%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS106+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 : n019.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 01:54:10 PM UTC 2026
% Result : Unsatisfiable 1.84s 1.27s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 7 unt; 0 def)
% Number of atoms : 217 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 256 ( 109 ~; 96 |; 42 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 137 ( 0 sgn 116 !; 21 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( cp1xcomp(X1)
& rf2(X0,X1) )
& ? [X1] :
( cp1(X1)
& rf1(X0,X1) )
& ? [X1] :
( cp2(X1)
& rf3(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f20,axiom,
! [X0] :
( cp1(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f21,axiom,
! [X0] :
( cp1xcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( rf1(X0,X2)
& rf1(X0,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( rf2(X0,X2)
& rf2(X0,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f25,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f26,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f27,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f28,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X3] :
( cp1xcomp(X3)
& rf2(X0,X3) )
& ? [X2] :
( cp1(X2)
& rf1(X0,X2) )
& ? [X1] :
( cp2(X1)
& rf3(X0,X1) ) ) ),
inference(rectify,[],[f19]) ).
fof(f61,plain,
! [X0] :
( cp1(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ rf1(X0,X2)
| ~ rf1(X0,X1)
| X1 = X2 ),
inference(ennf_transformation,[],[f22]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ rf1(X0,X2)
| ~ rf1(X0,X1)
| X1 = X2 ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ rf2(X0,X2)
| ~ rf2(X0,X1)
| X1 = X2 ),
inference(ennf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ rf2(X0,X2)
| ~ rf2(X0,X1)
| X1 = X2 ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( ~ rf3(X0,X1)
| rf1(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1] :
( ~ rf3(X0,X1)
| rf2(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X3] :
( cp1xcomp(X3)
& rf2(X0,X3) )
& ? [X2] :
( cp1(X2)
& rf1(X0,X2) )
& ? [X1] :
( cp2(X1)
& rf3(X0,X1) ) ) )
& ( ! [X3] :
( ~ cp1xcomp(X3)
| ~ rf2(X0,X3) )
| ! [X2] :
( ~ cp1(X2)
| ~ rf1(X0,X2) )
| ! [X1] :
( ~ cp2(X1)
| ~ rf3(X0,X1) )
| cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X3] :
( cp1xcomp(X3)
& rf2(X0,X3) )
& ? [X2] :
( cp1(X2)
& rf1(X0,X2) )
& ? [X1] :
( cp2(X1)
& rf3(X0,X1) ) ) )
& ( ! [X3] :
( ~ cp1xcomp(X3)
| ~ rf2(X0,X3) )
| ! [X2] :
( ~ cp1(X2)
| ~ rf1(X0,X2) )
| ! [X1] :
( ~ cp2(X1)
| ~ rf3(X0,X1) )
| cUnsatisfiable(X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( ? [X6] :
( cp1xcomp(X6)
& rf2(X0,X6) )
& ? [X5] :
( cp1(X5)
& rf1(X0,X5) )
& ? [X4] :
( cp2(X4)
& rf3(X0,X4) ) ) )
& ( ! [X3] :
( ~ cp1xcomp(X3)
| ~ rf2(X0,X3) )
| ! [X2] :
( ~ cp1(X2)
| ~ rf1(X0,X2) )
| ! [X1] :
( ~ cp2(X1)
| ~ rf3(X0,X1) )
| cUnsatisfiable(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ( ~ cUnsatisfiable(X0)
| ( cp1xcomp(sK2(X0))
& rf2(X0,sK2(X0))
& cp1(sK1(X0))
& rf1(X0,sK1(X0))
& cp2(sK0(X0))
& rf3(X0,sK0(X0)) ) )
& ( ! [X3] :
( ~ cp1xcomp(X3)
| ~ rf2(X0,X3) )
| ! [X2] :
( ~ cp1(X2)
| ~ rf1(X0,X2) )
| ! [X1] :
( ~ cp2(X1)
| ~ rf3(X0,X1) )
| cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X4,sK0(X0)),skolemize(X5,sK1(X0)),skolemize(X6,sK2(X0))],[f73]) ).
fof(f75,plain,
! [X0] :
( ( ~ cp1(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| cp1(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( ~ cp1(X0)
| ! [X2] : ~ ra_Px1(X0,X2) )
& ( ? [X1] : ra_Px1(X0,X1)
| cp1(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ( ~ cp1(X0)
| ! [X2] : ~ ra_Px1(X0,X2) )
& ( ra_Px1(X0,sK3(X0))
| cp1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( ~ cp1xcomp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| cp1xcomp(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f79,plain,
! [X0] :
( ( ~ cp1xcomp(X0)
| ? [X2] : ra_Px1(X0,X2) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| cp1xcomp(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( ~ cp1xcomp(X0)
| ra_Px1(X0,sK4(X0)) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| cp1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f79]) ).
fof(f101,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cp1xcomp(sK2(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rf2(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cp1(sK1(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rf1(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f106,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rf3(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f108,plain,
! [X2,X0] :
( ~ cp1(X0)
| ~ ra_Px1(X0,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f110,plain,
! [X0] :
( ~ cp1xcomp(X0)
| ra_Px1(X0,sK4(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ rf1(X0,X2)
| ~ rf1(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ rf2(X0,X2)
| ~ rf2(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[],[f25]) ).
fof(f116,plain,
! [X0,X1] :
( ~ rf3(X0,X1)
| rf1(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( ~ rf3(X0,X1)
| rf2(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,plain,
! [X0: $i] :
( rf3(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_56,plain,
! [X0: $i] :
( rf1(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_57,plain,
! [X0: $i] :
( cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_58,plain,
! [X0: $i] :
( rf2(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_59,plain,
! [X0: $i] :
( cp1xcomp(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ~ cp1(X0)
| ~ ra_Px1(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_63,plain,
! [X0: $i] :
( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ rf1(X0,X2)
| ~ rf1(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ rf2(X0,X2)
| ~ rf2(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_67,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[],[f115]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ~ cp1(X0)
| ~ ra_Px1(X0,X1) ),
inference(renaming,[status(thm)],[c_109]) ).
tcf(c_117,plain,
! [X0: $i] :
( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ cp1xcomp(X1)
| ~ cp1(X0)
| ( X0 != X1 )
| ( sK4(X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_110,c_117]) ).
tcf(c_413,plain,
! [X0: $i] :
( ~ cp1xcomp(X0)
| ~ cp1(X0) ),
inference(unflattening,[status(thm)],[c_412]) ).
tcf(c_571,plain,
! [X0: $i] :
( ~ cp1(X0)
| ~ cp1xcomp(X0) ),
inference(prop_impl_just,[status(thm)],[c_413]) ).
tcf(c_572,plain,
! [X0: $i] :
( ~ cp1xcomp(X0)
| ~ cp1(X0) ),
inference(renaming,[status(thm)],[c_571]) ).
tcf(c_1321,plain,
! [X0: $i] :
( ~ cUnsatisfiable(X0)
| ~ cp1xcomp(sK1(X0)) ),
inference(superposition,[status(thm)],[c_57,c_572]) ).
tcf(c_1355,plain,
! [X0: $i] :
( rf1(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_54,c_68]) ).
tcf(c_1363,plain,
! [X0: $i] :
( rf2(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_54,c_69]) ).
tcf(c_1373,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0) = X1 )
| ~ cUnsatisfiable(X0)
| ~ rf1(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_64]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i] :
( ( sK2(X0) = X1 )
| ~ cUnsatisfiable(X0)
| ~ rf2(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_65]) ).
tcf(c_1430,plain,
! [X0: $i] :
( ( sK0(X0) = sK1(X0) )
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_1355,c_1373]) ).
tcf(c_1438,plain,
sK0(i2003_11_14_17_20_57644) = sK1(i2003_11_14_17_20_57644),
inference(superposition,[status(thm)],[c_67,c_1430]) ).
tcf(c_1439,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_57644)
| ~ cp1xcomp(sK0(i2003_11_14_17_20_57644)) ),
inference(superposition,[status(thm)],[c_1438,c_1321]) ).
tcf(c_1444,plain,
~ cp1xcomp(sK0(i2003_11_14_17_20_57644)),
inference(forward_subsumption_resolution,[status(thm)],[c_1439,c_67]) ).
tcf(c_1466,plain,
! [X0: $i] :
( ( sK0(X0) = sK2(X0) )
| ~ cUnsatisfiable(X0) ),
inference(superposition,[status(thm)],[c_1363,c_1384]) ).
tcf(c_1498,plain,
sK0(i2003_11_14_17_20_57644) = sK2(i2003_11_14_17_20_57644),
inference(superposition,[status(thm)],[c_67,c_1466]) ).
tcf(c_1500,plain,
( cp1xcomp(sK0(i2003_11_14_17_20_57644))
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(superposition,[status(thm)],[c_1498,c_59]) ).
tcf(c_1501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1500,c_1444,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 19:24:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.84/1.27 % SZS status Started for theBenchmark.p
% 1.84/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/1.27
% 1.84/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/1.27
% 1.84/1.27 % ------ iProver source info
% 1.84/1.27
% 1.84/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/1.27 % git: non_committed_changes: false
% 1.84/1.27
% 1.84/1.27 % ------ Parsing...
% 1.84/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/1.27
% 1.84/1.27 % ------ 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: 3 0s sf_e pe_s pe_e %
% 1.84/1.27
% 1.84/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/1.27
% 1.84/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/1.27 % ------ Proving...
% 1.84/1.27 % ------ Problem Properties
% 1.84/1.27
% 1.84/1.27 %
% 1.84/1.27 % clauses 14
% 1.84/1.27 % conjectures 0
% 1.84/1.27 % EPR 8
% 1.84/1.27 % Horn 13
% 1.84/1.27 % unary 1
% 1.84/1.27 % binary 9
% 1.84/1.27 % lits 35
% 1.84/1.27 % lits eq 3
% 1.84/1.27 % fd_pure 0
% 1.84/1.27 % fd_pseudo 0
% 1.84/1.27 % fd_cond 0
% 1.84/1.27 % fd_pseudo_cond 3
% 1.84/1.27 % AC symbols 0
% 1.84/1.27
% 1.84/1.27 % ------ Schedule dynamic 5 is on
% 1.84/1.27
% 1.84/1.27 % ------ no conjectures: strip conj schedule
% 1.84/1.27
% 1.84/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/1.27
% 1.84/1.27
% 1.84/1.27 % ------
% 1.84/1.27 % Current options:
% 1.84/1.27 % ------
% 1.84/1.27
% 1.84/1.27
% 1.84/1.27 %
% 1.84/1.27
% 1.84/1.27 % ------ Proving...
% 1.84/1.27 %
% 1.84/1.27
% 1.84/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/1.27
% 1.84/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.27
% 1.84/1.27
%------------------------------------------------------------------------------