%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA089^1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:02 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA089^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:36:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (656316)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (656337)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2130614717:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.26 % (656337)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (656334)% WARNING: option uhcvi not known.
% 0.18/0.26 % (656333)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3111874028_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.26 % (656335)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=545426339:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.26 % (656336)dis+10_1_sil=32000:sp=arity:random_seed=91060859:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.26 % (656334)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3359908234:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.26 % (656334)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (656338)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1335469030:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.26 % Exception at run slice level% (656339)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3572815449:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.26
% 0.18/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.26 % (656334)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.26 % (656337) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-656316-656337"...
% 0.18/0.26 % (656337)...printing done.
% 0.18/0.26 % (656337)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% 0.18/0.26 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.18/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.26 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.26 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.18/0.26 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.18/0.26 thf(func_def_3, type, 'const/realax/real_neg': ('type/realax/real' > 'type/realax/real')).
% 0.18/0.26 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.18/0.26 thf(func_def_5, type, 'const/realax/real_abs': ('type/realax/real' > 'type/realax/real')).
% 0.18/0.26 thf(func_def_9, type, vAND: ($o > $o > $o)).
% 0.18/0.26 thf(func_def_10, type, sK0: ('type/realax/real' > 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.18/0.26 thf(func_def_11, type, sK1: ('type/realax/real' > $o)).
% 0.18/0.26 thf(func_def_12, type, sK2: 'type/realax/real').
% 0.18/0.26 thf(func_def_13, type, sK3: 'type/realax/real').
% 0.18/0.26 thf(f1,axiom,(
% 0.18/0.26 ! [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/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_BOUNDS_')).
% 0.18/0.26 thf(f2,axiom,(
% 0.18/0.26 ! [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))),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_')).
% 0.18/0.26 thf(f3,conjecture,(
% 0.18/0.26 ! [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/inf' @ X0)) @ X1))),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_ABS_INF_LE_')).
% 0.18/0.26 thf(f4,negated_conjecture,(
% 0.18/0.26 ~ ! [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/inf' @ X0)) @ X1))),
% 0.18/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.18/0.26 thf(f5,plain,(
% 0.18/0.26 ! [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/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.18/0.26 inference(rectify,[],[f1])).
% 0.18/0.26 thf(f6,plain,(
% 0.18/0.26 ! [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/inf' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true)))),
% 0.18/0.26 inference(fool_elimination,[],[f5])).
% 0.18/0.26 thf(f7,plain,(
% 0.18/0.26 ! [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))),
% 0.18/0.26 inference(rectify,[],[f2])).
% 0.18/0.26 thf(f8,plain,(
% 0.18/0.26 ! [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))))),
% 0.18/0.26 inference(fool_elimination,[],[f7])).
% 0.18/0.26 thf(f9,plain,(
% 0.18/0.26 ~ ! [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/inf' @ X0)) @ X1))),
% 0.18/0.26 inference(rectify,[],[f4])).
% 0.18/0.26 thf(f10,plain,(
% 0.18/0.26 ~ ! [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/inf' @ X0)) @ X1)) = $true))),
% 0.18/0.26 inference(fool_elimination,[],[f9])).
% 0.18/0.26 thf(f11,plain,(
% 0.18/0.26 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ 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)))),
% 0.18/0.26 inference(ennf_transformation,[],[f6])).
% 0.18/0.26 thf(f12,plain,(
% 0.18/0.26 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ 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))),
% 0.18/0.26 inference(flattening,[],[f11])).
% 0.18/0.26 thf(f13,plain,(
% 0.18/0.26 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ 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)))),
% 0.18/0.26 inference(ennf_transformation,[],[f10])).
% 0.18/0.26 thf(f14,plain,(
% 0.18/0.26 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ 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))),
% 0.18/0.26 inference(flattening,[],[f13])).
% 0.18/0.26 thf(f15,plain,(
% 0.18/0.26 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ 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))),
% 0.18/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f12])).
% 0.18/0.26 thf(f16,plain,(
% 0.18/0.26 ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2))) & ! [X2 : 'type/realax/real'] : (($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)),
% 0.18/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f14])).
% 0.18/0.26 thf(f17,plain,(
% 0.18/0.26 ( ! [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/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f15])).
% 0.18/0.26 thf(f18,plain,(
% 0.18/0.26 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f15])).
% 0.18/0.26 thf(f19,plain,(
% 0.18/0.26 ( ! [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/inf' @ X0) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f15])).
% 0.18/0.26 thf(f20,plain,(
% 0.18/0.26 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f15])).
% 0.18/0.26 thf(f21,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f8])).
% 0.18/0.26 thf(f22,plain,(
% 0.18/0.26 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.18/0.26 inference(cnf_transformation,[],[f16])).
% 0.18/0.26 thf(f23,plain,(
% 0.18/0.26 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2)))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f16])).
% 0.18/0.26 thf(f24,plain,(
% 0.18/0.26 ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2)))),
% 0.18/0.26 inference(cnf_transformation,[],[f16])).
% 0.18/0.26 thf(f26,definition,(
% 0.18/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.26 thf(f27,plain,(
% 0.18/0.26 ( ! [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)) )),
% 0.18/0.26 inference(iff_proxy_clausification,[],[f21])).
% 0.18/0.26 thf(f28,plain,(
% 0.18/0.26 ( ! [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))))) )),
% 0.18/0.26 inference(iff_proxy_clausification,[],[f21])).
% 0.18/0.26 thf(f29,plain,(
% 0.18/0.26 ( ! [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)) )),
% 0.18/0.26 inference(and_proxy_clausification,[],[f28])).
% 0.18/0.26 thf(f30,plain,(
% 0.18/0.26 ( ! [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)) )),
% 0.18/0.26 inference(and_proxy_clausification,[],[f28])).
% 0.18/0.26 thf(f31,plain,(
% 0.18/0.26 ( ! [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)) = $false)) )),
% 0.18/0.26 inference(and_proxy_clausification,[],[f27])).
% 0.18/0.26 thf(f55,plain,(
% 0.18/0.26 ($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2)) = $false)),
% 0.18/0.26 inference(constrained_superposition,[],[f24,f26])).
% 0.18/0.26 thf(f61,plain,(
% 0.18/0.26 ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2)) = $false)),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f55])).
% 0.18/0.26 thf(f66,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f23,f17])).
% 0.18/0.26 thf(f67,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f66])).
% 0.18/0.26 thf(f68,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f67,f22])).
% 0.18/0.26 thf(f72,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f23,f19])).
% 0.18/0.26 thf(f73,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f72])).
% 0.18/0.26 thf(f74,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)))) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f73,f22])).
% 0.18/0.26 thf(f88,plain,(
% 0.18/0.26 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0 @ X2) @ X1))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X1 @ X0 @ X2))))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f18,f26])).
% 0.18/0.26 thf(f89,plain,(
% 0.18/0.26 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0 @ X2) @ X1))) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X1 @ X0 @ X2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X2))))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f88])).
% 0.18/0.26 thf(f92,plain,(
% 0.18/0.26 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0 @ X2) @ X1))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X1 @ X0 @ X2))))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f20,f26])).
% 0.18/0.26 thf(f93,plain,(
% 0.18/0.26 ( ! [X2 : ('type/realax/real' > $o),X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0 @ X2) @ X1))) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ X1 @ X0 @ X2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X2) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X2) @ X1)))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f92])).
% 0.18/0.26 thf(f95,plain,(
% 0.18/0.26 ($true = $false) | ($false = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)))) | ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))),
% 0.18/0.26 inference(constrained_superposition,[],[f31,f61])).
% 0.18/0.26 thf(f102,plain,(
% 0.18/0.26 ($false = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)))) | ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f95])).
% 0.18/0.26 thf(f104,definition,(
% 0.18/0.26 spl4_5 <=> ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))),
% 0.18/0.26 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.18/0.26 thf(f106,plain,(
% 0.18/0.26 ($false = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | ~spl4_5),
% 0.18/0.26 inference(avatar_component_clause,[],[f104])).
% 0.18/0.26 thf(f108,definition,(
% 0.18/0.26 spl4_6 <=> ($false = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1))))),
% 0.18/0.26 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.18/0.26 thf(f110,plain,(
% 0.18/0.26 ($false = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)))) | ~spl4_6),
% 0.18/0.26 inference(avatar_component_clause,[],[f108])).
% 0.18/0.26 thf(f113,plain,(
% 0.18/0.26 spl4_5 | spl4_6),
% 0.18/0.26 inference(avatar_split_clause,[],[f102,f108,f104])).
% 0.18/0.26 thf(f129,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f74,f29])).
% 0.18/0.26 thf(f130,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f68,f29])).
% 0.18/0.26 thf(f135,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f130])).
% 0.18/0.26 thf(f136,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f129])).
% 0.18/0.26 thf(f156,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f89,f135])).
% 0.18/0.26 thf(f162,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(duplicate_literal_removal,[],[f156])).
% 0.18/0.26 thf(f163,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f162])).
% 0.18/0.26 thf(f170,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f163,f22])).
% 0.18/0.26 thf(f188,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f93,f136])).
% 0.18/0.26 thf(f198,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(duplicate_literal_removal,[],[f188])).
% 0.18/0.26 thf(f199,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f198])).
% 0.18/0.26 thf(f202,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2)))) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f199,f22])).
% 0.18/0.26 thf(f205,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) ) | ~spl4_5),
% 0.18/0.26 inference(forward_demodulation,[],[f202,f106])).
% 0.18/0.26 thf(f206,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))) ) | ~spl4_5),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f205])).
% 0.18/0.26 thf(f245,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1))))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f74,f30])).
% 0.18/0.26 thf(f246,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = $false) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1))))) )),
% 0.18/0.26 inference(constrained_superposition,[],[f68,f30])).
% 0.18/0.26 thf(f251,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f246])).
% 0.18/0.26 thf(f252,plain,(
% 0.18/0.26 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)))) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f245])).
% 0.18/0.26 thf(f352,plain,(
% 0.18/0.26 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1))))),
% 0.18/0.26 inference(constrained_superposition,[],[f251,f170])).
% 0.18/0.26 thf(f385,plain,(
% 0.18/0.26 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1))))),
% 0.18/0.26 inference(duplicate_literal_removal,[],[f352])).
% 0.18/0.26 thf(f386,plain,(
% 0.18/0.26 ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1))))),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f385])).
% 0.18/0.26 thf(f398,plain,(
% 0.18/0.26 ($true = $false) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | ~spl4_5),
% 0.18/0.26 inference(constrained_superposition,[],[f252,f206])).
% 0.18/0.26 thf(f427,plain,(
% 0.18/0.26 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2))) | ~spl4_5),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f398])).
% 0.18/0.26 thf(f445,plain,(
% 0.18/0.26 ($true = $false) | ~spl4_5),
% 0.18/0.26 inference(forward_demodulation,[],[f427,f106])).
% 0.18/0.26 thf(f446,plain,(
% 0.18/0.26 $false | ~spl4_5),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f445])).
% 0.18/0.26 thf(f447,plain,(
% 0.18/0.26 ~spl4_5),
% 0.18/0.26 inference(avatar_contradiction_clause,[],[f446])).
% 0.18/0.26 thf(f476,plain,(
% 0.18/0.26 ($true = $false) | ~spl4_6),
% 0.18/0.26 inference(forward_demodulation,[],[f386,f110])).
% 0.18/0.26 thf(f477,plain,(
% 0.18/0.26 $false | ~spl4_6),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f476])).
% 0.18/0.26 thf(f478,plain,(
% 0.18/0.26 ~spl4_6),
% 0.18/0.26 inference(avatar_contradiction_clause,[],[f477])).
% 0.18/0.26 cnf(s5, plain, spl4_5 | spl4_6, inference(sat_conversion,[],[f113])).
% 0.18/0.26 cnf(s8, plain, ~spl4_5, inference(sat_conversion,[],[f447])).
% 0.18/0.26 cnf(s13, plain, ~spl4_6, inference(sat_conversion,[],[f478])).
% 0.18/0.26 cnf(s21, plain, $false, inference(rat,[],[s5,s13,s8])).
% 0.18/0.26 thf(f507,plain,(
% 0.18/0.26 $false),
% 0.18/0.26 inference(avatar_sat_refutation,[],[s21])).
% 0.18/0.26 % SZS output end Proof for theBenchmark
% 0.18/0.26 % (656337)------------------------------
% 0.18/0.26 % (656337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (656337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (656337)CaDiCaL version: 2.1.3
% 0.18/0.26 % (656337)Termination reason: Refutation
% 0.18/0.26 % (656337)Time elapsed: 0.013 s
% 0.18/0.26 % (656337)Peak memory usage: 12 MB
% 0.18/0.26 % (656337)Instructions burned: 44 (million)
% 0.18/0.26 % (656316)Success in time 0.05 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------