%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 0.44s 1.30s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 4 unt; 3 def)
% Number of atoms : 269 ( 65 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 354 ( 129 ~; 111 |; 100 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 126 ( 0 sgn 92 !; 34 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1,X2] :
( ( rtt(X0,X2)
& rtt(X0,X1) )
=> X1 = X2 )
& ! [X1,X2] :
( ( rtt(X0,X2)
& rtt(X0,X1) )
=> X1 = X2 )
& ! [X4] :
( rtt(X0,X4)
=> ca(X4) )
& ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f17,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X7,X8] :
( ( rtt(X0,X8)
& rtt(X0,X7) )
=> X7 = X8 )
& ! [X5,X6] :
( ( rtt(X0,X6)
& rtt(X0,X5) )
=> X5 = X6 )
& ! [X4] :
( rtt(X0,X4)
=> ca(X4) )
& ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) ) ),
inference(rectify,[],[f13]) ).
fof(f38,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X7,X8] :
( ~ rtt(X0,X8)
| ~ rtt(X0,X7)
| X7 = X8 )
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f39,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X7,X8] :
( ~ rtt(X0,X8)
| ~ rtt(X0,X7)
| X7 = X8 )
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) ) ),
inference(flattening,[],[f38]) ).
fof(f48,plain,
! [X0] :
( ( ~ sP2(X0)
| ( sP0(X0)
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& sP1(X0) ) )
& ( ~ sP0(X0)
| ? [X5,X6] :
( rtt(X0,X6)
& rtt(X0,X5)
& X5 != X6 )
| ? [X4] :
( rtt(X0,X4)
& ~ ca(X4) )
| ~ sP1(X0)
| sP2(X0) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f49,plain,
! [X0] :
( ( ~ sP2(X0)
| ( sP0(X0)
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& sP1(X0) ) )
& ( ~ sP0(X0)
| ? [X5,X6] :
( rtt(X0,X6)
& rtt(X0,X5)
& X5 != X6 )
| ? [X4] :
( rtt(X0,X4)
& ~ ca(X4) )
| ~ sP1(X0)
| sP2(X0) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( ~ sP2(X0)
| ( sP0(X0)
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& sP1(X0) ) )
& ( ~ sP0(X0)
| ? [X2,X3] :
( rtt(X0,X3)
& rtt(X0,X2)
& X2 != X3 )
| ? [X1] :
( rtt(X0,X1)
& ~ ca(X1) )
| ~ sP1(X0)
| sP2(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( ~ sP2(X0)
| ( sP0(X0)
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& sP1(X0) ) )
& ( ~ sP0(X0)
| ( rtt(X0,sK5(X0))
& rtt(X0,sK4(X0))
& sK4(X0) != sK5(X0) )
| ( rtt(X0,sK3(X0))
& ~ ca(sK3(X0)) )
| ~ sP1(X0)
| sP2(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0)),skolemize(X3,sK5(X0))],[f50]) ).
fof(f52,plain,
! [X0] :
( ( ~ sP1(X0)
| ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rtt(X0,X3)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
| sP1(X0) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f53,plain,
! [X0] :
( ( ~ sP1(X0)
| ? [X4,X5,X6] :
( X5 != X6
& X4 != X6
& X4 != X5
& rtt(X0,X6)
& rtt(X0,X5)
& rtt(X0,X4) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rtt(X0,X3)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
| sP1(X0) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( ~ sP1(X0)
| ( sK7(X0) != sK8(X0)
& sK6(X0) != sK8(X0)
& sK6(X0) != sK7(X0)
& rtt(X0,sK8(X0))
& rtt(X0,sK7(X0))
& rtt(X0,sK6(X0)) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rtt(X0,X3)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
| sP1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0)),skolemize(X5,sK7(X0)),skolemize(X6,sK8(X0))],[f53]) ).
fof(f58,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| sP2(X0) )
& ( ~ sP2(X0)
| cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X0] :
( ~ sP2(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f84,plain,
! [X0] :
( ~ sP1(X0)
| sK6(X0) != sK8(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f86,plain,
! [X0] :
( ~ sP1(X0)
| rtt(X0,sK8(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f88,plain,
! [X0] :
( ~ sP1(X0)
| rtt(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f94,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f98,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[],[f16]) ).
tcf(c_59,plain,
! [X0: $i] :
( sP1(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_62,plain,
! [X0: $i] :
( sP0(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_64,plain,
! [X0: $i] :
( rtt(X0,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_66,plain,
! [X0: $i] :
( rtt(X0,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_68,plain,
! [X0: $i] :
( ~ sP1(X0)
| ( sK6(X0) != sK8(X0) ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_75,plain,
! [X0: $i] :
( sP2(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_78,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[],[f98]) ).
tcf(c_82,plain,
( sP2(i2003_11_14_17_20_29215)
| ~ cUnsatisfiable(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_83,plain,
( sP0(i2003_11_14_17_20_29215)
| ~ sP2(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_84,plain,
( sP1(i2003_11_14_17_20_29215)
| ~ sP2(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_96,plain,
( ~ sP1(i2003_11_14_17_20_29215)
| ( sK6(i2003_11_14_17_20_29215) != sK8(i2003_11_14_17_20_29215) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
fof(f43,definition,
! [X0] :
( sP0(X0)
<=> ! [X7,X8] :
( ~ rtt(X0,X8)
| ~ rtt(X0,X7)
| X7 = X8 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f44,definition,
! [X0] :
( sP1(X0)
<=> ? [X1,X2,X3] :
( X2 != X3
& X1 != X3
& X1 != X2
& rtt(X0,X3)
& rtt(X0,X2)
& rtt(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f45,definition,
! [X0] :
( sP2(X0)
<=> ( sP0(X0)
& ! [X5,X6] :
( ~ rtt(X0,X6)
| ~ rtt(X0,X5)
| X5 = X6 )
& ! [X4] :
( ~ rtt(X0,X4)
| ca(X4) )
& sP1(X0) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP2(X0) ),
inference(definition_folding,[],[f39,f45,f44,f43]) ).
fof(f55,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X7,X8] :
( ~ rtt(X0,X8)
| ~ rtt(X0,X7)
| X7 = X8 ) )
& ( ? [X7,X8] :
( rtt(X0,X8)
& rtt(X0,X7)
& X7 != X8 )
| sP0(X0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f56,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X3,X4] :
( ~ rtt(X0,X4)
| ~ rtt(X0,X3)
| X3 = X4 ) )
& ( ? [X1,X2] :
( rtt(X0,X2)
& rtt(X0,X1)
& X1 != X2 )
| sP0(X0) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ( ~ sP0(X0)
| ! [X3,X4] :
( ~ rtt(X0,X4)
| ~ rtt(X0,X3)
| X3 = X4 ) )
& ( ( rtt(X0,sK10(X0))
& rtt(X0,sK9(X0))
& sK9(X0) != sK10(X0) )
| sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X1,sK9(X0)),skolemize(X2,sK10(X0))],[f56]) ).
fof(f90,plain,
! [X3,X0,X4] :
( ~ sP0(X0)
| ~ rtt(X0,X4)
| ~ rtt(X0,X3)
| X3 = X4 ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ sP0(X0)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_3447,plain,
! [X0: $i,X1: $i] :
( ( sK6(X0) = X1 )
| ~ sP0(X0)
| ~ sP1(X0)
| ~ rtt(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_73]) ).
tcf(c_3517,plain,
! [X0: $i] :
( ( sK6(X0) = sK8(X0) )
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(superposition,[status(thm)],[c_66,c_3447]) ).
tcf(c_3526,plain,
( ( sK6(i2003_11_14_17_20_29215) = sK8(i2003_11_14_17_20_29215) )
| ~ sP0(i2003_11_14_17_20_29215)
| ~ sP1(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_3517]) ).
tcf(c_3527,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3526,c_96,c_84,c_83,c_82,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 19:23:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 0.44/1.30 % SZS status Started for theBenchmark.p
% 0.44/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 0.44/1.30
% 0.44/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/1.30
% 0.44/1.30 % ------ iProver source info
% 0.44/1.30
% 0.44/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/1.30 % git: non_committed_changes: false
% 0.44/1.30
% 0.44/1.30 % ------ Parsing...
% 0.44/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/1.30
% 0.44/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.44/1.30
% 0.44/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.44/1.30
% 0.44/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.44/1.30 % ------ Proving...
% 0.44/1.30 % ------ Problem Properties
% 0.44/1.30
% 0.44/1.30 %
% 0.44/1.30 % clauses 22
% 0.44/1.30 % conjectures 0
% 0.44/1.30 % EPR 7
% 0.44/1.30 % Horn 14
% 0.44/1.30 % unary 1
% 0.44/1.30 % binary 11
% 0.44/1.30 % lits 71
% 2.13/1.30 % lits eq 11
% 2.13/1.30 % fd_pure 0
% 2.13/1.30 % fd_pseudo 0
% 2.13/1.30 % fd_cond 0
% 2.13/1.30 % fd_pseudo_cond 3
% 2.13/1.30 % AC symbols 0
% 2.13/1.30
% 2.13/1.30 % ------ Schedule dynamic 5 is on
% 2.13/1.30
% 2.13/1.30 % ------ no conjectures: strip conj schedule
% 2.13/1.30
% 2.13/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.13/1.30
% 2.13/1.30
% 2.13/1.30 % ------
% 2.13/1.30 % Current options:
% 2.13/1.30 % ------
% 2.13/1.30
% 2.13/1.30
% 2.13/1.30 %
% 2.13/1.30
% 2.13/1.30 % ------ Proving...
% 2.13/1.30 %
% 2.13/1.30
% 2.13/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.13/1.30
% 2.13/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.30
% 2.13/1.30
%------------------------------------------------------------------------------