%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP018_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 01:47:51 PM UTC 2026
% Result : Theorem 2.18s 1.35s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 63 unt; 0 typ; 13 def)
% Number of atoms : 285 ( 45 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 48 ( 25 ~; 19 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 180 ( 180 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 70 !; 2 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bool: del ).
tff(pred_def_1,type,
mem: ( del * $i ) > $o ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( $i * del ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
ty_2Erealax_2Ereal: del ).
tff(func_def_7,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
tff(func_def_8,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
tff(func_def_10,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
tff(func_def_11,type,
ty_2Ebinary__ieee_2Efloat: ( del * del ) > del ).
tff(func_def_12,type,
c_2Ebinary__ieee_2Efloat__negate: ( del * del ) > $i ).
tff(func_def_13,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(func_def_14,type,
ty_2Ebool_2Eitself: del > del ).
tff(func_def_15,type,
c_2Ebinary__ieee_2Efloat__plus__min: ( del * del ) > $i ).
tff(func_def_16,type,
c_2Ebinary__ieee_2Efloat__to__real: ( del * del ) > $i ).
tff(func_def_17,type,
c_2Ebool_2Ethe__value: del > $i ).
tff(func_def_18,type,
c_2Ebinary__ieee_2Eulp: ( del * del ) > $i ).
tff(func_def_19,type,
inj__o: tp__o > $i ).
tff(func_def_20,type,
surj__o: $i > tp__o ).
tff(func_def_22,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_23,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_24,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_25,type,
sK0: ( $i * ( $i * del ) ) > $i ).
tff(func_def_26,type,
sK1: ( $i * del ) > $i ).
tff(func_def_27,type,
sK2: del ).
tff(func_def_28,type,
sK3: del ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax',ap_tp) ).
tff(f6,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).
tff(f8,axiom,
! [X0: $i] :
( mem(X0,ty_2Erealax_2Ereal)
=> ( X0 = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).
tff(f9,axiom,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).
tff(f12,axiom,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0,X1)),ty_2Ebinary__ieee_2Efloat(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).
tff(f13,axiom,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),arr(ty_2Ebinary__ieee_2Efloat(X0,X1),ty_2Erealax_2Ereal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).
tff(f14,axiom,
! [X0: del] : mem(c_2Ebool_2Ethe__value(X0),ty_2Ebool_2Eitself(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
tff(f15,axiom,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Eulp(X0,X1),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0,X1)),ty_2Erealax_2Ereal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).
tff(f26,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,ty_2Ebinary__ieee_2Efloat(X0,X1))
=> ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),X2))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
tff(f27,axiom,
! [X0: del,X1: del] : ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).
tff(f30,conjecture,
! [X0: del,X1: del] : ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).
tff(f31,negated_conjecture,
~ ! [X0: del,X1: del] : ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1)))))) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
tff(f33,plain,
! [X0: del,X1: del,X2: $i] :
( ~ mem(X2,arr(X0,X1))
| ! [X3: $i] :
( ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ) ),
inference(ennf_transformation,[],[f1]) ).
tff(f40,plain,
! [X0: $i] :
( ~ mem(X0,ty_2Erealax_2Ereal)
| ( X0 = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f44,plain,
! [X0: del,X1: del,X2: $i] :
( ~ mem(X2,ty_2Ebinary__ieee_2Efloat(X0,X1))
| ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),X2))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),X2))) ) ),
inference(ennf_transformation,[],[f26]) ).
tff(f46,plain,
? [X0: del,X1: del] : ( surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1))))) != surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1)))))) ),
inference(ennf_transformation,[],[f31]) ).
tff(f53,plain,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3))))) != surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__negate(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3)))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f46]) ).
tff(f54,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f61,plain,
! [X0: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0)) = X0 ),
inference(cnf_transformation,[],[f6]) ).
tff(f63,plain,
! [X0: $i] :
( ~ mem(X0,ty_2Erealax_2Ereal)
| ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f64,plain,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f9]) ).
tff(f67,plain,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0,X1)),ty_2Ebinary__ieee_2Efloat(X0,X1))),
inference(cnf_transformation,[],[f12]) ).
tff(f68,plain,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),arr(ty_2Ebinary__ieee_2Efloat(X0,X1),ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f13]) ).
tff(f69,plain,
! [X0: del] : mem(c_2Ebool_2Ethe__value(X0),ty_2Ebool_2Eitself(X0)),
inference(cnf_transformation,[],[f14]) ).
tff(f70,plain,
! [X0: del,X1: del] : mem(c_2Ebinary__ieee_2Eulp(X0,X1),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0,X1)),ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f15]) ).
tff(f84,plain,
! [X2: $i,X0: del,X1: del] :
( ~ mem(X2,ty_2Ebinary__ieee_2Efloat(X0,X1))
| ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__negate(X0,X1),X2))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),X2))) ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f85,plain,
! [X0: del,X1: del] : ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0,X1),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0,X1),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0,X1))))) ),
inference(cnf_transformation,[],[f27]) ).
tff(f87,plain,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3))))) != surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__negate(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3)))))),
inference(cnf_transformation,[],[f53]) ).
tcf(c_49,plain,
! [X0: $i,X0_del: del,X1: $i,X1_del: del] :
( mem(ap(X0,X1),X1_del)
| ~ mem(X1,X0_del)
| ~ mem(X0,arr(X0_del,X1_del)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0_tp__ty_2Erealax_2Ereal)) = X0_tp__ty_2Erealax_2Ereal,
inference(cnf_transformation,[],[f61]) ).
tcf(c_58,plain,
! [X0: $i] :
( ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_59,plain,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_62,plain,
! [X0_del: del,X1_del: del] : mem(c_2Ebinary__ieee_2Efloat__plus__min(X0_del,X1_del),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0_del,X1_del)),ty_2Ebinary__ieee_2Efloat(X0_del,X1_del))),
inference(cnf_transformation,[],[f67]) ).
tcf(c_63,plain,
! [X0_del: del,X1_del: del] : mem(c_2Ebinary__ieee_2Efloat__to__real(X0_del,X1_del),arr(ty_2Ebinary__ieee_2Efloat(X0_del,X1_del),ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f68]) ).
tcf(c_64,plain,
! [X0_del: del] : mem(c_2Ebool_2Ethe__value(X0_del),ty_2Ebool_2Eitself(X0_del)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_65,plain,
! [X0_del: del,X1_del: del] : mem(c_2Ebinary__ieee_2Eulp(X0_del,X1_del),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(X0_del,X1_del)),ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f70]) ).
tcf(c_79,plain,
! [X0: $i,X0_del: del,X1_del: del] :
( ( surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0_del,X1_del),ap(c_2Ebinary__ieee_2Efloat__negate(X0_del,X1_del),X0))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(X0_del,X1_del),X0))) )
| ~ mem(X0,ty_2Ebinary__ieee_2Efloat(X0_del,X1_del)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_80,plain,
! [X0_del: del,X1_del: del] : surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(X0_del,X1_del),ap(c_2Ebinary__ieee_2Efloat__plus__min(X0_del,X1_del),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0_del,X1_del))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(X0_del,X1_del),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(X0_del,X1_del)))),
inference(cnf_transformation,[],[f85]) ).
tcf(c_81,negated_conjecture,
surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__negate(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3)))))) != surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK2,sK3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK2,sK3))))),
inference(cnf_transformation,[],[f87]) ).
tcf(c_332,definition,
iPr_def_10 = c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_333,definition,
iPr_def_11 = c_2Ebinary__ieee_2Efloat__negate(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_334,definition,
iPr_def_12 = c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_335,definition,
iPr_def_13 = ty_2Epair_2Eprod(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_336,definition,
iPr_def_14 = c_2Ebool_2Ethe__value(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_337,definition,
iPr_def_15 = ap(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_338,definition,
iPr_def_16 = ap(iPr_def_11,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_339,definition,
iPr_def_17 = ap(iPr_def_10,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_340,definition,
iPr_def_18 = surj__ty_2Erealax_2Ereal(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_341,definition,
iPr_def_19 = c_2Ebinary__ieee_2Eulp(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_342,definition,
iPr_def_20 = ap(iPr_def_19,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_343,definition,
iPr_def_21 = ap(c_2Erealax_2Ereal__neg,iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_344,definition,
iPr_def_22 = surj__ty_2Erealax_2Ereal(iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_345,negated_conjecture,
iPr_def_18 != iPr_def_22,
inference(demodulation,[status(thm)],[c_81,c_341,c_342,c_343,c_344,c_335,c_336,c_334,c_337,c_333,c_338,c_332,c_339,c_340]) ).
tcf(c_659,plain,
mem(iPr_def_14,ty_2Ebool_2Eitself(iPr_def_13)),
inference(superposition,[status(thm)],[c_336,c_64]) ).
tcf(c_661,plain,
mem(iPr_def_10,arr(ty_2Ebinary__ieee_2Efloat(sK2,sK3),ty_2Erealax_2Ereal)),
inference(superposition,[status(thm)],[c_332,c_63]) ).
tcf(c_667,plain,
mem(c_2Ebinary__ieee_2Eulp(sK2,sK3),arr(ty_2Ebool_2Eitself(iPr_def_13),ty_2Erealax_2Ereal)),
inference(superposition,[status(thm)],[c_335,c_65]) ).
tcf(c_668,plain,
mem(iPr_def_19,arr(ty_2Ebool_2Eitself(iPr_def_13),ty_2Erealax_2Ereal)),
inference(light_normalisation,[status(thm)],[c_667,c_341]) ).
tcf(c_742,plain,
mem(c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),arr(ty_2Ebool_2Eitself(iPr_def_13),ty_2Ebinary__ieee_2Efloat(sK2,sK3))),
inference(superposition,[status(thm)],[c_335,c_62]) ).
tcf(c_745,plain,
mem(iPr_def_12,arr(ty_2Ebool_2Eitself(iPr_def_13),ty_2Ebinary__ieee_2Efloat(sK2,sK3))),
inference(light_normalisation,[status(thm)],[c_742,c_334]) ).
tcf(c_767,plain,
! [X0: $i] :
( mem(ap(c_2Erealax_2Ereal__neg,X0),ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(superposition,[status(thm)],[c_59,c_49]) ).
tcf(c_774,plain,
! [X0: $i] :
( mem(ap(iPr_def_10,X0),ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Ebinary__ieee_2Efloat(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_661,c_49]) ).
tcf(c_775,plain,
! [X0: $i] :
( mem(ap(iPr_def_19,X0),ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Ebool_2Eitself(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_668,c_49]) ).
tcf(c_777,plain,
! [X0: $i] :
( mem(ap(iPr_def_12,X0),ty_2Ebinary__ieee_2Efloat(sK2,sK3))
| ~ mem(X0,ty_2Ebool_2Eitself(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_745,c_49]) ).
tcf(c_865,plain,
( mem(iPr_def_21,ty_2Erealax_2Ereal)
| ~ mem(iPr_def_20,ty_2Erealax_2Ereal) ),
inference(superposition,[status(thm)],[c_343,c_767]) ).
tcf(c_888,plain,
( mem(iPr_def_20,ty_2Erealax_2Ereal)
| ~ mem(iPr_def_14,ty_2Ebool_2Eitself(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_342,c_775]) ).
tcf(c_892,plain,
mem(iPr_def_20,ty_2Erealax_2Ereal),
inference(forward_subsumption_resolution,[status(thm)],[c_888,c_659]) ).
tcf(c_899,plain,
mem(iPr_def_21,ty_2Erealax_2Ereal),
inference(backward_subsumption_resolution,[status(thm)],[c_865,c_892]) ).
tcf(c_905,plain,
inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_892,c_58]) ).
tcf(c_909,plain,
inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(iPr_def_21)) = iPr_def_21,
inference(superposition,[status(thm)],[c_899,c_58]) ).
tcf(c_910,plain,
inj__ty_2Erealax_2Ereal(iPr_def_22) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_909,c_344]) ).
tcf(c_915,plain,
surj__ty_2Erealax_2Ereal(iPr_def_21) = iPr_def_22,
inference(superposition,[status(thm)],[c_910,c_56]) ).
tcf(c_1073,plain,
surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK2,sK3),c_2Ebool_2Ethe__value(iPr_def_13)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(sK2,sK3),c_2Ebool_2Ethe__value(iPr_def_13))),
inference(superposition,[status(thm)],[c_335,c_80]) ).
tcf(c_1074,plain,
surj__ty_2Erealax_2Ereal(ap(iPr_def_10,iPr_def_15)) = surj__ty_2Erealax_2Ereal(iPr_def_20),
inference(light_normalisation,[status(thm)],[c_1073,c_332,c_334,c_336,c_337,c_341,c_342]) ).
tcf(c_1170,plain,
( mem(iPr_def_15,ty_2Ebinary__ieee_2Efloat(sK2,sK3))
| ~ mem(iPr_def_14,ty_2Ebool_2Eitself(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_337,c_777]) ).
tcf(c_1175,plain,
mem(iPr_def_15,ty_2Ebinary__ieee_2Efloat(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1170,c_659]) ).
tcf(c_1193,plain,
surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),ap(c_2Ebinary__ieee_2Efloat__negate(sK2,sK3),iPr_def_15))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(sK2,sK3),iPr_def_15))),
inference(superposition,[status(thm)],[c_1175,c_79]) ).
tcf(c_1194,plain,
mem(ap(iPr_def_10,iPr_def_15),ty_2Erealax_2Ereal),
inference(superposition,[status(thm)],[c_1175,c_774]) ).
tcf(c_1195,plain,
surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(iPr_def_10,iPr_def_15))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_1193,c_332,c_333,c_338,c_339,c_340]) ).
tcf(c_1213,plain,
inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(ap(iPr_def_10,iPr_def_15))) = ap(iPr_def_10,iPr_def_15),
inference(superposition,[status(thm)],[c_1194,c_58]) ).
tcf(c_1214,plain,
ap(iPr_def_10,iPr_def_15) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_1213,c_905,c_1074]) ).
tcf(c_1218,plain,
iPr_def_18 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_1195,c_343,c_915,c_1214]) ).
tcf(c_1219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1218,c_345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.54 % Computer : n003.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Wed Sep 23 17:45:51 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.58 Running first-order theorem proving
% 0.13/0.58 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.59
% 0.13/0.59 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.59
% 0.13/0.59 % Detected problem language: tptp
% 0.13/0.61 % Proving...
% 2.18/1.35 % SZS status Started for theBenchmark.p
% 2.18/1.35 % SZS status Theorem for theBenchmark.p
% 2.18/1.35
% 2.18/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.18/1.35
% 2.18/1.35 % ------ iProver source info
% 2.18/1.35
% 2.18/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 2.18/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.18/1.35 % git: non_committed_changes: false
% 2.18/1.35
% 2.18/1.35 % ------ Parsing...
% 2.18/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.18/1.35 %
% 2.18/1.35
% 2.18/1.35 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 2.18/1.35
% 2.18/1.35 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.18/1.35 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.18/1.35 %
% 2.18/1.35
% 2.18/1.35 % ------ Preprocessing...
% 2.18/1.35 % ------ Proving...
% 2.18/1.35 % ------ Problem Properties
% 2.18/1.35
% 2.18/1.35 %
% 2.18/1.35 % clauses 46
% 2.18/1.35 % conjectures 1
% 2.18/1.35 % EPR 5
% 2.18/1.35 % Horn 43
% 2.18/1.35 % unary 31
% 2.18/1.35 % binary 6
% 2.18/1.35 % lits 78
% 2.18/1.35 % lits eq 30
% 2.18/1.35 % fd_pure 0
% 2.18/1.35 % fd_pseudo 0
% 2.18/1.35 % fd_cond 0
% 2.18/1.35 % fd_pseudo_cond 5
% 2.18/1.35 % AC symbols 0
% 2.18/1.35
% 2.18/1.35 % ------ Schedule dynamic 5 is on
% 2.18/1.35
% 2.18/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.18/1.35
% 2.18/1.35
% 2.18/1.35 % ------
% 2.18/1.35 % Current options:
% 2.18/1.35 % ------
% 2.18/1.35
% 2.18/1.35
% 2.18/1.35 %
% 2.18/1.35
% 2.18/1.35 % ------ Proving...
% 2.18/1.35 %
% 2.18/1.35
% 2.18/1.35 % SZS status Theorem for theBenchmark.p
% 2.18/1.35
% 2.18/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.18/1.35
% 2.18/1.35
%------------------------------------------------------------------------------