%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 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 01:54:09 PM UTC 2026
% Result : Unsatisfiable 1.84s 6.29s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 4 unt; 1 def)
% Number of atoms : 246 ( 34 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 328 ( 127 ~; 118 |; 70 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 130 ( 0 sgn 97 !; 33 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( ~ ! [X2,X3] :
( ( rs(X1,X3)
& rs(X1,X2) )
=> X2 = X3 )
& rr(X0,X1) )
& ! [X1] :
( rr(X0,X1)
=> ( cc(X1)
| ~ ? [X2,X3] :
( X2 != X3
& rs(X1,X3)
& rs(X1,X2) ) ) )
& ! [X1] :
( rr(X0,X1)
=> cd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f15,axiom,
! [X0] :
( cc(X0)
=> ~ cd(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f17,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( ~ ! [X6,X7] :
( ( rs(X5,X7)
& rs(X5,X6) )
=> X6 = X7 )
& rr(X0,X5) )
& ! [X2] :
( rr(X0,X2)
=> ( cc(X2)
| ~ ? [X3,X4] :
( X3 != X4
& rs(X2,X4)
& rs(X2,X3) ) ) )
& ! [X1] :
( rr(X0,X1)
=> cd(X1) ) ) ),
inference(rectify,[],[f14]) ).
fof(f40,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( ? [X6,X7] :
( rs(X5,X7)
& rs(X5,X6)
& X6 != X7 )
& rr(X0,X5) )
& ! [X2] :
( ~ rr(X0,X2)
| cc(X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X4)
| ~ rs(X2,X3) ) )
& ! [X1] :
( ~ rr(X0,X1)
| cd(X1) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( ? [X6,X7] :
( rs(X5,X7)
& rs(X5,X6)
& X6 != X7 )
& rr(X0,X5) )
& ! [X2] :
( ~ rr(X0,X2)
| cc(X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X4)
| ~ rs(X2,X3) ) )
& ! [X1] :
( ~ rr(X0,X1)
| cd(X1) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ cc(X0)
| ~ cd(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X5] :
( ? [X6,X7] :
( rs(X5,X7)
& rs(X5,X6)
& X6 != X7 )
& rr(X0,X5) )
& sP0(X0)
& ! [X1] :
( ~ rr(X0,X1)
| cd(X1) ) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ~ rs(X5,X7)
| ~ rs(X5,X6)
| X6 = X7 )
| ~ rr(X0,X5) )
| ~ sP0(X0)
| ? [X1] :
( rr(X0,X1)
& ~ cd(X1) )
| cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f50,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X5] :
( ? [X6,X7] :
( rs(X5,X7)
& rs(X5,X6)
& X6 != X7 )
& rr(X0,X5) )
& sP0(X0)
& ! [X1] :
( ~ rr(X0,X1)
| cd(X1) ) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ~ rs(X5,X7)
| ~ rs(X5,X6)
| X6 = X7 )
| ~ rr(X0,X5) )
| ~ sP0(X0)
| ? [X1] :
( rr(X0,X1)
& ~ cd(X1) )
| cUnsatisfiable(X0) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X6] :
( ? [X7,X8] :
( rs(X6,X8)
& rs(X6,X7)
& X7 != X8 )
& rr(X0,X6) )
& sP0(X0)
& ! [X5] :
( ~ rr(X0,X5)
| cd(X5) ) ) )
& ( ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X4)
| ~ rs(X2,X3)
| X3 = X4 )
| ~ rr(X0,X2) )
| ~ sP0(X0)
| ? [X1] :
( rr(X0,X1)
& ~ cd(X1) )
| cUnsatisfiable(X0) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( rs(sK5(X0),sK7(X0))
& rs(sK5(X0),sK6(X0))
& sK6(X0) != sK7(X0)
& rr(X0,sK5(X0))
& sP0(X0)
& ! [X5] :
( ~ rr(X0,X5)
| cd(X5) ) ) )
& ( ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X4)
| ~ rs(X2,X3)
| X3 = X4 )
| ~ rr(X0,X2) )
| ~ sP0(X0)
| ( rr(X0,sK4(X0))
& ~ cd(sK4(X0)) )
| cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X1,sK4(X0)),skolemize(X6,sK5(X0)),skolemize(X7,sK6(X0)),skolemize(X8,sK7(X0))],[f51]) ).
fof(f74,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rs(sK5(X0),sK7(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rs(sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f76,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK6(X0) != sK7(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f77,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rr(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f78,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X0,X5] :
( ~ cUnsatisfiable(X0)
| ~ rr(X0,X5)
| cd(X5) ),
inference(cnf_transformation,[],[f52]) ).
fof(f82,plain,
! [X0] :
( ~ cc(X0)
| ~ cd(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f83,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(cnf_transformation,[],[f16]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( cd(X1)
| ~ cUnsatisfiable(X0)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_62,plain,
! [X0: $i] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_63,plain,
! [X0: $i] :
( rr(X0,sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_64,plain,
! [X0: $i] :
( ~ cUnsatisfiable(X0)
| ( sK6(X0) != sK7(X0) ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_65,plain,
! [X0: $i] :
( rs(sK5(X0),sK6(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_66,plain,
! [X0: $i] :
( rs(sK5(X0),sK7(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_67,plain,
! [X0: $i] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_68,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(cnf_transformation,[],[f83]) ).
tcf(c_72,plain,
( sP0(i2003_11_14_17_20_36582)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_77,plain,
( rr(i2003_11_14_17_20_36582,sK5(i2003_11_14_17_20_36582))
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_84,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ( sK6(i2003_11_14_17_20_36582) != sK7(i2003_11_14_17_20_36582) ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_2726,plain,
! [X0: $i] :
( cd(sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_2737,plain,
! [X0: $i] :
( ~ cUnsatisfiable(X0)
| ~ cc(sK5(X0)) ),
inference(superposition,[status(thm)],[c_2726,c_67]) ).
fof(f43,definition,
! [X0] :
( sP0(X0)
<=> ! [X2] :
( ~ rr(X0,X2)
| cc(X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X4)
| ~ rs(X2,X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f44,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( ? [X6,X7] :
( rs(X5,X7)
& rs(X5,X6)
& X6 != X7 )
& rr(X0,X5) )
& sP0(X0)
& ! [X1] :
( ~ rr(X0,X1)
| cd(X1) ) ) ),
inference(definition_folding,[],[f41,f43]) ).
fof(f46,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X2] :
( ~ rr(X0,X2)
| cc(X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X4)
| ~ rs(X2,X3) ) ) )
& ( ? [X2] :
( rr(X0,X2)
& ~ cc(X2)
& ? [X3,X4] :
( X3 != X4
& rs(X2,X4)
& rs(X2,X3) ) )
| sP0(X0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X4] :
( ~ rr(X0,X4)
| cc(X4)
| ! [X5,X6] :
( X5 = X6
| ~ rs(X4,X6)
| ~ rs(X4,X5) ) ) )
& ( ? [X1] :
( rr(X0,X1)
& ~ cc(X1)
& ? [X2,X3] :
( X2 != X3
& rs(X1,X3)
& rs(X1,X2) ) )
| sP0(X0) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X4] :
( ~ rr(X0,X4)
| cc(X4)
| ! [X5,X6] :
( X5 = X6
| ~ rs(X4,X6)
| ~ rs(X4,X5) ) ) )
& ( ( rr(X0,sK1(X0))
& ~ cc(sK1(X0))
& sK2(X0) != sK3(X0)
& rs(sK1(X0),sK3(X0))
& rs(sK1(X0),sK2(X0)) )
| sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X3,sK3(X0))],[f47]) ).
fof(f68,plain,
! [X0,X6,X4,X5] :
( ~ sP0(X0)
| ~ rr(X0,X4)
| cc(X4)
| X5 = X6
| ~ rs(X4,X6)
| ~ rs(X4,X5) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cc(X0)
| ( X1 = X2 )
| ~ sP0(X3)
| ~ rr(X3,X0)
| ~ rs(X0,X2)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_2765,plain,
! [X0: $i,X1: $i,X2: $i] :
( cc(sK5(X0))
| ( sK6(X0) = X1 )
| ~ cUnsatisfiable(X0)
| ~ sP0(X2)
| ~ rr(X2,sK5(X0))
| ~ rs(sK5(X0),X1) ),
inference(superposition,[status(thm)],[c_65,c_58]) ).
tcf(c_2828,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ rs(sK5(X0),X1)
| ~ rr(X2,sK5(X0))
| ~ sP0(X2)
| ~ cUnsatisfiable(X0)
| ( sK6(X0) = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_2765,c_2737,c_2765]) ).
tcf(c_2829,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(X0) = X1 )
| ~ cUnsatisfiable(X0)
| ~ sP0(X2)
| ~ rr(X2,sK5(X0))
| ~ rs(sK5(X0),X1) ),
inference(renaming,[status(thm)],[c_2828]) ).
tcf(c_2842,plain,
! [X0: $i,X1: $i] :
( ( sK6(X1) = sK7(X1) )
| ~ cUnsatisfiable(X1)
| ~ sP0(X0)
| ~ rr(X0,sK5(X1)) ),
inference(superposition,[status(thm)],[c_66,c_2829]) ).
tcf(c_2847,plain,
( ( sK6(i2003_11_14_17_20_36582) = sK7(i2003_11_14_17_20_36582) )
| ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ sP0(i2003_11_14_17_20_36582)
| ~ rr(i2003_11_14_17_20_36582,sK5(i2003_11_14_17_20_36582)) ),
inference(instantiation,[status(thm)],[c_2842]) ).
tcf(c_2848,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2847,c_84,c_77,c_72,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n016.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 19:27:47 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 1.84/6.29 % SZS status Started for theBenchmark.p
% 1.84/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/6.29
% 1.84/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/6.29
% 1.84/6.29 % ------ iProver source info
% 1.84/6.29
% 1.84/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/6.29 % git: non_committed_changes: false
% 1.84/6.29
% 1.84/6.29 % ------ Parsing...
% 1.84/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/6.29 % ------ Proving...
% 1.84/6.29 % ------ Problem Properties
% 1.84/6.29
% 1.84/6.29 %
% 1.84/6.29 % clauses 16
% 1.84/6.29 % conjectures 0
% 1.84/6.29 % EPR 5
% 1.84/6.29 % Horn 10
% 1.84/6.29 % unary 1
% 1.84/6.29 % binary 11
% 1.84/6.29 % lits 46
% 1.84/6.29 % lits eq 5
% 1.84/6.29 % fd_pure 0
% 1.84/6.29 % fd_pseudo 0
% 1.84/6.29 % fd_cond 0
% 1.84/6.29 % fd_pseudo_cond 3
% 1.84/6.29 % AC symbols 0
% 1.84/6.29
% 1.84/6.29 % ------ Schedule dynamic 5 is on
% 1.84/6.29
% 1.84/6.29 % ------ no conjectures: strip conj schedule
% 1.84/6.29
% 1.84/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/6.29
% 1.84/6.29
% 1.84/6.29 % ------
% 1.84/6.29 % Current options:
% 1.84/6.29 % ------
% 1.84/6.29
% 1.84/6.29
% 1.84/6.29 %
% 1.84/6.29
% 1.84/6.29 % ------ Proving...
% 1.84/6.29 %
% 1.84/6.29
% 1.84/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/6.29
% 1.84/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/6.29
% 1.84/6.29
%------------------------------------------------------------------------------