%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA092^1 : 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 : n016.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 07:46:03 AM UTC 2026
% Result : Theorem 0.65s 0.43s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA092^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 % Computer : n016.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 17:45:50 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.27/0.30 Running first-order model finding
% 0.27/0.30 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
% 0.65/0.43 % (681547)Will run a generic schedule for satisfiability detection.
% 0.65/0.43 % (681556)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2606319458:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.65/0.43 % (681556)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.65/0.43 % (681554)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1097018276:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.65/0.43 % (681553)% WARNING: option uhcvi not known.
% 0.65/0.43 % (681552)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3380544284_2999 on theBenchmark for (2999ds/0Mi)
% 0.65/0.43 % (681553)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2784820885:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.65/0.43 % (681555)dis+10_1_sil=32000:sp=arity:random_seed=2092832043:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.65/0.43 % (681558)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3743002903:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.65/0.43 % (681557)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1346954052:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.65/0.43 % (681553)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.65/0.43 % Exception at run slice level
% 0.65/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.65/0.43 % (681553)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.65/0.43 % (681566)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=938570742:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.65/0.43 % Exception at run slice level
% 0.65/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.65/0.43 % (681556)Instruction limit reached!
% 0.65/0.43 % (681556)------------------------------
% 0.65/0.43 % (681556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.43 % (681556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.43 % (681556)CaDiCaL version: 2.1.3
% 0.65/0.43 % (681556)Termination reason: Instruction limit
% 0.65/0.43 % (681556)Termination phase: Saturation
% 0.65/0.43 % (681556)Time elapsed: 0.053 s
% 0.65/0.43 % (681556)Peak memory usage: 12 MB
% 0.65/0.43 % (681556)Instructions burned: 118 (million)
% 0.65/0.43 % (681568)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2633989152:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.65/0.43 % (681553) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-681547-681553"...
% 0.65/0.43 % (681569)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=395645442:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.65/0.43 % (681569)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.65/0.43 % (681553)...printing done.
% 0.65/0.43 % (681555) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-681547-681555"...
% 0.65/0.43 % (681553)Refutation found. Thanks to Tanya!
% 0.65/0.43 % SZS status Theorem for theBenchmark
% 0.65/0.43 % SZS output start Proof for theBenchmark
% 0.65/0.43 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.65/0.43 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.65/0.43 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.65/0.43 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.65/0.43 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.65/0.43 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.65/0.43 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.65/0.43 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.65/0.43 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.65/0.43 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.65/0.43 thf(func_def_11, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.65/0.43 thf(func_def_12, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.65/0.43 thf(func_def_13, type, sK2: 'type/realax/real').
% 0.65/0.43 thf(func_def_14, type, sK3: ('type/realax/real' > $o)).
% 0.65/0.43 thf(func_def_15, type, sK4: 'type/realax/real').
% 0.65/0.43 thf(func_def_16, type, sK5: 'type/realax/real').
% 0.65/0.43 thf(func_def_18, type, sK7: 'type/realax/real').
% 0.65/0.43 thf(f1,axiom,(
% 0.65/0.43 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.65/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.65/0.43 thf(f2,axiom,(
% 0.65/0.43 ! [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))))),
% 0.65/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.65/0.43 thf(f3,conjecture,(
% 0.65/0.43 ! [X0 : $tType,X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X3 : X0] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & (X2 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4))))),
% 0.65/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_EQ_')).
% 0.65/0.43 thf(f4,negated_conjecture,(
% 0.65/0.43 ~ ! [X0 : $tType,X1 : 'type/realax/real',X2 : ('type/realax/real' > $o),X3 : X0] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & (X2 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4))))),
% 0.65/0.43 inference(negated_conjecture,[status(cth)],[f3])).
% 0.65/0.43 thf(f5,plain,(
% 0.65/0.43 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.65/0.43 inference(rectify,[],[f1])).
% 0.65/0.43 thf(f6,plain,(
% 0.65/0.43 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ X1 @ X2)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) => ((('const/realax/real_le' @ X0 @ X2)) = $true))),
% 0.65/0.43 inference(fool_elimination,[],[f5])).
% 0.65/0.43 thf(f7,plain,(
% 0.65/0.43 ! [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))))),
% 0.65/0.43 inference(rectify,[],[f2])).
% 0.65/0.43 thf(f8,plain,(
% 0.65/0.43 ! [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)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('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))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))))),
% 0.65/0.43 inference(fool_elimination,[],[f7])).
% 0.65/0.43 thf(f9,plain,(
% 0.65/0.43 ~ ! [X1 : 'type/realax/real',X2 : ('type/realax/real' > $o)] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & (X2 != 'const/sets/EMPTY' @ 'type/realax/real')) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ! [X6 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X6 @ X2) => ('const/realax/real_le' @ X1 @ X6))))),
% 0.65/0.43 inference(rectify,[],[f4])).
% 0.65/0.43 thf(f10,plain,(
% 0.65/0.43 ~ ! [X1 : 'type/realax/real',X2 : ('type/realax/real' > $o)] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X2)) = $true) => ((('const/realax/real_le' @ X4 @ X5)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X2) => ('const/realax/real_le' @ X1 @ Y0)))))))),
% 0.65/0.43 inference(fool_elimination,[],[f9])).
% 0.65/0.43 thf(f11,plain,(
% 0.65/0.43 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1))) => ($true = (('const/realax/real_le' @ X2 @ X3)))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1)) => ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))) = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ X0 @ Y0)))))))),
% 0.65/0.43 inference(rectify,[],[f10])).
% 0.65/0.43 thf(f12,plain,(
% 0.65/0.43 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 0.65/0.43 inference(ennf_transformation,[],[f6])).
% 0.65/0.43 thf(f13,plain,(
% 0.65/0.43 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true))),
% 0.65/0.43 inference(flattening,[],[f12])).
% 0.65/0.43 thf(f14,plain,(
% 0.65/0.43 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | (! [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)))),
% 0.65/0.43 inference(ennf_transformation,[],[f8])).
% 0.65/0.43 thf(f15,plain,(
% 0.65/0.43 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | ! [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))),
% 0.65/0.43 inference(flattening,[],[f14])).
% 0.65/0.43 thf(f16,plain,(
% 0.65/0.43 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ X0 @ Y0)))))) & (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X2 @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1)))),
% 0.65/0.43 inference(ennf_transformation,[],[f11])).
% 0.65/0.43 thf(f17,plain,(
% 0.65/0.43 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ X0 @ Y0)))))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X2 @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 0.65/0.43 inference(flattening,[],[f16])).
% 0.65/0.43 thf(f18,plain,(
% 0.65/0.43 ! [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'] : (((('const/realax/real_le' @ X4 @ X5)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.65/0.43 inference(rectify,[],[f15])).
% 0.65/0.43 thf(f19,plain,(
% 0.65/0.43 ! [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)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.65/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f18])).
% 0.65/0.43 thf(f20,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0)))))) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK4 @ X3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK3)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK3)),
% 0.65/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f17])).
% 0.65/0.43 thf(f21,plain,(
% 0.65/0.43 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f13])).
% 0.65/0.43 thf(f22,plain,(
% 0.65/0.43 ( ! [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)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f23,plain,(
% 0.65/0.43 ( ! [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)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f24,plain,(
% 0.65/0.43 ( ! [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)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f25,plain,(
% 0.65/0.43 ( ! [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)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f26,plain,(
% 0.65/0.43 ( ! [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)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f27,plain,(
% 0.65/0.43 ( ! [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))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.65/0.43 inference(cnf_transformation,[],[f19])).
% 0.65/0.43 thf(f28,plain,(
% 0.65/0.43 ('const/sets/EMPTY' @ 'type/realax/real' != sK3)),
% 0.65/0.43 inference(cnf_transformation,[],[f20])).
% 0.65/0.43 thf(f29,plain,(
% 0.65/0.43 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK3))) | ($true = (('const/realax/real_le' @ sK4 @ X3)))) )),
% 0.65/0.43 inference(cnf_transformation,[],[f20])).
% 0.65/0.43 thf(f30,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) != ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0))))))),
% 0.65/0.43 inference(cnf_transformation,[],[f20])).
% 0.65/0.43 thf(f32,definition,(
% 0.65/0.43 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.65/0.43 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.65/0.43 thf(f33,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0))))))),
% 0.65/0.43 inference(xor_proxy_clausification,[],[f30])).
% 0.65/0.43 thf(f34,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0))))) = $false)),
% 0.65/0.43 inference(xor_proxy_clausification,[],[f30])).
% 0.65/0.43 thf(f35,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | ($false = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0))) @ sK5)))),
% 0.65/0.43 inference(sigma_proxy_clausification,[],[f34])).
% 0.65/0.43 thf(f36,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | ($false = ((('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK3) => ('const/realax/real_le' @ sK2 @ sK5))))),
% 0.65/0.43 inference(beta-eta_normalization,[],[f35])).
% 0.65/0.43 thf(f37,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | ($false = (('const/realax/real_le' @ sK2 @ sK5)))),
% 0.65/0.43 inference(imp_proxy_clausification,[],[f36])).
% 0.65/0.43 thf(f38,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK3)))),
% 0.65/0.43 inference(imp_proxy_clausification,[],[f36])).
% 0.65/0.43 thf(f39,plain,(
% 0.65/0.43 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = (((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK3) => ('const/realax/real_le' @ sK2 @ Y0))) @ X1)))) )),
% 0.65/0.43 inference(pi_proxy_clausification,[],[f33])).
% 0.65/0.43 thf(f40,plain,(
% 0.65/0.43 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3) => ('const/realax/real_le' @ sK2 @ X1))))) )),
% 0.65/0.43 inference(beta-eta_normalization,[],[f39])).
% 0.65/0.43 thf(f41,plain,(
% 0.65/0.43 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ($true = (('const/realax/real_le' @ sK2 @ X1)))) )),
% 0.65/0.43 inference(imp_proxy_clausification,[],[f40])).
% 0.65/0.43 thf(f43,definition,(
% 0.65/0.43 spl6_1 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK3)))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.65/0.43 thf(f45,plain,(
% 0.65/0.43 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK3))) | ~spl6_1),
% 0.65/0.43 inference(avatar_component_clause,[],[f43])).
% 0.65/0.43 thf(f47,definition,(
% 0.65/0.43 spl6_2 <=> ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false)),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.65/0.43 thf(f49,plain,(
% 0.65/0.43 ((('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))) = $false) | ~spl6_2),
% 0.65/0.43 inference(avatar_component_clause,[],[f47])).
% 0.65/0.43 thf(f50,plain,(
% 0.65/0.43 spl6_1 | spl6_2),
% 0.65/0.43 inference(avatar_split_clause,[],[f38,f47,f43])).
% 0.65/0.43 thf(f52,definition,(
% 0.65/0.43 spl6_3 <=> ($false = (('const/realax/real_le' @ sK2 @ sK5)))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.65/0.43 thf(f54,plain,(
% 0.65/0.43 ($false = (('const/realax/real_le' @ sK2 @ sK5))) | ~spl6_3),
% 0.65/0.43 inference(avatar_component_clause,[],[f52])).
% 0.65/0.43 thf(f55,plain,(
% 0.65/0.43 spl6_3 | spl6_2),
% 0.65/0.43 inference(avatar_split_clause,[],[f37,f47,f52])).
% 0.65/0.43 thf(f57,definition,(
% 0.65/0.43 spl6_4 <=> ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ($true = (('const/realax/real_le' @ sK2 @ X1))))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.65/0.43 thf(f58,plain,(
% 0.65/0.43 ( ! [X1 : 'type/realax/real'] : (($false = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ($true = (('const/realax/real_le' @ sK2 @ X1)))) ) | ~spl6_4),
% 0.65/0.43 inference(avatar_component_clause,[],[f57])).
% 0.65/0.43 thf(f60,definition,(
% 0.65/0.43 spl6_5 <=> ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3))))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.65/0.43 thf(f61,plain,(
% 0.65/0.43 ($true != (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | spl6_5),
% 0.65/0.43 inference(avatar_component_clause,[],[f60])).
% 0.65/0.43 thf(f62,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ~spl6_5),
% 0.65/0.43 inference(avatar_component_clause,[],[f60])).
% 0.65/0.43 thf(f63,plain,(
% 0.65/0.43 spl6_4 | spl6_5),
% 0.65/0.43 inference(avatar_split_clause,[],[f41,f60,f57])).
% 0.65/0.43 thf(f94,plain,(
% 0.65/0.43 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.65/0.43 inference(constrained_superposition,[],[f21,f32])).
% 0.65/0.43 thf(f95,plain,(
% 0.65/0.43 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f94])).
% 0.65/0.43 thf(f98,plain,(
% 0.65/0.43 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.65/0.43 inference(constrained_superposition,[],[f22,f32])).
% 0.65/0.43 thf(f99,plain,(
% 0.65/0.43 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X2 @ X1) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))) )),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f98])).
% 0.65/0.43 thf(f124,definition,(
% 0.65/0.43 spl6_10 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3)))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.65/0.43 thf(f125,plain,(
% 0.65/0.43 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3)))) ) | ~spl6_10),
% 0.65/0.43 inference(avatar_component_clause,[],[f124])).
% 0.65/0.43 thf(f131,definition,(
% 0.65/0.43 spl6_12 <=> ! [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)))))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.65/0.43 thf(f132,plain,(
% 0.65/0.43 ( ! [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))))) ) | ~spl6_12),
% 0.65/0.43 inference(avatar_component_clause,[],[f131])).
% 0.65/0.43 thf(f134,definition,(
% 0.65/0.43 spl6_13 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK4 @ (sK1 @ X0 @ sK3))))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 0.65/0.43 thf(f135,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK4 @ (sK1 @ X0 @ sK3))))) ) | ~spl6_13),
% 0.65/0.43 inference(avatar_component_clause,[],[f134])).
% 0.65/0.43 thf(f154,definition,(
% 0.65/0.43 spl6_14 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3)))))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 0.65/0.43 thf(f155,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl6_14),
% 0.65/0.43 inference(avatar_component_clause,[],[f154])).
% 0.65/0.43 thf(f190,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK4 @ (sK1 @ X0 @ sK3))))) ) | ~spl6_10),
% 0.65/0.43 inference(constrained_superposition,[],[f29,f125])).
% 0.65/0.43 thf(f193,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK4 @ (sK1 @ X0 @ sK3))))) ) | ~spl6_10),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f190])).
% 0.65/0.43 thf(f198,plain,(
% 0.65/0.43 spl6_13 | ~spl6_10),
% 0.65/0.43 inference(avatar_split_clause,[],[f193,f124,f134])).
% 0.65/0.43 thf(f205,plain,(
% 0.65/0.43 ($true = $false) | (~spl6_2 | ~spl6_5)),
% 0.65/0.43 inference(constrained_superposition,[],[f49,f62])).
% 0.65/0.43 thf(f210,plain,(
% 0.65/0.43 $false | (~spl6_2 | ~spl6_5)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f205])).
% 0.65/0.43 thf(f211,plain,(
% 0.65/0.43 ~spl6_2 | ~spl6_5),
% 0.65/0.43 inference(avatar_contradiction_clause,[],[f210])).
% 0.65/0.43 thf(f217,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(constrained_superposition,[],[f25,f135])).
% 0.65/0.43 thf(f218,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(constrained_superposition,[],[f27,f135])).
% 0.65/0.43 thf(f219,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(constrained_superposition,[],[f23,f135])).
% 0.65/0.43 thf(f220,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f219])).
% 0.65/0.43 thf(f221,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f218])).
% 0.65/0.43 thf(f222,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_13),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f217])).
% 0.65/0.43 thf(f224,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)))) ) | ~spl6_13),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f220,f28])).
% 0.65/0.43 thf(f225,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl6_13),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f221,f28])).
% 0.65/0.43 thf(f226,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl6_13),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f222,f28])).
% 0.65/0.43 thf(f227,plain,(
% 0.65/0.43 spl6_12 | ~spl6_13),
% 0.65/0.43 inference(avatar_split_clause,[],[f226,f134,f131])).
% 0.65/0.43 thf(f253,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ X0))) | ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0)))) ) | ~spl6_5),
% 0.65/0.43 inference(constrained_superposition,[],[f95,f62])).
% 0.65/0.43 thf(f261,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ X0))) | ($true = (('const/realax/real_le' @ sK2 @ X0)))) ) | ~spl6_5),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f253])).
% 0.65/0.43 thf(f285,definition,(
% 0.65/0.43 spl6_17 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK5)))),
% 0.65/0.43 introduced(definition,[new_symbols(definition,[spl6_17])],[avatar_definition])).
% 0.65/0.43 thf(f287,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK5))) | ~spl6_17),
% 0.65/0.43 inference(avatar_component_clause,[],[f285])).
% 0.65/0.43 thf(f454,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ sK2 @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)))) ) | ~spl6_5),
% 0.65/0.43 inference(constrained_superposition,[],[f261,f99])).
% 0.65/0.43 thf(f456,plain,(
% 0.65/0.43 ($true = $false) | ($true = (('const/realax/real_le' @ sK2 @ sK5))) | (~spl6_5 | ~spl6_17)),
% 0.65/0.43 inference(constrained_superposition,[],[f261,f287])).
% 0.65/0.43 thf(f472,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ sK2 @ sK5))) | (~spl6_5 | ~spl6_17)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f456])).
% 0.65/0.43 thf(f474,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)))) ) | ~spl6_5),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f454])).
% 0.65/0.43 thf(f479,plain,(
% 0.65/0.43 ($true = $false) | (~spl6_3 | ~spl6_5 | ~spl6_17)),
% 0.65/0.43 inference(forward_demodulation,[],[f472,f54])).
% 0.65/0.43 thf(f480,plain,(
% 0.65/0.43 $false | (~spl6_3 | ~spl6_5 | ~spl6_17)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f479])).
% 0.65/0.43 thf(f481,plain,(
% 0.65/0.43 ~spl6_3 | ~spl6_5 | ~spl6_17),
% 0.65/0.43 inference(avatar_contradiction_clause,[],[f480])).
% 0.65/0.43 thf(f522,plain,(
% 0.65/0.43 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK5))) | (~spl6_1 | ~spl6_13)),
% 0.65/0.43 inference(constrained_superposition,[],[f224,f45])).
% 0.65/0.43 thf(f567,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($false = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)))) ) | ~spl6_5),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f474,f28])).
% 0.65/0.43 thf(f585,plain,(
% 0.65/0.43 spl6_10 | spl6_4 | ~spl6_5),
% 0.65/0.43 inference(avatar_split_clause,[],[f567,f60,f57,f124])).
% 0.65/0.43 thf(f615,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_4),
% 0.65/0.43 inference(constrained_superposition,[],[f58,f24])).
% 0.65/0.43 thf(f617,plain,(
% 0.65/0.43 ($true = $false) | ($true = (('const/realax/real_le' @ sK2 @ sK5))) | (~spl6_1 | ~spl6_4)),
% 0.65/0.43 inference(constrained_superposition,[],[f58,f45])).
% 0.65/0.43 thf(f628,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3))))) ) | (~spl6_4 | ~spl6_12)),
% 0.65/0.43 inference(constrained_superposition,[],[f132,f58])).
% 0.65/0.43 thf(f631,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3))))) ) | (~spl6_4 | ~spl6_12)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f628])).
% 0.65/0.43 thf(f639,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ sK2 @ sK5))) | (~spl6_1 | ~spl6_4)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f617])).
% 0.65/0.43 thf(f641,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_4),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f615])).
% 0.65/0.43 thf(f652,plain,(
% 0.65/0.43 spl6_14 | ~spl6_4 | ~spl6_12),
% 0.65/0.43 inference(avatar_split_clause,[],[f631,f131,f57,f154])).
% 0.65/0.43 thf(f659,plain,(
% 0.65/0.43 ($true = $false) | (~spl6_1 | ~spl6_3 | ~spl6_4)),
% 0.65/0.43 inference(forward_demodulation,[],[f639,f54])).
% 0.65/0.43 thf(f660,plain,(
% 0.65/0.43 $false | (~spl6_1 | ~spl6_3 | ~spl6_4)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f659])).
% 0.65/0.43 thf(f661,plain,(
% 0.65/0.43 ~spl6_1 | ~spl6_3 | ~spl6_4),
% 0.65/0.43 inference(avatar_contradiction_clause,[],[f660])).
% 0.65/0.43 thf(f662,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ (sK0 @ X0 @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK3) @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK3))))) ) | ~spl6_4),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f641,f28])).
% 0.65/0.43 thf(f674,plain,(
% 0.65/0.43 spl6_10 | spl6_14 | ~spl6_4),
% 0.65/0.43 inference(avatar_split_clause,[],[f662,f57,f154,f124])).
% 0.65/0.43 thf(f689,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('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 @ ('const/sets/inf' @ sK3))))) ) | ~spl6_14),
% 0.65/0.43 inference(constrained_superposition,[],[f26,f155])).
% 0.65/0.43 thf(f690,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_14),
% 0.65/0.43 inference(duplicate_literal_removal,[],[f689])).
% 0.65/0.43 thf(f691,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl6_14),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f690])).
% 0.65/0.43 thf(f696,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | (spl6_5 | ~spl6_14)),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f691,f61])).
% 0.65/0.43 thf(f698,plain,(
% 0.65/0.43 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK3) @ sK3)))) ) | (spl6_5 | ~spl6_14)),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f696,f28])).
% 0.65/0.43 thf(f700,plain,(
% 0.65/0.43 spl6_10 | spl6_5 | ~spl6_14),
% 0.65/0.43 inference(avatar_split_clause,[],[f698,f154,f60,f124])).
% 0.65/0.43 thf(f724,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK3) @ sK5))) | (~spl6_1 | ~spl6_13)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f522])).
% 0.65/0.43 thf(f746,plain,(
% 0.65/0.43 spl6_17 | ~spl6_1 | ~spl6_13),
% 0.65/0.43 inference(avatar_split_clause,[],[f724,f134,f43,f285])).
% 0.65/0.43 thf(f924,plain,(
% 0.65/0.43 ($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | (~spl6_13 | ~spl6_14)),
% 0.65/0.43 inference(constrained_superposition,[],[f225,f155])).
% 0.65/0.43 thf(f930,plain,(
% 0.65/0.43 ($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | (~spl6_13 | ~spl6_14)),
% 0.65/0.43 inference(duplicate_literal_removal,[],[f924])).
% 0.65/0.43 thf(f931,plain,(
% 0.65/0.43 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/inf' @ sK3)))) | (~spl6_13 | ~spl6_14)),
% 0.65/0.43 inference(trivial_inequality_removal,[],[f930])).
% 0.65/0.43 thf(f937,plain,(
% 0.65/0.43 $false | (spl6_5 | ~spl6_13 | ~spl6_14)),
% 0.65/0.43 inference(forward_subsumption_resolution,[],[f931,f61])).
% 0.65/0.43 thf(f938,plain,(
% 0.65/0.43 spl6_5 | ~spl6_13 | ~spl6_14),
% 0.65/0.43 inference(avatar_contradiction_clause,[],[f937])).
% 0.65/0.43 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f50])).
% 0.65/0.43 cnf(s2, plain, spl6_2 | spl6_3, inference(sat_conversion,[],[f55])).
% 0.65/0.43 cnf(s3, plain, spl6_4 | spl6_5, inference(sat_conversion,[],[f63])).
% 0.65/0.43 cnf(s17, plain, ~spl6_10 | spl6_13, inference(sat_conversion,[],[f198])).
% 0.65/0.43 cnf(s23, plain, ~spl6_2 | ~spl6_5, inference(sat_conversion,[],[f211])).
% 0.65/0.43 cnf(s24, plain, spl6_12 | ~spl6_13, inference(sat_conversion,[],[f227])).
% 0.65/0.43 cnf(s33, plain, ~spl6_3 | ~spl6_5 | ~spl6_17, inference(sat_conversion,[],[f481])).
% 0.65/0.43 cnf(s60, plain, spl6_4 | ~spl6_5 | spl6_10, inference(sat_conversion,[],[f585])).
% 0.65/0.43 cnf(s70, plain, ~spl6_4 | ~spl6_12 | spl6_14, inference(sat_conversion,[],[f652])).
% 0.65/0.43 cnf(s71, plain, ~spl6_1 | ~spl6_3 | ~spl6_4, inference(sat_conversion,[],[f661])).
% 0.65/0.43 cnf(s79, plain, ~spl6_4 | spl6_10 | spl6_14, inference(sat_conversion,[],[f674])).
% 0.65/0.43 cnf(s85, plain, spl6_5 | spl6_10 | ~spl6_14, inference(sat_conversion,[],[f700])).
% 0.65/0.43 cnf(s103, plain, ~spl6_1 | ~spl6_13 | spl6_17, inference(sat_conversion,[],[f746])).
% 0.65/0.43 cnf(s126, plain, spl6_5 | ~spl6_13 | ~spl6_14, inference(sat_conversion,[],[f938])).
% 0.65/0.43 cnf(s128, plain, spl6_10 | spl6_5, inference(rat,[],[s79,s85,s3])).
% 0.65/0.43 cnf(s129, plain, spl6_5, inference(rat,[],[s70,s24,s126,s17,s128,s3])).
% 0.65/0.43 cnf(s130, plain, ~spl6_2, inference(rat,[],[s23,s129])).
% 0.65/0.43 cnf(s131, plain, spl6_3, inference(rat,[],[s2,s130])).
% 0.65/0.43 cnf(s132, plain, spl6_1, inference(rat,[],[s1,s130])).
% 0.65/0.43 cnf(s133, plain, ~spl6_4, inference(rat,[],[s71,s132,s131])).
% 0.65/0.43 cnf(s134, plain, ~spl6_17, inference(rat,[],[s33,s129,s131])).
% 0.65/0.43 cnf(s135, plain, spl6_10, inference(rat,[],[s60,s129,s133])).
% 0.65/0.43 cnf(s136, plain, ~spl6_13, inference(rat,[],[s103,s132,s134])).
% 0.65/0.43 cnf(s138, plain, $false, inference(rat,[],[s17,s136,s135])).
% 0.65/0.43 thf(f940,plain,(
% 0.65/0.43 $false),
% 0.65/0.43 inference(avatar_sat_refutation,[],[s138])).
% 0.65/0.43 % SZS output end Proof for theBenchmark
% 0.65/0.43 % (681553)------------------------------
% 0.65/0.43 % (681553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.43 % (681553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.43 % (681553)CaDiCaL version: 2.1.3
% 0.65/0.43 % (681553)Termination reason: Refutation
% 0.65/0.43 % (681553)Time elapsed: 0.081 s
% 0.65/0.43 % (681553)Peak memory usage: 13 MB
% 0.65/0.43 % (681553)Instructions burned: 89 (million)
% 0.65/0.43 % (681547)Success in time 0.12 s
% 0.65/0.43 % Vampire exiting
%------------------------------------------------------------------------------