%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n004.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 07:45:53 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA089^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:40:52 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (1619208)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1619228)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3233673743:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (1619228) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1619208-1619228"...
% 0.22/0.28 % (1619230)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1619230)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (1619228)...printing done.
% 0.22/0.28 % (1619228)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.28 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.28 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.22/0.28 thf(func_def_3, type, 'const/realax/real_neg': ('type/realax/real' > 'type/realax/real')).
% 0.22/0.28 thf(func_def_4, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.22/0.28 thf(func_def_5, type, 'const/realax/real_abs': ('type/realax/real' > 'type/realax/real')).
% 0.22/0.28 thf(func_def_9, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real' > 'type/realax/real')).
% 0.22/0.28 thf(func_def_10, type, sK1: 'type/realax/real').
% 0.22/0.28 thf(func_def_11, type, sK2: ('type/realax/real' > $o)).
% 0.22/0.28 thf(func_def_12, type, sK3: 'type/realax/real').
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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)))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) & ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_BOUNDS_')).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 ! [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))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_')).
% 0.22/0.28 thf(f3,conjecture,(
% 0.22/0.28 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_ABS_INF_LE_')).
% 0.22/0.28 thf(f4,negated_conjecture,(
% 0.22/0.28 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X0 @ X3)))) => (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) & ('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)))),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) = $true) => (((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X0 @ X3)) = $true)))) => (((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true) & ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))))),
% 0.22/0.28 inference(fool_elimination,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.22/0.28 inference(rectify,[],[f4])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ~ ! [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/inf' @ X0)) @ X1)) = $true))),
% 0.22/0.28 inference(fool_elimination,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ! [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))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) <=> ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true))),
% 0.22/0.28 inference(fool_elimination,[],[f9])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true) & ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) | (('const/sets/EMPTY' @ 'type/realax/real' = X1) | ? [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) = $true) & (((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X3)) != $true)))))),
% 0.22/0.28 inference(ennf_transformation,[],[f6])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true) & ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ? [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) = $true) & (((('const/realax/real_le' @ X3 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X3)) != $true))))),
% 0.22/0.28 inference(flattening,[],[f11])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ? [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/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)))),
% 0.22/0.28 inference(ennf_transformation,[],[f8])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1)) != $true) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1)) = $true)))),
% 0.22/0.28 inference(flattening,[],[f13])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true) & ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X1))) & (((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ (sK0 @ X2 @ X1 @ X0))) != $true))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f12])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X1)) @ X0)) != $true) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) != $true) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X0)) = $true)))),
% 0.22/0.28 inference(rectify,[],[f14])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) & ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK2)) @ sK1))) & ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK1)) = $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f16])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) != $true)) & (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | (((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true))))),
% 0.22/0.28 inference(nnf_transformation,[],[f10])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true) & ((('const/realax/real_le' @ X0 @ X1)) = $true)) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) != $true)) & (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true)))),
% 0.22/0.28 inference(flattening,[],[f18])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2)) != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ((('const/realax/real_le' @ X0 @ (sK0 @ X2 @ X1 @ X0))) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f15])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f15])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ X0 @ (sK0 @ X2 @ X1 @ X0))) != $true) | ((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f15])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X1)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f15])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 ( ! [X2 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK1)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f17])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 ($true != (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK2)) @ sK1)))),
% 0.22/0.28 inference(cnf_transformation,[],[f17])).
% 0.22/0.28 thf(f26,plain,(
% 0.22/0.28 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.22/0.28 inference(cnf_transformation,[],[f17])).
% 0.22/0.28 thf(f27,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f19])).
% 0.22/0.28 thf(f28,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f19])).
% 0.22/0.28 thf(f29,plain,(
% 0.22/0.28 ( ! [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)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f19])).
% 0.22/0.28 thf(f40,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true != $true)) )),
% 0.22/0.28 inference(superposition,[],[f24,f21])).
% 0.22/0.28 thf(f41,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f40])).
% 0.22/0.28 thf(f42,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true)) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f41,f26])).
% 0.22/0.28 thf(f43,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK0 @ X0 @ sK2 @ X1))))) )),
% 0.22/0.28 inference(superposition,[],[f29,f42])).
% 0.22/0.28 thf(f44,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true) | ($true != $true) | ((('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ X1) @ sK1)) = $true)) )),
% 0.22/0.28 inference(superposition,[],[f28,f42])).
% 0.22/0.28 thf(f45,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK0 @ X0 @ sK2 @ X1)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f43])).
% 0.22/0.28 thf(f46,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ X1) @ sK1)) = $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))) = $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f44])).
% 0.22/0.28 thf(f49,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(superposition,[],[f24,f23])).
% 0.22/0.28 thf(f50,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f49])).
% 0.22/0.28 thf(f51,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ sK2 @ X1)) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f50,f26])).
% 0.22/0.28 thf(f52,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK0 @ X0 @ sK2 @ X1)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(superposition,[],[f29,f51])).
% 0.22/0.28 thf(f53,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ X1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != $true)) )),
% 0.22/0.28 inference(superposition,[],[f28,f51])).
% 0.22/0.28 thf(f54,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK0 @ X0 @ sK2 @ X1)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f52])).
% 0.22/0.28 thf(f55,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ X1) @ sK1)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f53])).
% 0.22/0.28 thf(f59,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ X0 @ (sK0 @ sK1 @ sK2 @ X0))) != $true) | ($true != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) )),
% 0.22/0.28 inference(superposition,[],[f20,f46])).
% 0.22/0.28 thf(f60,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ (sK0 @ sK1 @ sK2 @ X0))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) )),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f59])).
% 0.22/0.28 thf(f61,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ X0 @ (sK0 @ sK1 @ sK2 @ X0))) != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f60])).
% 0.22/0.28 thf(f63,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ (sK0 @ sK1 @ sK2 @ X0))) != $true) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f61,f26])).
% 0.22/0.28 thf(f65,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ ('const/realax/real_neg' @ sK1)) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != $true)) )),
% 0.22/0.28 inference(superposition,[],[f22,f54])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ ('const/realax/real_neg' @ sK1)) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f65])).
% 0.22/0.28 thf(f69,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ ('const/realax/real_neg' @ sK1)) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f68])).
% 0.22/0.28 thf(f71,plain,(
% 0.22/0.28 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2 @ ('const/realax/real_neg' @ sK1)) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0)))) )),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f69,f26])).
% 0.22/0.28 thf(f73,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ($true != $true)),
% 0.22/0.28 inference(superposition,[],[f63,f45])).
% 0.22/0.28 thf(f75,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ($true != $true)),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f73])).
% 0.22/0.28 thf(f76,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/inf' @ sK2))) = $true)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f75])).
% 0.22/0.28 thf(f77,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) != $true) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK2)) @ sK1)))),
% 0.22/0.28 inference(superposition,[],[f27,f76])).
% 0.22/0.28 thf(f78,plain,(
% 0.22/0.28 ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK2)) @ sK1))) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) != $true)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.28 thf(f79,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) != $true)),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f78,f25])).
% 0.22/0.28 thf(f80,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) = $true) | ($true != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) = $true)),
% 0.22/0.28 inference(superposition,[],[f71,f55])).
% 0.22/0.28 thf(f82,plain,(
% 0.22/0.28 ($true != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) = $true)),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f80])).
% 0.22/0.28 thf(f83,plain,(
% 0.22/0.28 ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK1)) = $true)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f82])).
% 0.22/0.28 thf(f85,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f83,f79])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (1619228)------------------------------
% 0.22/0.28 % (1619228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1619228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1619228)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1619228)Termination reason: Refutation
% 0.22/0.28 % (1619228)Time elapsed: 0.004 s
% 0.22/0.28 % (1619228)Peak memory usage: 12 MB
% 0.22/0.28 % (1619228)Instructions burned: 12 (million)
% 0.22/0.28 % (1619208)Success in time 0.034 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------