%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA077^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:01 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA077^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:42:53 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (403156)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (403166)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3650629080:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (403162)% WARNING: option uhcvi not known.
% 0.21/0.28 % (403162)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=822187270:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (403161)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2784858544_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (403165)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1331972741:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (403163)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1501780978:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (403162)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (403164)dis+10_1_sil=32000:sp=arity:random_seed=4093425868:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (403165)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (403162)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28 % (403167)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3969726085:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % Exception at run slice level
% 0.21/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.28 % (403166) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-403156-403166"...
% 0.21/0.28 % (403166)...printing done.
% 0.21/0.28 % (403166)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.28 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.28 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.28 thf(func_def_3, type, 'const/realax/real_neg': ('type/realax/real' > 'type/realax/real')).
% 0.21/0.28 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.28 thf(func_def_5, type, 'const/realax/real_abs': ('type/realax/real' > 'type/realax/real')).
% 0.21/0.28 thf(func_def_9, type, vAND: ($o > $o > $o)).
% 0.21/0.28 thf(func_def_10, type, sK0: ('type/realax/real' > 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.28 thf(func_def_11, type, sK1: ('type/realax/real' > $o)).
% 0.21/0.28 thf(func_def_12, type, sK2: 'type/realax/real').
% 0.21/0.28 thf(func_def_13, type, sK3: 'type/realax/real').
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_')).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = ('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_')).
% 0.21/0.28 thf(f3,conjecture,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_ABS_SUP_LE_')).
% 0.21/0.28 thf(f4,negated_conjecture,(
% 0.21/0.28 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => (((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = ('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))))),
% 0.21/0.28 inference(fool_elimination,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ~ ! [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' @ ('const/realax/real_abs' @ X2) @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) | (? [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.21/0.28 inference(ennf_transformation,[],[f6])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) | ? [X3 : 'type/realax/real'] : ((((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.28 inference(flattening,[],[f11])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) != $true) & (! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.21/0.28 inference(ennf_transformation,[],[f10])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1)) != $true) & ! [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.21/0.28 inference(flattening,[],[f13])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) | ((($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0))))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f12])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2))) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f14])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f15])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f15])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f15])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) = $true) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f15])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.21/0.28 inference(cnf_transformation,[],[f16])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f16])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2)))),
% 0.21/0.28 inference(cnf_transformation,[],[f16])).
% 0.21/0.28 thf(f26,definition,(
% 0.21/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | (((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))) = $false)) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f21])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $false) | ($true = ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))))) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f21])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $true)) )),
% 0.21/0.28 inference(and_proxy_clausification,[],[f28])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $false) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true)) )),
% 0.21/0.28 inference(and_proxy_clausification,[],[f28])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $false) | ((('const/realax/real_le' @ X0 @ X1)) = $false)) )),
% 0.21/0.28 inference(and_proxy_clausification,[],[f27])).
% 0.21/0.28 thf(f66,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f23,f17])).
% 0.21/0.28 thf(f67,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.28 thf(f68,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) )),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f67,f22])).
% 0.21/0.28 thf(f72,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(constrained_superposition,[],[f23,f19])).
% 0.21/0.28 thf(f73,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f72])).
% 0.21/0.28 thf(f74,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f73,f22])).
% 0.21/0.28 thf(f93,plain,(
% 0.21/0.28 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X0 @ X1 @ X2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ X2) @ X0)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f18,f26])).
% 0.21/0.28 thf(f94,plain,(
% 0.21/0.28 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X0 @ X1 @ X2)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ X2) @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f93])).
% 0.21/0.28 thf(f105,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f74,f29])).
% 0.21/0.28 thf(f106,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f68,f29])).
% 0.21/0.28 thf(f109,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f106])).
% 0.21/0.28 thf(f110,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f105])).
% 0.21/0.28 thf(f180,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f74,f30])).
% 0.21/0.28 thf(f181,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f68,f30])).
% 0.21/0.28 thf(f192,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f181])).
% 0.21/0.28 thf(f193,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f180])).
% 0.21/0.28 thf(f285,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f20,f110])).
% 0.21/0.28 thf(f288,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f285])).
% 0.21/0.28 thf(f289,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f288])).
% 0.21/0.28 thf(f296,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) )),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f289,f22])).
% 0.21/0.28 thf(f300,definition,(
% 0.21/0.28 spl4_5 <=> ! [X0 : 'type/realax/real'] : ($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.21/0.28 thf(f301,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) ) | ~spl4_5),
% 0.21/0.28 inference(avatar_component_clause,[],[f300])).
% 0.21/0.28 thf(f303,definition,(
% 0.21/0.28 spl4_6 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.21/0.28 thf(f305,plain,(
% 0.21/0.28 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_6),
% 0.21/0.28 inference(avatar_component_clause,[],[f303])).
% 0.21/0.28 thf(f306,plain,(
% 0.21/0.28 spl4_5 | spl4_6),
% 0.21/0.28 inference(avatar_split_clause,[],[f296,f303,f300])).
% 0.21/0.28 thf(f315,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f94,f192])).
% 0.21/0.28 thf(f316,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0)))) )),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f315])).
% 0.21/0.28 thf(f317,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f316])).
% 0.21/0.28 thf(f321,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0)))) )),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f317,f22])).
% 0.21/0.28 thf(f324,definition,(
% 0.21/0.28 spl4_8 <=> ! [X0 : 'type/realax/real'] : ($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition])).
% 0.21/0.28 thf(f325,plain,(
% 0.21/0.28 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ (sK0 @ X0 @ ('const/realax/real_neg' @ sK2) @ sK1) @ X0)))) ) | ~spl4_8),
% 0.21/0.28 inference(avatar_component_clause,[],[f324])).
% 0.21/0.28 thf(f327,definition,(
% 0.21/0.28 spl4_9 <=> ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition])).
% 0.21/0.28 thf(f328,plain,(
% 0.21/0.28 ($true != (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | spl4_9),
% 0.21/0.28 inference(avatar_component_clause,[],[f327])).
% 0.21/0.28 thf(f329,plain,(
% 0.21/0.28 ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ~spl4_9),
% 0.21/0.28 inference(avatar_component_clause,[],[f327])).
% 0.21/0.28 thf(f330,plain,(
% 0.21/0.28 spl4_8 | spl4_9),
% 0.21/0.28 inference(avatar_split_clause,[],[f321,f327,f324])).
% 0.21/0.28 thf(f336,plain,(
% 0.21/0.28 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2))) | ($false = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_9),
% 0.21/0.28 inference(constrained_superposition,[],[f31,f329])).
% 0.21/0.28 thf(f337,plain,(
% 0.21/0.28 ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK1)) @ sK2))) | ($false = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_9),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f336])).
% 0.21/0.28 thf(f339,plain,(
% 0.21/0.28 ($false = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_9),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f337,f24])).
% 0.21/0.28 thf(f352,plain,(
% 0.21/0.28 ($true = $false) | (~spl4_6 | ~spl4_9)),
% 0.21/0.28 inference(constrained_superposition,[],[f339,f305])).
% 0.21/0.28 thf(f370,plain,(
% 0.21/0.28 $false | (~spl4_6 | ~spl4_9)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f352])).
% 0.21/0.28 thf(f371,plain,(
% 0.21/0.28 ~spl4_6 | ~spl4_9),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f370])).
% 0.21/0.28 thf(f374,plain,(
% 0.21/0.28 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_5),
% 0.21/0.28 inference(constrained_superposition,[],[f301,f193])).
% 0.21/0.28 thf(f379,plain,(
% 0.21/0.28 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK2))) | ~spl4_5),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f374])).
% 0.21/0.28 thf(f380,plain,(
% 0.21/0.28 ($true = $false) | (~spl4_5 | ~spl4_9)),
% 0.21/0.28 inference(forward_demodulation,[],[f379,f339])).
% 0.21/0.28 thf(f381,plain,(
% 0.21/0.28 $false | (~spl4_5 | ~spl4_9)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f380])).
% 0.21/0.28 thf(f382,plain,(
% 0.21/0.28 ~spl4_5 | ~spl4_9),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f381])).
% 0.21/0.28 thf(f427,plain,(
% 0.21/0.28 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ~spl4_8),
% 0.21/0.28 inference(constrained_superposition,[],[f325,f109])).
% 0.21/0.28 thf(f436,plain,(
% 0.21/0.28 ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/sup' @ sK1)))) | ~spl4_8),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f427])).
% 0.21/0.28 thf(f440,plain,(
% 0.21/0.28 $false | (~spl4_8 | spl4_9)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f436,f328])).
% 0.21/0.28 thf(f441,plain,(
% 0.21/0.28 ~spl4_8 | spl4_9),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f440])).
% 0.21/0.28 cnf(s3, plain, spl4_5 | spl4_6, inference(sat_conversion,[],[f306])).
% 0.21/0.28 cnf(s6, plain, spl4_8 | spl4_9, inference(sat_conversion,[],[f330])).
% 0.21/0.28 cnf(s10, plain, ~spl4_6 | ~spl4_9, inference(sat_conversion,[],[f371])).
% 0.21/0.28 cnf(s11, plain, ~spl4_5 | ~spl4_9, inference(sat_conversion,[],[f382])).
% 0.21/0.28 cnf(s15, plain, ~spl4_8 | spl4_9, inference(sat_conversion,[],[f441])).
% 0.21/0.28 cnf(s16, plain, spl4_9, inference(rat,[],[s6,s15])).
% 0.21/0.28 cnf(s17, plain, ~spl4_5, inference(rat,[],[s11,s16])).
% 0.21/0.28 cnf(s18, plain, ~spl4_6, inference(rat,[],[s10,s16])).
% 0.21/0.28 cnf(s19, plain, $false, inference(rat,[],[s3,s18,s17])).
% 0.21/0.28 thf(f442,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s19])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (403166)------------------------------
% 0.21/0.28 % (403166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (403166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (403166)CaDiCaL version: 2.1.3
% 0.21/0.28 % (403166)Termination reason: Refutation
% 0.21/0.28 % (403166)Time elapsed: 0.013 s
% 0.21/0.28 % (403166)Peak memory usage: 12 MB
% 0.21/0.28 % (403166)Instructions burned: 42 (million)
% 0.21/0.28 % (403156)Success in time 0.029 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------