%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:54:00 PM UTC 2026
% Result : Unsatisfiable 2.35s 1.27s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 5 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 186 ( 87 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0] :
( ~ c(X0)
| t2least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f5,axiom,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f9,axiom,
! [X0] :
( ~ d(X0)
| t1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ t(X2,X1)
| ~ t(X2,X0)
| ~ t1most(X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
fof(f15,axiom,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
fof(f16,axiom,
! [X0,X1] :
( ~ s2least(X0)
| ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ s(X0,X2)
| ~ s(X0,X1)
| equalish(X1,X2)
| s2least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
fof(f28,axiom,
! [X0] :
( ~ s1most(u6r1(X0))
| f(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
fof(f29,axiom,
! [X0] :
( r(X0,u6r1(X0))
| f(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
fof(f31,axiom,
! [X0] :
( ~ equalish(u7r2(X0),u7r1(X0))
| s1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
fof(f32,axiom,
! [X0] :
( s(X0,u7r1(X0))
| s1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
fof(f33,axiom,
! [X0] :
( s(X0,u7r2(X0))
| s1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
tcf(c_82,negated_conjecture,
e(exist),
inference(cnf_transformation,[],[f1]) ).
tcf(c_83,negated_conjecture,
~ f(exist),
inference(cnf_transformation,[],[f2]) ).
tcf(c_84,plain,
! [X0: $i] :
( t2least(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_86,plain,
! [X0: $i] :
( ~ t2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,plain,
! [X0: $i] :
( t(X0,u1r1(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_88,plain,
! [X0: $i] :
( t(X0,u1r2(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_90,plain,
! [X0: $i] :
( t1most(X0)
| ~ d(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ t1most(X0)
| ~ t(X0,X2)
| ~ t(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( d(X1)
| ~ e(X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( c(X1)
| ~ s2least(X1)
| ~ e(X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( s2least(X0)
| equalish(X1,X2)
| ~ s(X0,X2)
| ~ s(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,plain,
! [X0: $i] :
( f(X0)
| ~ s1most(u6r1(X0)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,plain,
! [X0: $i] :
( f(X0)
| r(X0,u6r1(X0)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_112,plain,
! [X0: $i] :
( s1most(X0)
| ~ equalish(u7r2(X0),u7r1(X0)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_113,plain,
! [X0: $i] :
( s1most(X0)
| s(X0,u7r1(X0)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_114,plain,
! [X0: $i] :
( s1most(X0)
| s(X0,u7r2(X0)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_121,plain,
( f(exist)
| r(exist,u6r1(exist)) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_145,plain,
! [X0: $i] :
( t1most(X0)
| ~ d(X0) ),
inference(prop_impl_just,[status(thm)],[c_90]) ).
tcf(c_147,plain,
! [X0: $i] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_84,c_86]) ).
tcf(c_148,plain,
! [X0: $i] :
( ~ c(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(renaming,[status(thm)],[c_147]) ).
tcf(c_149,plain,
! [X0: $i] :
( t(X0,u1r1(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_84,c_87]) ).
tcf(c_151,plain,
! [X0: $i] :
( t(X0,u1r2(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_84,c_88]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ s1most(u6r1(X0))
| f(X0) ),
inference(prop_impl_just,[status(thm)],[c_109]) ).
tcf(c_172,plain,
! [X0: $i] :
( f(X0)
| ~ s1most(u6r1(X0)) ),
inference(renaming,[status(thm)],[c_171]) ).
tcf(c_177,plain,
! [X0: $i] :
( ~ equalish(u7r2(X0),u7r1(X0))
| s1most(X0) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_178,plain,
! [X0: $i] :
( s1most(X0)
| ~ equalish(u7r2(X0),u7r1(X0)) ),
inference(renaming,[status(thm)],[c_177]) ).
tcf(c_179,plain,
! [X0: $i] :
( s(X0,u7r1(X0))
| s1most(X0) ),
inference(prop_impl_just,[status(thm)],[c_113]) ).
tcf(c_180,plain,
! [X0: $i] :
( s1most(X0)
| s(X0,u7r1(X0)) ),
inference(renaming,[status(thm)],[c_179]) ).
tcf(c_181,plain,
! [X0: $i] :
( s(X0,u7r2(X0))
| s1most(X0) ),
inference(prop_impl_just,[status(thm)],[c_114]) ).
tcf(c_182,plain,
! [X0: $i] :
( s1most(X0)
| s(X0,u7r2(X0)) ),
inference(renaming,[status(thm)],[c_181]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ d(X0)
| ~ t(X0,X2)
| ~ t(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_92,c_145]) ).
tcf(c_537,plain,
! [X0: $i] :
( f(X0)
| s(u6r1(X0),u7r2(u6r1(X0))) ),
inference(resolution,[status(thm)],[c_172,c_182]) ).
tcf(c_538,plain,
( f(exist)
| s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_537]) ).
tcf(c_545,plain,
! [X0: $i] :
( f(X0)
| s(u6r1(X0),u7r1(u6r1(X0))) ),
inference(resolution,[status(thm)],[c_172,c_180]) ).
tcf(c_546,plain,
( f(exist)
| s(u6r1(exist),u7r1(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_545]) ).
tcf(c_553,plain,
! [X0: $i] :
( f(X0)
| ~ equalish(u7r2(u6r1(X0)),u7r1(u6r1(X0))) ),
inference(resolution,[status(thm)],[c_172,c_178]) ).
tcf(c_554,plain,
( f(exist)
| ~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_553]) ).
tcf(c_3210,plain,
! [X0: $i,X1: $i] :
( s2least(u6r1(X0))
| equalish(u7r2(u6r1(X0)),X1)
| ~ s(u6r1(X0),X1)
| ~ s(u6r1(X0),u7r2(u6r1(X0))) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_3213,plain,
! [X0: $i,X1: $i] :
( c(u6r1(X1))
| ~ e(X0)
| ~ s2least(u6r1(X1))
| ~ r(X0,u6r1(X1)) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_3214,plain,
( c(u6r1(exist))
| ~ e(exist)
| ~ s2least(u6r1(exist))
| ~ r(exist,u6r1(exist)) ),
inference(instantiation,[status(thm)],[c_3213]) ).
tcf(c_3225,plain,
! [X0: $i] :
( t(u6r1(X0),u1r2(u6r1(X0)))
| ~ c(u6r1(X0)) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_3226,plain,
! [X0: $i] :
( t(u6r1(X0),u1r1(u6r1(X0)))
| ~ c(u6r1(X0)) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_3227,plain,
! [X0: $i] :
( ~ c(u6r1(X0))
| ~ equalish(u1r2(u6r1(X0)),u1r1(u6r1(X0))) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_3228,plain,
( ~ c(u6r1(exist))
| ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_3227]) ).
tcf(c_3229,plain,
( t(u6r1(exist),u1r1(u6r1(exist)))
| ~ c(u6r1(exist)) ),
inference(instantiation,[status(thm)],[c_3226]) ).
tcf(c_3230,plain,
( t(u6r1(exist),u1r2(u6r1(exist)))
| ~ c(u6r1(exist)) ),
inference(instantiation,[status(thm)],[c_3225]) ).
tcf(c_3243,plain,
! [X0: $i] :
( s2least(u6r1(X0))
| equalish(u7r2(u6r1(X0)),u7r1(u6r1(X0)))
| ~ s(u6r1(X0),u7r1(u6r1(X0)))
| ~ s(u6r1(X0),u7r2(u6r1(X0))) ),
inference(instantiation,[status(thm)],[c_3210]) ).
tcf(c_3244,plain,
( s2least(u6r1(exist))
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_3243]) ).
tcf(c_3272,plain,
! [X0: $i,X1: $i] :
( equalish(X1,u1r1(u6r1(X0)))
| ~ d(u6r1(X0))
| ~ t(u6r1(X0),X1)
| ~ t(u6r1(X0),u1r1(u6r1(X0))) ),
inference(instantiation,[status(thm)],[c_256]) ).
tcf(c_3314,plain,
! [X0: $i,X1: $i] :
( d(u6r1(X1))
| ~ e(X0)
| ~ r(X0,u6r1(X1)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_3315,plain,
( d(u6r1(exist))
| ~ e(exist)
| ~ r(exist,u6r1(exist)) ),
inference(instantiation,[status(thm)],[c_3314]) ).
tcf(c_3330,plain,
! [X0: $i] :
( equalish(u1r2(u6r1(X0)),u1r1(u6r1(X0)))
| ~ d(u6r1(X0))
| ~ t(u6r1(X0),u1r1(u6r1(X0)))
| ~ t(u6r1(X0),u1r2(u6r1(X0))) ),
inference(instantiation,[status(thm)],[c_3272]) ).
tcf(c_3331,plain,
( equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist)))
| ~ d(u6r1(exist))
| ~ t(u6r1(exist),u1r1(u6r1(exist)))
| ~ t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(instantiation,[status(thm)],[c_3330]) ).
tcf(c_3332,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3331,c_3315,c_3244,c_3230,c_3229,c_3228,c_3214,c_554,c_546,c_538,c_121,c_83,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 19:10:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 2.35/1.27 % SZS status Started for theBenchmark.p
% 2.35/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.27
% 2.35/1.27 % ------ iProver source info
% 2.35/1.27
% 2.35/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.27 % git: non_committed_changes: false
% 2.35/1.27
% 2.35/1.27 % ------ Parsing...% successful
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 % ------ Problem Properties
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27 % clauses 29
% 2.35/1.27 % conjectures 2
% 2.35/1.27 % EPR 9
% 2.35/1.27 % Horn 17
% 2.35/1.27 % unary 2
% 2.35/1.27 % binary 14
% 2.35/1.27 % lits 74
% 2.35/1.27 % lits eq 0
% 2.35/1.27 % fd_pure 0
% 2.35/1.27 % fd_pseudo 0
% 2.35/1.27 % fd_cond 0
% 2.35/1.27 % fd_pseudo_cond 0
% 2.35/1.27 % AC symbols 0
% 2.35/1.27
% 2.35/1.27 % ------ Schedule dynamic 5 is on
% 2.35/1.27
% 2.35/1.27 % ------ no equalities: superposition off
% 2.35/1.27
% 2.35/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 % ------
% 2.35/1.27 % Current options:
% 2.35/1.27 % ------
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.27
% 2.35/1.27
%------------------------------------------------------------------------------