%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 : Unsatisfiable 2.21s 1.28s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 3 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 122 ( 64 ~; 58 |; 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 : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f2,axiom,
! [X0] :
( ~ c(X0)
| s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f4,axiom,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f5,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f8,axiom,
! [X0] :
( ~ d(X0)
| s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ s(X2,X1)
| ~ s(X2,X0)
| ~ s1most(X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
fof(f14,axiom,
! [X0] :
( ~ e(X0)
| r(X0,u4r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
fof(f15,axiom,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f16,axiom,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
tcf(c_67,negated_conjecture,
e(exist),
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] :
( s2least(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_70,plain,
! [X0: $i] :
( ~ s2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i] :
( s(X0,u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i] :
( s(X0,u1r2(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,plain,
! [X0: $i] :
( s1most(X0)
| ~ d(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ s1most(X0)
| ~ s(X0,X2)
| ~ s(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i] :
( r(X0,u4r2(X0))
| ~ e(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( d(X1)
| ~ e(X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( c(X1)
| ~ e(X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_91,plain,
( r(exist,u4r2(exist))
| ~ e(exist) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_106,plain,
! [X0: $i] :
( s1most(X0)
| ~ d(X0) ),
inference(prop_impl_just,[status(thm)],[c_74]) ).
tcf(c_108,plain,
! [X0: $i] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_68,c_70]) ).
tcf(c_109,plain,
! [X0: $i] :
( ~ c(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(renaming,[status(thm)],[c_108]) ).
tcf(c_110,plain,
! [X0: $i] :
( s(X0,u1r1(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_68,c_71]) ).
tcf(c_112,plain,
! [X0: $i] :
( s(X0,u1r2(X0))
| ~ c(X0) ),
inference(prop_impl_just,[status(thm)],[c_68,c_72]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ d(X0)
| ~ s(X0,X2)
| ~ s(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_76,c_106]) ).
tcf(c_1260,plain,
! [X0: $i] :
( c(u4r2(X0))
| ~ e(X0)
| ~ r(X0,u4r2(X0)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_1261,plain,
( c(u4r2(exist))
| ~ e(exist)
| ~ r(exist,u4r2(exist)) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_1262,plain,
! [X0: $i] :
( s(u4r2(X0),u1r2(u4r2(X0)))
| ~ c(u4r2(X0)) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_1263,plain,
! [X0: $i] :
( s(u4r2(X0),u1r1(u4r2(X0)))
| ~ c(u4r2(X0)) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_1264,plain,
! [X0: $i] :
( ~ c(u4r2(X0))
| ~ equalish(u1r2(u4r2(X0)),u1r1(u4r2(X0))) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_1265,plain,
( ~ c(u4r2(exist))
| ~ equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist))) ),
inference(instantiation,[status(thm)],[c_1264]) ).
tcf(c_1266,plain,
( s(u4r2(exist),u1r1(u4r2(exist)))
| ~ c(u4r2(exist)) ),
inference(instantiation,[status(thm)],[c_1263]) ).
tcf(c_1267,plain,
( s(u4r2(exist),u1r2(u4r2(exist)))
| ~ c(u4r2(exist)) ),
inference(instantiation,[status(thm)],[c_1262]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i] :
( equalish(X1,u1r1(u4r2(X0)))
| ~ d(u4r2(X0))
| ~ s(u4r2(X0),X1)
| ~ s(u4r2(X0),u1r1(u4r2(X0))) ),
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i] :
( d(u4r2(X1))
| ~ e(X0)
| ~ r(X0,u4r2(X1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1283,plain,
( d(u4r2(exist))
| ~ e(exist)
| ~ r(exist,u4r2(exist)) ),
inference(instantiation,[status(thm)],[c_1282]) ).
tcf(c_1298,plain,
! [X0: $i] :
( equalish(u1r2(u4r2(X0)),u1r1(u4r2(X0)))
| ~ d(u4r2(X0))
| ~ s(u4r2(X0),u1r1(u4r2(X0)))
| ~ s(u4r2(X0),u1r2(u4r2(X0))) ),
inference(instantiation,[status(thm)],[c_1272]) ).
tcf(c_1299,plain,
( equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist)))
| ~ d(u4r2(exist))
| ~ s(u4r2(exist),u1r1(u4r2(exist)))
| ~ s(u4r2(exist),u1r2(u4r2(exist))) ),
inference(instantiation,[status(thm)],[c_1298]) ).
tcf(c_1300,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1299,c_1283,c_1267,c_1266,c_1265,c_1261,c_91,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.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 19:16:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 2.21/1.28 % SZS status Started for theBenchmark.p
% 2.21/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.21/1.28
% 2.21/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.21/1.28
% 2.21/1.28 % ------ iProver source info
% 2.21/1.28
% 2.21/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.21/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.21/1.28 % git: non_committed_changes: false
% 2.21/1.28
% 2.21/1.28 % ------ Parsing...% successful
% 2.21/1.28
% 2.21/1.28
% 2.21/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.21/1.28
% 2.21/1.28 % ------ 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 %
% 2.21/1.28
% 2.21/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.21/1.28 % ------ Proving...
% 2.21/1.28 % ------ Problem Properties
% 2.21/1.28
% 2.21/1.28 %
% 2.21/1.28 % clauses 14
% 2.21/1.28 % conjectures 1
% 2.21/1.28 % EPR 5
% 2.21/1.28 % Horn 10
% 2.21/1.28 % unary 1
% 2.21/1.28 % binary 7
% 2.21/1.28 % lits 36
% 2.21/1.28 % lits eq 0
% 2.21/1.28 % fd_pure 0
% 2.21/1.28 % fd_pseudo 0
% 2.21/1.28 % fd_cond 0
% 2.21/1.28 % fd_pseudo_cond 0
% 2.21/1.28 % AC symbols 0
% 2.21/1.28
% 2.21/1.28 % ------ Schedule dynamic 5 is on
% 2.21/1.28
% 2.21/1.28 % ------ no equalities: superposition off
% 2.21/1.28
% 2.21/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.21/1.28
% 2.21/1.28
% 2.21/1.28 % ------
% 2.21/1.28 % Current options:
% 2.21/1.28 % ------
% 2.21/1.28
% 2.21/1.28
% 2.21/1.28 %
% 2.21/1.28
% 2.21/1.28 % ------ Proving...
% 2.21/1.28 %
% 2.21/1.28
% 2.21/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.21/1.28
% 2.21/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.21/1.28
% 2.21/1.28
%------------------------------------------------------------------------------