%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS077+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 : 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 01:54:06 PM UTC 2026
% Result : Unsatisfiable 2.08s 1.27s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 6 unt; 1 def)
% Number of atoms : 232 ( 23 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 287 ( 109 ~; 101 |; 65 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 128 ( 0 sgn 103 !; 25 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X3] :
( cp(X3)
& rs(X0,X3) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( rinvS(X3,X4)
=> cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ( rr(X0,X2)
& rr(X0,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f16,axiom,
! [X0,X1] :
( rinvS(X0,X1)
<=> rs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f17,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f18,axiom,
! [X0,X1] :
( rs(X0,X1)
=> rr(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f19,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( rinvS(X3,X4)
=> cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ( rr(X0,X2)
& rr(X0,X1) )
=> X1 = X2 ) ) ),
inference(rectify,[],[f15]) ).
fof(f44,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( ~ rinvS(X3,X4)
| cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ~ rr(X0,X2)
| ~ rr(X0,X1)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( ~ rinvS(X3,X4)
| cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ~ rr(X0,X2)
| ~ rr(X0,X1)
| X1 = X2 ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ rs(X0,X1)
| rr(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f54,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| sP0(X0) )
& ( ~ sP0(X0)
| cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f55,plain,
! [X0,X1] :
( ( ~ rinvS(X0,X1)
| rs(X1,X0) )
& ( ~ rs(X1,X0)
| rinvS(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f84,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f87,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f88,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(cnf_transformation,[],[f17]) ).
fof(f89,plain,
! [X0,X1] :
( ~ rs(X0,X1)
| rr(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( rinvS(X1,X0)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_69,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(cnf_transformation,[],[f88]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( rr(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_74,plain,
( sP0(i2003_11_14_17_19_09372)
| ~ cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_91,plain,
! [X0: $i] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ~ rs(X0,X1)
| rr(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_70]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( rr(X0,X1)
| ~ rs(X0,X1) ),
inference(renaming,[status(thm)],[c_93]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( rinvS(X1,X0)
| ~ rs(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
fof(f47,definition,
! [X0] :
( sP0(X0)
<=> ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( ~ rinvS(X3,X4)
| cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ~ rr(X0,X2)
| ~ rr(X0,X1)
| X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f48,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f45,f47]) ).
fof(f50,plain,
! [X0] :
( ( ~ sP0(X0)
| ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( ~ rinvS(X3,X4)
| cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ~ rr(X0,X2)
| ~ rr(X0,X1)
| X1 = X2 ) ) )
& ( ! [X5] :
( ~ cp(X5)
| ~ rs(X0,X5) )
| cp(X0)
| ! [X3] :
( ? [X4] :
( rinvS(X3,X4)
& ~ cp(X4) )
| ~ rr(X0,X3) )
| ? [X1,X2] :
( rr(X0,X2)
& rr(X0,X1)
& X1 != X2 )
| sP0(X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ( ~ sP0(X0)
| ( ? [X5] :
( cp(X5)
& rs(X0,X5) )
& ~ cp(X0)
& ? [X3] :
( ! [X4] :
( ~ rinvS(X3,X4)
| cp(X4) )
& rr(X0,X3) )
& ! [X1,X2] :
( ~ rr(X0,X2)
| ~ rr(X0,X1)
| X1 = X2 ) ) )
& ( ! [X5] :
( ~ cp(X5)
| ~ rs(X0,X5) )
| cp(X0)
| ! [X3] :
( ? [X4] :
( rinvS(X3,X4)
& ~ cp(X4) )
| ~ rr(X0,X3) )
| ? [X1,X2] :
( rr(X0,X2)
& rr(X0,X1)
& X1 != X2 )
| sP0(X0) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( ~ sP0(X0)
| ( ? [X10] :
( cp(X10)
& rs(X0,X10) )
& ~ cp(X0)
& ? [X8] :
( ! [X9] :
( ~ rinvS(X8,X9)
| cp(X9) )
& rr(X0,X8) )
& ! [X6,X7] :
( ~ rr(X0,X7)
| ~ rr(X0,X6)
| X6 = X7 ) ) )
& ( ! [X5] :
( ~ cp(X5)
| ~ rs(X0,X5) )
| cp(X0)
| ! [X3] :
( ? [X4] :
( rinvS(X3,X4)
& ~ cp(X4) )
| ~ rr(X0,X3) )
| ? [X1,X2] :
( rr(X0,X2)
& rr(X0,X1)
& X1 != X2 )
| sP0(X0) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ( ~ sP0(X0)
| ( cp(sK5(X0))
& rs(X0,sK5(X0))
& ~ cp(X0)
& ! [X9] :
( ~ rinvS(sK4(X0),X9)
| cp(X9) )
& rr(X0,sK4(X0))
& ! [X6,X7] :
( ~ rr(X0,X7)
| ~ rr(X0,X6)
| X6 = X7 ) ) )
& ( ! [X5] :
( ~ cp(X5)
| ~ rs(X0,X5) )
| cp(X0)
| ! [X3] :
( ( rinvS(X3,sK3(X3))
& ~ cp(sK3(X3)) )
| ~ rr(X0,X3) )
| ( rr(X0,sK2(X0))
& rr(X0,sK1(X0))
& sK1(X0) != sK2(X0) )
| sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X4,sK3(X3)),skolemize(X8,sK4(X0)),skolemize(X10,sK5(X0))],[f52]) ).
fof(f73,plain,
! [X0] :
( ~ sP0(X0)
| rs(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f74,plain,
! [X0] :
( ~ sP0(X0)
| ~ cp(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f75,plain,
! [X0,X9] :
( ~ sP0(X0)
| ~ rinvS(sK4(X0),X9)
| cp(X9) ),
inference(cnf_transformation,[],[f53]) ).
fof(f76,plain,
! [X0] :
( ~ sP0(X0)
| rr(X0,sK4(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f77,plain,
! [X0,X6,X7] :
( ~ sP0(X0)
| ~ rr(X0,X7)
| ~ rr(X0,X6)
| X6 = X7 ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ sP0(X0)
| ~ rr(X0,X2)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_60,plain,
! [X0: $i] :
( rr(X0,sK4(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( cp(X1)
| ~ sP0(X0)
| ~ rinvS(sK4(X0),X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_62,plain,
! [X0: $i] :
( ~ cp(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_63,plain,
! [X0: $i] :
( rs(X0,sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_76,plain,
( ~ cp(i2003_11_14_17_19_09372)
| ~ sP0(i2003_11_14_17_19_09372) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_83,plain,
( cp(i2003_11_14_17_19_09372)
| ~ sP0(i2003_11_14_17_19_09372)
| ~ rinvS(sK4(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_97,plain,
! [X0: $i] :
( rr(X0,sK4(X0))
| ~ cUnsatisfiable(X0) ),
inference(prop_impl_just,[status(thm)],[c_66,c_60]) ).
tcf(c_101,plain,
! [X0: $i] :
( rs(X0,sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(prop_impl_just,[status(thm)],[c_66,c_63]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ cUnsatisfiable(X0)
| ~ rr(X0,X2)
| ~ rr(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_59,c_91]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i,X2: $i] :
( rr(X2,X1)
| ~ cUnsatisfiable(X0)
| ( X0 != X2 )
| ( sK5(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_94]) ).
tcf(c_827,plain,
! [X0: $i] :
( rr(X0,sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(unflattening,[status(thm)],[c_826]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i,X2: $i] :
( rinvS(X1,X2)
| ~ cUnsatisfiable(X0)
| ( X0 != X2 )
| ( sK5(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_107]) ).
tcf(c_836,plain,
! [X0: $i] :
( rinvS(sK5(X0),X0)
| ~ cUnsatisfiable(X0) ),
inference(unflattening,[status(thm)],[c_835]) ).
tcf(c_3958,plain,
! [X0: $i,X1: $i] :
( ( sK4(X0) = X1 )
| ~ cUnsatisfiable(X0)
| ~ rr(X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_164]) ).
tcf(c_3981,plain,
! [X0: $i] :
( ( sK4(X0) = sK5(X0) )
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_827,c_3958]) ).
tcf(c_4021,plain,
sK4(i2003_11_14_17_19_09372) = sK5(i2003_11_14_17_19_09372),
inference(superposition,[status(thm)],[c_69,c_3981]) ).
tcf(c_4023,plain,
( rinvS(sK4(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(superposition,[status(thm)],[c_4021,c_836]) ).
tcf(c_4028,plain,
rinvS(sK4(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(forward_subsumption_resolution,[status(thm)],[c_4023,c_69]) ).
tcf(c_4030,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4028,c_83,c_76,c_74,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS077+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.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 19:19:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 2.08/1.27 % SZS status Started for theBenchmark.p
% 2.08/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.08/1.27
% 2.08/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.27
% 2.08/1.27 % ------ iProver source info
% 2.08/1.27
% 2.08/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.27 % git: non_committed_changes: false
% 2.08/1.27
% 2.08/1.27 % ------ Parsing...
% 2.08/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.27
% 2.08/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.08/1.27
% 2.08/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.08/1.27
% 2.08/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.27 % ------ Proving...
% 2.08/1.27 % ------ Problem Properties
% 2.08/1.27
% 2.08/1.27 %
% 2.08/1.27 % clauses 15
% 2.08/1.27 % conjectures 0
% 2.08/1.27 % EPR 4
% 2.08/1.27 % Horn 9
% 2.08/1.27 % unary 1
% 2.08/1.27 % binary 6
% 2.08/1.27 % lits 62
% 2.08/1.27 % lits eq 3
% 2.08/1.27 % fd_pure 0
% 2.08/1.27 % fd_pseudo 0
% 2.08/1.27 % fd_cond 0
% 2.08/1.27 % fd_pseudo_cond 1
% 2.08/1.27 % AC symbols 0
% 2.08/1.27
% 2.08/1.27 % ------ Schedule dynamic 5 is on
% 2.08/1.27
% 2.08/1.27 % ------ no conjectures: strip conj schedule
% 2.08/1.27
% 2.08/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.08/1.27
% 2.08/1.27
% 2.08/1.27 % ------
% 2.08/1.27 % Current options:
% 2.08/1.27 % ------
% 2.08/1.27
% 2.08/1.27
% 2.08/1.27 %
% 2.08/1.27
% 2.08/1.27 % ------ Proving...
% 2.08/1.27 %
% 2.08/1.27
% 2.08/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.08/1.27
% 2.08/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.27
% 2.08/1.27
%------------------------------------------------------------------------------