%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:53:59 PM UTC 2026
% Result : Theorem 1.19s 1.27s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 120 ( 60 ~; 49 |; 4 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
u1r1: unreal > real ).
tff(pred_def_1,type,
f: unreal > $o ).
tff(pred_def_2,type,
d: unreal > $o ).
tff(pred_def_3,type,
e: unreal > $o ).
tff(pred_def_4,type,
s1most: unreal > $o ).
tff(pred_def_5,type,
s: ( real * unreal ) > $o ).
tff(pred_def_6,type,
c: unreal > $o ).
tff(pred_def_7,type,
equalish: ( real * real ) > $o ).
tff(pred_def_8,type,
s2least: unreal > $o ).
tff(f1,axiom,
! [X0: unreal] :
( c(X0)
=> s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(f3,axiom,
! [X0: unreal] :
~ ( equalish(u1r2(X0),u1r1(X0))
& s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(f4,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(f5,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(f7,axiom,
! [X0: unreal] :
( d(X0)
=> s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(f9,axiom,
! [X0: real,X1: real,X2: unreal] :
( ( s(X2,X0)
& s(X2,X1)
& s1most(X2) )
=> equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
tff(f13,axiom,
! [X0: unreal] :
( e(X0)
=> c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
tff(f14,axiom,
! [X0: unreal] :
( f(X0)
=> d(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
tff(f15,conjecture,
( ~ f(exist)
| ~ e(exist) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1__clause_2) ).
tff(f16,negated_conjecture,
~ ( ~ f(exist)
| ~ e(exist) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f17,plain,
! [X0: unreal] :
( ~ c(X0)
| s2least(X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f19,plain,
! [X0: unreal] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f20,plain,
! [X0: unreal] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
inference(ennf_transformation,[],[f4]) ).
tff(f21,plain,
! [X0: unreal] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
inference(ennf_transformation,[],[f5]) ).
tff(f24,plain,
! [X0: unreal] :
( ~ d(X0)
| s1most(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f26,plain,
! [X0: real,X1: real,X2: unreal] :
( ~ s(X2,X0)
| ~ s(X2,X1)
| ~ s1most(X2)
| equalish(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f27,plain,
! [X0: real,X1: real,X2: unreal] :
( ~ s(X2,X0)
| ~ s(X2,X1)
| ~ s1most(X2)
| equalish(X1,X0) ),
inference(flattening,[],[f26]) ).
tff(f29,plain,
! [X0: unreal] :
( ~ e(X0)
| c(X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f30,plain,
! [X0: unreal] :
( ~ f(X0)
| d(X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f31,plain,
( f(exist)
& e(exist) ),
inference(ennf_transformation,[],[f16]) ).
tff(f32,plain,
! [X0: unreal] :
( ~ c(X0)
| s2least(X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f34,plain,
! [X0: unreal] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f35,plain,
! [X0: unreal] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f36,plain,
! [X0: unreal] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
inference(cnf_transformation,[],[f21]) ).
tff(f38,plain,
! [X0: unreal] :
( ~ d(X0)
| s1most(X0) ),
inference(cnf_transformation,[],[f24]) ).
tff(f40,plain,
! [X2: unreal,X0: real,X1: real] :
( ~ s(X2,X0)
| ~ s(X2,X1)
| ~ s1most(X2)
| equalish(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f44,plain,
! [X0: unreal] :
( ~ e(X0)
| c(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f45,plain,
! [X0: unreal] :
( ~ f(X0)
| d(X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f46,plain,
f(exist),
inference(cnf_transformation,[],[f31]) ).
tff(f47,plain,
e(exist),
inference(cnf_transformation,[],[f31]) ).
tcf(c_49,plain,
! [X0_unreal: unreal] :
( s2least(X0_unreal)
| ~ c(X0_unreal) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0_unreal: unreal] :
( ~ s2least(X0_unreal)
| ~ equalish(u1r2(X0_unreal),u1r1(X0_unreal)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0_unreal: unreal] :
( s(X0_unreal,u1r1(X0_unreal))
| ~ s2least(X0_unreal) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0_unreal: unreal] :
( s(X0_unreal,u1r2(X0_unreal))
| ~ s2least(X0_unreal) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0_unreal: unreal] :
( s1most(X0_unreal)
| ~ d(X0_unreal) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0_unreal: unreal,X0_real: real,X1_real: real] :
( equalish(X1_real,X0_real)
| ~ s1most(X0_unreal)
| ~ s(X0_unreal,X1_real)
| ~ s(X0_unreal,X0_real) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_61,plain,
! [X0_unreal: unreal] :
( c(X0_unreal)
| ~ e(X0_unreal) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_62,plain,
! [X0_unreal: unreal] :
( d(X0_unreal)
| ~ f(X0_unreal) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_63,negated_conjecture,
e(exist),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,negated_conjecture,
f(exist),
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
( d(exist)
| ~ f(exist) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_66,plain,
( c(exist)
| ~ e(exist) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_68,plain,
( s1most(exist)
| ~ d(exist) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_70,plain,
( s2least(exist)
| ~ c(exist) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_73,plain,
( s(exist,u1r2(exist))
| ~ s2least(exist) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_74,plain,
( s(exist,u1r1(exist))
| ~ s2least(exist) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_87,plain,
! [X0_unreal: unreal] :
( ~ equalish(u1r2(X0_unreal),u1r1(X0_unreal))
| ~ s2least(X0_unreal) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_88,plain,
! [X0_unreal: unreal] :
( ~ s2least(X0_unreal)
| ~ equalish(u1r2(X0_unreal),u1r1(X0_unreal)) ),
inference(renaming,[status(thm)],[c_87]) ).
tcf(c_360,plain,
! [X0_unreal: unreal,X1_unreal: unreal] :
( ~ s2least(X1_unreal)
| ~ s1most(X0_unreal)
| ~ s(X0_unreal,u1r2(X1_unreal))
| ~ s(X0_unreal,u1r1(X1_unreal)) ),
inference(resolution,[status(thm)],[c_88,c_57]) ).
tcf(c_361,plain,
( ~ s2least(exist)
| ~ s1most(exist)
| ~ s(exist,u1r2(exist))
| ~ s(exist,u1r1(exist)) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_362,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_361,c_74,c_73,c_70,c_68,c_66,c_65,c_63,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 19:18:41 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 1.19/1.27 % SZS status Started for theBenchmark.p
% 1.19/1.27 % SZS status Theorem for theBenchmark.p
% 1.19/1.27
% 1.19/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/1.27
% 1.19/1.27 % ------ iProver source info
% 1.19/1.27
% 1.19/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/1.27 % git: non_committed_changes: false
% 1.19/1.27
% 1.19/1.27 % ------ Parsing...
% 1.19/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.19/1.27 %
% 1.19/1.27
% 1.19/1.27 % ------ Preprocessing... pe_s pe:1:0s pe:2:0s pe:4:0s%
% 1.19/1.27
% 1.19/1.27 % SZS status Theorem for theBenchmark.p
% 1.19/1.27
% 1.19/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/1.27
% 1.19/1.27
%------------------------------------------------------------------------------