar_split_clause,[],[f222,f153,f224])).
% 0.12/0.29 thf(f300,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) )),
% 0.12/0.29 inference(constrained_superposition,[],[f135,f37])).
% 0.12/0.29 thf(f303,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) )),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f300])).
% 0.12/0.29 thf(f304,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) )),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f303,f38])).
% 0.12/0.29 thf(f306,definition,(
% 0.12/0.29 spl5_12 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition])).
% 0.12/0.29 thf(f307,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(avatar_component_clause,[],[f306])).
% 0.12/0.29 thf(f308,plain,(
% 0.12/0.29 spl5_8 | spl5_12),
% 0.12/0.29 inference(avatar_split_clause,[],[f304,f306,f150])).
% 0.12/0.29 thf(f340,definition,(
% 0.12/0.29 spl5_13 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK3)))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition])).
% 0.12/0.29 thf(f341,plain,(
% 0.12/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_13),
% 0.12/0.29 inference(avatar_component_clause,[],[f340])).
% 0.12/0.29 thf(f343,definition,(
% 0.12/0.29 spl5_14 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition])).
% 0.12/0.29 thf(f344,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3))))) ) | ~spl5_14),
% 0.12/0.29 inference(avatar_component_clause,[],[f343])).
% 0.12/0.29 thf(f348,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3)))) ) | ~spl5_8),
% 0.12/0.29 inference(constrained_superposition,[],[f36,f151])).
% 0.12/0.29 thf(f349,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3)))) ) | ~spl5_8),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f348])).
% 0.12/0.29 thf(f352,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3)))) ) | ~spl5_8),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f349,f38])).
% 0.12/0.29 thf(f353,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK1 @ X0 @ sK3))))) ) | ~spl5_8),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f352,f37])).
% 0.12/0.29 thf(f354,plain,(
% 0.12/0.29 spl5_14 | ~spl5_8),
% 0.12/0.29 inference(avatar_split_clause,[],[f353,f150,f343])).
% 0.12/0.29 thf(f421,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_13),
% 0.12/0.29 inference(constrained_superposition,[],[f36,f341])).
% 0.12/0.29 thf(f422,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_13),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f421])).
% 0.12/0.29 thf(f425,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_13),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f422,f38])).
% 0.12/0.29 thf(f427,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_13),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f425,f37])).
% 0.12/0.29 thf(f432,plain,(
% 0.12/0.29 spl5_12 | ~spl5_13),
% 0.12/0.29 inference(avatar_split_clause,[],[f427,f340,f306])).
% 0.12/0.29 thf(f434,plain,(
% 0.12/0.29 ($true = $false) | (~spl5_10 | ~spl5_14)),
% 0.12/0.29 inference(constrained_superposition,[],[f344,f225])).
% 0.12/0.29 thf(f436,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl5_14),
% 0.12/0.29 inference(constrained_superposition,[],[f30,f344])).
% 0.12/0.29 thf(f444,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl5_14),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f436])).
% 0.12/0.29 thf(f446,plain,(
% 0.12/0.29 $false | (~spl5_10 | ~spl5_14)),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f434])).
% 0.12/0.29 thf(f447,plain,(
% 0.12/0.29 ~spl5_10 | ~spl5_14),
% 0.12/0.29 inference(avatar_contradiction_clause,[],[f446])).
% 0.12/0.29 thf(f451,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl5_14),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f444,f38])).
% 0.12/0.29 thf(f454,plain,(
% 0.12/0.29 spl5_13 | ~spl5_14),
% 0.12/0.29 inference(avatar_split_clause,[],[f451,f343,f340])).
% 0.12/0.29 thf(f550,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(constrained_superposition,[],[f307,f129])).
% 0.12/0.29 thf(f552,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(constrained_superposition,[],[f120,f307])).
% 0.12/0.29 thf(f556,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(duplicate_literal_removal,[],[f552])).
% 0.12/0.29 thf(f557,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f556])).
% 0.12/0.29 thf(f560,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl5_12),
% 0.12/0.29 inference(duplicate_literal_removal,[],[f550])).
% 0.12/0.29 thf(f561,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl5_12),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f560])).
% 0.12/0.29 thf(f563,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ($false = (('const/realax/real_le' @ X0 @ (sK1 @ X0 @ sK3))))) ) | ~spl5_12),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f557,f38])).
% 0.12/0.29 thf(f565,plain,(
% 0.12/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3)))) ) | ~spl5_12),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f561,f38])).
% 0.12/0.29 thf(f567,definition,(
% 0.12/0.29 spl5_18 <=> ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition])).
% 0.12/0.29 thf(f569,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ ('const/sets/inf' @ sK3)))) | ~spl5_18),
% 0.12/0.29 inference(avatar_component_clause,[],[f567])).
% 0.12/0.29 thf(f571,plain,(
% 0.12/0.29 spl5_10 | spl5_18 | ~spl5_12),
% 0.12/0.29 inference(avatar_split_clause,[],[f563,f306,f567,f224])).
% 0.12/0.29 thf(f573,plain,(
% 0.12/0.29 spl5_8 | spl5_18 | ~spl5_12),
% 0.12/0.29 inference(avatar_split_clause,[],[f565,f306,f567,f150])).
% 0.12/0.29 thf(f596,plain,(
% 0.12/0.29 ($true = $false) | ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ((('const/sets/inf' @ sK3)) = ((sK2 @ sK3))) | ~spl5_18),
% 0.12/0.29 inference(constrained_superposition,[],[f569,f46])).
% 0.12/0.29 thf(f603,plain,(
% 0.12/0.29 ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ((('const/sets/inf' @ sK3)) = ((sK2 @ sK3))) | ~spl5_18),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f596])).
% 0.12/0.29 thf(f605,definition,(
% 0.12/0.29 spl5_19 <=> ((('const/sets/inf' @ sK3)) = ((sK2 @ sK3)))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition])).
% 0.12/0.29 thf(f607,plain,(
% 0.12/0.29 ((('const/sets/inf' @ sK3)) = ((sK2 @ sK3))) | ~spl5_19),
% 0.12/0.29 inference(avatar_component_clause,[],[f605])).
% 0.12/0.29 thf(f609,definition,(
% 0.12/0.29 spl5_20 <=> ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition])).
% 0.12/0.29 thf(f611,plain,(
% 0.12/0.29 ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ (sK2 @ sK3)))) | ~spl5_20),
% 0.12/0.29 inference(avatar_component_clause,[],[f609])).
% 0.12/0.29 thf(f615,plain,(
% 0.12/0.29 spl5_19 | spl5_20 | ~spl5_18),
% 0.12/0.29 inference(avatar_split_clause,[],[f603,f567,f609,f605])).
% 0.12/0.29 thf(f742,plain,(
% 0.12/0.29 ($true = $false) | (~spl5_9 | ~spl5_20)),
% 0.12/0.29 inference(constrained_superposition,[],[f611,f155])).
% 0.12/0.29 thf(f754,plain,(
% 0.12/0.29 $false | (~spl5_9 | ~spl5_20)),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f742])).
% 0.12/0.29 thf(f755,plain,(
% 0.12/0.29 ~spl5_9 | ~spl5_20),
% 0.12/0.29 inference(avatar_contradiction_clause,[],[f754])).
% 0.12/0.29 thf(f770,plain,(
% 0.12/0.29 ($true = (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK3) @ sK3))) | ~spl5_19),
% 0.12/0.29 inference(constrained_superposition,[],[f108,f607])).
% 0.12/0.29 thf(f785,plain,(
% 0.12/0.29 spl5_1 | ~spl5_19),
% 0.12/0.29 inference(avatar_split_clause,[],[f770,f605,f52])).
% 0.12/0.29 thf(f791,plain,(
% 0.12/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ~spl5_2),
% 0.12/0.29 inference(constrained_superposition,[],[f36,f58])).
% 0.12/0.29 thf(f792,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ~spl5_2),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f791])).
% 0.12/0.29 thf(f796,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ sK4))) | ($true != (('const/sets/FINITE' @ 'type/realax/real' @ sK3))) | ~spl5_2),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f792,f38])).
% 0.12/0.29 thf(f800,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ (sK2 @ sK3) @ sK4))) | ~spl5_2),
% 0.12/0.29 inference(forward_subsumption_resolution,[],[f796,f37])).
% 0.12/0.29 thf(f803,plain,(
% 0.12/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK4))) | (~spl5_2 | ~spl5_19)),
% 0.12/0.29 inference(forward_demodulation,[],[f800,f607])).
% 0.12/0.29 thf(f804,plain,(
% 0.12/0.29 spl5_3 | ~spl5_2 | ~spl5_19),
% 0.12/0.29 inference(avatar_split_clause,[],[f803,f605,f56,f61])).
% 0.12/0.29 cnf(s1, plain, ~spl5_1 | spl5_2, inference(sat_conversion,[],[f59])).
% 0.12/0.29 cnf(s2, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f64])).
% 0.12/0.29 cnf(s6, plain, spl5_8 | spl5_9, inference(sat_conversion,[],[f156])).
% 0.12/0.29 cnf(s8, plain, spl5_9 | spl5_10, inference(sat_conversion,[],[f230])).
% 0.12/0.29 cnf(s9, plain, spl5_8 | spl5_12, inference(sat_conversion,[],[f308])).
% 0.12/0.29 cnf(s14, plain, ~spl5_8 | spl5_14, inference(sat_conversion,[],[f354])).
% 0.12/0.29 cnf(s16, plain, spl5_12 | ~spl5_13, inference(sat_conversion,[],[f432])).
% 0.12/0.29 cnf(s18, plain, ~spl5_10 | ~spl5_14, inference(sat_conversion,[],[f447])).
% 0.12/0.29 cnf(s19, plain, spl5_13 | ~spl5_14, inference(sat_conversion,[],[f454])).
% 0.12/0.29 cnf(s41, plain, spl5_10 | ~spl5_12 | spl5_18, inference(sat_conversion,[],[f571])).
% 0.12/0.29 cnf(s43, plain, spl5_8 | ~spl5_12 | spl5_18, inference(sat_conversion,[],[f573])).
% 0.12/0.29 cnf(s47, plain, ~spl5_18 | spl5_19 | spl5_20, inference(sat_conversion,[],[f615])).
% 0.12/0.29 cnf(s49, plain, ~spl5_9 | ~spl5_20, inference(sat_conversion,[],[f755])).
% 0.12/0.29 cnf(s55, plain, spl5_1 | ~spl5_19, inference(sat_conversion,[],[f785])).
% 0.12/0.29 cnf(s60, plain, ~spl5_2 | spl5_3 | ~spl5_19, inference(sat_conversion,[],[f804])).
% 0.12/0.29 cnf(s61, plain, spl5_8 | spl5_19, inference(rat,[],[s47,s49,s43,s6,s9])).
% 0.12/0.29 cnf(s62, plain, spl5_19, inference(rat,[],[s47,s49,s41,s8,s16,s18,s19,s14,s61])).
% 0.12/0.29 cnf(s63, plain, spl5_1, inference(rat,[],[s55,s62])).
% 0.12/0.29 cnf(s65, plain, ~spl5_3, inference(rat,[],[s2,s63])).
% 0.12/0.29 cnf(s66, plain, spl5_2, inference(rat,[],[s1,s63])).
% 0.12/0.29 cnf(s67, plain, $false, inference(rat,[],[s60,s62,s65,s66])).
% 0.12/0.29 thf(f805,plain,(
% 0.12/0.29 $false),
% 0.12/0.29 inference(avatar_sat_refutation,[],[s67])).
% 0.12/0.29 % SZS output end Proof for theBenchmark
% 0.12/0.29 % (774641)------------------------------
% 0.12/0.29 % (774641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.29 % (774641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.29 % (774641)CaDiCaL version: 2.1.3
% 0.12/0.29 % (774641)Termination reason: Refutation
% 0.12/0.29 % (774641)Time elapsed: 0.024 s
% 0.12/0.29 % (774641)Peak memory usage: 13 MB
% 0.12/0.29 % (774641)Instructions burned: 83 (million)
% 0.12/0.29 % (774635)Success in time 0.061 s
% 0.12/0.29 % Vampire exiting
%------------------------------------------------------------------------------