TSTP Solution File: KRS099+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : KRS099+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:33:37 EDT 2024
% Result : Unsatisfiable 2.23s 1.15s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 4 unt; 0 def)
% Number of atoms : 297 ( 75 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 390 ( 141 ~; 111 |; 120 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% 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 : 138 ( 0 sgn 84 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X3] :
( cUnsatisfiable(X3)
<=> ( ! [X4,X5] :
( ( rtt(X3,X5)
& rtt(X3,X4) )
=> X4 = X5 )
& ! [X4,X5] :
( ( rtt(X3,X5)
& rtt(X3,X4) )
=> X4 = X5 )
& ! [X7] :
( rtt(X3,X7)
=> ca(X7) )
& ? [X4,X5,X6] :
( X5 != X6
& X4 != X6
& X4 != X5
& rtt(X3,X6)
& rtt(X3,X5)
& rtt(X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f19,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1,X2] :
( ( rtt(X0,X2)
& rtt(X0,X1) )
=> X1 = X2 )
& ! [X3,X4] :
( ( rtt(X0,X4)
& rtt(X0,X3) )
=> X3 = X4 )
& ! [X5] :
( rtt(X0,X5)
=> ca(X5) )
& ? [X6,X7,X8] :
( X7 != X8
& X6 != X8
& X6 != X7
& rtt(X0,X8)
& rtt(X0,X7)
& rtt(X0,X6) ) ) ),
inference(rectify,[],[f13]) ).
fof(f42,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) )
& ! [X5] :
( ca(X5)
| ~ rtt(X0,X5) )
& ? [X6,X7,X8] :
( X7 != X8
& X6 != X8
& X6 != X7
& rtt(X0,X8)
& rtt(X0,X7)
& rtt(X0,X6) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) )
& ! [X5] :
( ca(X5)
| ~ rtt(X0,X5) )
& ? [X6,X7,X8] :
( X7 != X8
& X6 != X8
& X6 != X7
& rtt(X0,X8)
& rtt(X0,X7)
& rtt(X0,X6) ) ) ),
inference(flattening,[],[f42]) ).
fof(f47,plain,
! [X0] :
( sP0(X0)
<=> ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f48,plain,
! [X0] :
( sP1(X0)
<=> ? [X6,X7,X8] :
( X7 != X8
& X6 != X8
& X6 != X7
& rtt(X0,X8)
& rtt(X0,X7)
& rtt(X0,X6) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f49,plain,
! [X0] :
( sP2(X0)
<=> ( ! [X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
& sP0(X0)
& ! [X5] :
( ca(X5)
| ~ rtt(X0,X5) )
& sP1(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f50,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP2(X0) ),
inference(definition_folding,[],[f43,f49,f48,f47]) ).
fof(f52,plain,
! [X0] :
( ( sP2(X0)
| ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) )
| ~ sP0(X0)
| ? [X5] :
( ~ ca(X5)
& rtt(X0,X5) )
| ~ sP1(X0) )
& ( ( ! [X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
& sP0(X0)
& ! [X5] :
( ca(X5)
| ~ rtt(X0,X5) )
& sP1(X0) )
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f53,plain,
! [X0] :
( ( sP2(X0)
| ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) )
| ~ sP0(X0)
| ? [X5] :
( ~ ca(X5)
& rtt(X0,X5) )
| ~ sP1(X0) )
& ( ( ! [X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) )
& sP0(X0)
& ! [X5] :
( ca(X5)
| ~ rtt(X0,X5) )
& sP1(X0) )
| ~ sP2(X0) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( sP2(X0)
| ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) )
| ~ sP0(X0)
| ? [X3] :
( ~ ca(X3)
& rtt(X0,X3) )
| ~ sP1(X0) )
& ( ( ! [X4,X5] :
( X4 = X5
| ~ rtt(X0,X5)
| ~ rtt(X0,X4) )
& sP0(X0)
& ! [X6] :
( ca(X6)
| ~ rtt(X0,X6) )
& sP1(X0) )
| ~ sP2(X0) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) )
=> ( sK3(X0) != sK4(X0)
& rtt(X0,sK4(X0))
& rtt(X0,sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ? [X3] :
( ~ ca(X3)
& rtt(X0,X3) )
=> ( ~ ca(sK5(X0))
& rtt(X0,sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0] :
( ( sP2(X0)
| ( sK3(X0) != sK4(X0)
& rtt(X0,sK4(X0))
& rtt(X0,sK3(X0)) )
| ~ sP0(X0)
| ( ~ ca(sK5(X0))
& rtt(X0,sK5(X0)) )
| ~ sP1(X0) )
& ( ( ! [X4,X5] :
( X4 = X5
| ~ rtt(X0,X5)
| ~ rtt(X0,X4) )
& sP0(X0)
& ! [X6] :
( ca(X6)
| ~ rtt(X0,X6) )
& sP1(X0) )
| ~ sP2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f54,f56,f55]) ).
fof(f58,plain,
! [X0] :
( ( sP1(X0)
| ! [X6,X7,X8] :
( X7 = X8
| X6 = X8
| X6 = X7
| ~ rtt(X0,X8)
| ~ rtt(X0,X7)
| ~ rtt(X0,X6) ) )
& ( ? [X6,X7,X8] :
( X7 != X8
& X6 != X8
& X6 != X7
& rtt(X0,X8)
& rtt(X0,X7)
& rtt(X0,X6) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f59,plain,
! [X0] :
( ( sP1(X0)
| ! [X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rtt(X0,X3)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) ) )
& ( ? [X4,X5,X6] :
( X5 != X6
& X4 != X6
& X4 != X5
& rtt(X0,X6)
& rtt(X0,X5)
& rtt(X0,X4) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ? [X4,X5,X6] :
( X5 != X6
& X4 != X6
& X4 != X5
& rtt(X0,X6)
& rtt(X0,X5)
& rtt(X0,X4) )
=> ( sK7(X0) != sK8(X0)
& sK6(X0) != sK8(X0)
& sK6(X0) != sK7(X0)
& rtt(X0,sK8(X0))
& rtt(X0,sK7(X0))
& rtt(X0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0] :
( ( sP1(X0)
| ! [X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rtt(X0,X3)
| ~ rtt(X0,X2)
| ~ rtt(X0,X1) ) )
& ( ( sK7(X0) != sK8(X0)
& sK6(X0) != sK8(X0)
& sK6(X0) != sK7(X0)
& rtt(X0,sK8(X0))
& rtt(X0,sK7(X0))
& rtt(X0,sK6(X0)) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f59,f60]) ).
fof(f62,plain,
! [X0] :
( ( sP0(X0)
| ? [X3,X4] :
( X3 != X4
& rtt(X0,X4)
& rtt(X0,X3) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& rtt(X0,X2)
& rtt(X0,X1) )
=> ( sK9(X0) != sK10(X0)
& rtt(X0,sK10(X0))
& rtt(X0,sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ( sP0(X0)
| ( sK9(X0) != sK10(X0)
& rtt(X0,sK10(X0))
& rtt(X0,sK9(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f63,f64]) ).
fof(f66,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ sP2(X0) )
& ( sP2(X0)
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f81,plain,
! [X0] :
( sP1(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f83,plain,
! [X0] :
( sP0(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f91,plain,
! [X0] :
( rtt(X0,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
! [X0] :
( rtt(X0,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
! [X0] :
( sK6(X0) != sK8(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f98,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ rtt(X0,X4)
| ~ rtt(X0,X3)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f102,plain,
! [X0] :
( sP2(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f106,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[],[f16]) ).
cnf(c_60,plain,
( ~ sP2(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_62,plain,
( ~ sP2(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_65,plain,
( sK8(X0) != sK6(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_67,plain,
( ~ sP1(X0)
| rtt(X0,sK8(X0)) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_69,plain,
( ~ sP1(X0)
| rtt(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_73,plain,
( ~ rtt(X0,X1)
| ~ rtt(X0,X2)
| ~ sP0(X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_75,plain,
( ~ cUnsatisfiable(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_78,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[],[f106]) ).
cnf(c_82,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| sP2(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_83,plain,
( ~ sP2(i2003_11_14_17_20_29215)
| sP1(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_84,plain,
( ~ sP2(i2003_11_14_17_20_29215)
| sP0(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_96,plain,
( sK8(i2003_11_14_17_20_29215) != sK6(i2003_11_14_17_20_29215)
| ~ sP1(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_3441,plain,
( ~ rtt(X0,X1)
| ~ sP0(X0)
| ~ sP1(X0)
| sK8(X0) = X1 ),
inference(superposition,[status(thm)],[c_67,c_73]) ).
cnf(c_3511,plain,
( ~ sP0(X0)
| ~ sP1(X0)
| sK8(X0) = sK6(X0) ),
inference(superposition,[status(thm)],[c_69,c_3441]) ).
cnf(c_3520,plain,
( ~ sP0(i2003_11_14_17_20_29215)
| ~ sP1(i2003_11_14_17_20_29215)
| sK8(i2003_11_14_17_20_29215) = sK6(i2003_11_14_17_20_29215) ),
inference(instantiation,[status(thm)],[c_3511]) ).
cnf(c_3521,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3520,c_96,c_84,c_83,c_82,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS099+1 : TPTP v8.1.2. Released v3.1.0.
% 0.14/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 22:51:01 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.23/1.15 % SZS status Started for theBenchmark.p
% 2.23/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 2.23/1.15
% 2.23/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.23/1.15
% 2.23/1.15 ------ iProver source info
% 2.23/1.15
% 2.23/1.15 git: date: 2024-05-02 19:28:25 +0000
% 2.23/1.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.23/1.15 git: non_committed_changes: false
% 2.23/1.15
% 2.23/1.15 ------ Parsing...
% 2.23/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.23/1.15
% 2.23/1.15 ------ 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
% 2.23/1.15
% 2.23/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.23/1.15
% 2.23/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.23/1.15 ------ Proving...
% 2.23/1.15 ------ Problem Properties
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15 clauses 22
% 2.23/1.15 conjectures 0
% 2.23/1.15 EPR 7
% 2.23/1.15 Horn 14
% 2.23/1.15 unary 1
% 2.23/1.15 binary 11
% 2.23/1.15 lits 71
% 2.23/1.15 lits eq 11
% 2.23/1.15 fd_pure 0
% 2.23/1.15 fd_pseudo 0
% 2.23/1.15 fd_cond 0
% 2.23/1.15 fd_pseudo_cond 3
% 2.23/1.15 AC symbols 0
% 2.23/1.15
% 2.23/1.15 ------ Schedule dynamic 5 is on
% 2.23/1.15
% 2.23/1.15 ------ no conjectures: strip conj schedule
% 2.23/1.15
% 2.23/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15 ------
% 2.23/1.15 Current options:
% 2.23/1.15 ------
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15 ------ Proving...
% 2.23/1.15
% 2.23/1.15
% 2.23/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 2.23/1.15
% 2.23/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.23/1.15
% 2.23/1.15
%------------------------------------------------------------------------------