%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP018_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Tue Sep 29 11:28:23 AM UTC 2026
% Result : Theorem 1.72s 1.72s
% Output : Refutation 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 14 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 7 con; 0-4 aty)
% Number of variables : 16 ( 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Ebinary__ieee_2Efloat: ( $tType * $tType ) > $tType ).
tff(type_def_6,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(type_def_7,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_8,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
tyop_2Erealax_2Ereal: $tType ).
tff(type_def_11,type,
sK0: $tType ).
tff(type_def_12,type,
sK1: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_16,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_17,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_18,type,
c_2Ebinary__ieee_2Efloat__negate_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1)) ).
tff(func_def_19,type,
c_2Ebinary__ieee_2Efloat__negate_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebinary__ieee_2Efloat(X0,X1) > tyop_2Ebinary__ieee_2Efloat(X0,X1) ) ).
tff(func_def_20,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Ebinary__ieee_2Efloat(X0,X1)) ).
tff(func_def_21,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)) > tyop_2Ebinary__ieee_2Efloat(X0,X1) ) ).
tff(func_def_22,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal) ).
tff(func_def_23,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebinary__ieee_2Efloat(X0,X1) > tyop_2Erealax_2Ereal ) ).
tff(func_def_24,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(func_def_25,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(func_def_26,type,
c_2Ebool_2Ethe__value_2E0:
!>[X0: $tType] : tyop_2Ebool_2Eitself(X0) ).
tff(func_def_27,type,
c_2Ebinary__ieee_2Eulp_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Erealax_2Ereal) ).
tff(func_def_28,type,
c_2Ebinary__ieee_2Eulp_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)) > tyop_2Erealax_2Ereal ) ).
tff(func_def_29,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_30,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP2: tyop_2Erealax_2Ereal > $o ).
tff(f30,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2)) = c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
tff(f31,axiom,
! [X0: $tType,X1: $tType] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
tff(f34,conjecture,
! [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
tff(f35,negated_conjecture,
~ ! [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
tff(f36,plain,
? [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) ),
inference(ennf_transformation,[],[f35]) ).
tff(f37,plain,
c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f36]) ).
tff(f38,plain,
c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
inference(cnf_transformation,[],[f37]) ).
tff(f39,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2)) = c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f40,plain,
! [X1: $tType,X0: $tType] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) ),
inference(cnf_transformation,[],[f31]) ).
tff(f41,definition,
~ sP2(c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
tff(f42,plain,
sP2(c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))))),
inference(inequality_splitting,[],[f38,f41]) ).
tff(f43,plain,
~ sP2(c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))))),
inference(forward_demodulation,[],[f41,f40]) ).
tff(f44,plain,
~ sP2(c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))))),
inference(forward_demodulation,[],[f43,f39]) ).
tff(f45,plain,
$false,
inference(forward_subsumption_resolution,[],[f44,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n003.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 27 12:06:40 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.72/1.72 % (411609)Detected formulas, will run a generic FOF schedule.
% 1.72/1.72 % (411616)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=810497290:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.72/1.72 % (411616)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.72/1.72 % (411614)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3693904055:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.72/1.72 % (411615)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1566343629:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.72/1.72 % (411620)dis-21_1_sil=8000:lcm=predicate:random_seed=676346316:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.72/1.72 % (411619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3863442559:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.72/1.72 % (411617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1155252155:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.72/1.72 % (411618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4289898153:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.72/1.72 % (411617)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.72/1.72 % (411617)First to succeed.
% 1.72/1.72 % (411618)Also succeeded, but the first one will report.
% 1.72/1.72 % (411617)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-411609"
% 1.72/1.72 % (411619)Also succeeded, but the first one will report.
% 1.72/1.72 % (411620)Instruction limit reached!
% 1.72/1.72 % (411620)------------------------------
% 1.72/1.72 % (411620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/1.72 % (411620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/1.72 % (411620)CaDiCaL version: 2.1.3
% 1.72/1.72 % (411620)Termination reason: Instruction limit
% 1.72/1.72 % (411620)Termination phase: Saturation
% 1.72/1.72 % (411620)Time elapsed: 0.104 s
% 1.72/1.72 % (411620)Peak memory usage: 89 MB
% 1.72/1.72 % (411620)Instructions burned: 130 (million)
% 1.72/1.72 % Exception at run slice level
% 1.72/1.72 User error: GNN currently only supports monomorphic FOL.
% 1.72/1.72 % (411628)lrs+10_1_sil=8000:sp=occurrence:random_seed=679988997:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 1.72/1.72 % (411628)Also succeeded, but the first one will report.
% 1.72/1.72 % (411617)Refutation found. Thanks to Tanya!
% 1.72/1.72 % SZS status Theorem for theBenchmark
% 1.72/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 5.76/1.99 % (411617)------------------------------
% 5.76/1.99 % (411617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.99 % (411617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.99 % (411617)CaDiCaL version: 2.1.3
% 5.76/1.99 % (411617)Termination reason: Refutation
% 5.76/1.99 % (411617)Time elapsed: 0.003 s
% 5.76/1.99 % (411617)Peak memory usage: 88 MB
% 5.76/1.99 % (411617)Instructions burned: 1 (million)
% 5.76/1.99 % (411617)------------------------------
% 5.76/1.99 % (411617)------------------------------
% 5.76/1.99 % (411609)Success in time 0.695 s
% 5.76/1.99 % Vampire exiting
%------------------------------------------------------------------------------