%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV089+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 03:16:23 PM UTC 2026
% Result : Theorem 0.74s 1.21s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 31 unt; 0 def)
% Number of atoms : 248 ( 202 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 270 ( 108 ~; 140 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 115 ( 0 sgn 115 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',totality) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(f45,axiom,
! [X0,X1,X2,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel3_update_1) ).
fof(f46,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( a_select3(X4,X2,X3) = X5
& X1 = X3
& X0 != X2 )
=> a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel3_update_2) ).
fof(f48,axiom,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel2_update_1) ).
fof(f49,axiom,
! [X0,X1,X2,X3,X4] :
( ( a_select2(X2,X1) = X3
& X0 != X1 )
=> a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel2_update_2) ).
fof(f53,conjecture,
( true
=> ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0001) ).
fof(f54,negated_conjecture,
~ ( true
=> ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,axiom,
gt(n5,n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
fof(f64,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
fof(f65,axiom,
gt(n2,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
fof(f69,axiom,
gt(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
fof(f74,axiom,
gt(n4,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
fof(f75,axiom,
gt(n5,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
fof(f88,plain,
~ ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) = use ),
inference(pure_predicate_removal,[],[f54]) ).
fof(f90,plain,
( use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(X2,X1) != X3
| X0 = X1
| a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
inference(ennf_transformation,[],[f49]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(X2,X1) != X3
| X0 = X1
| a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
inference(flattening,[],[f95]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2
| a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
inference(ennf_transformation,[],[f46]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2
| a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
inference(flattening,[],[f99]) ).
fof(f128,plain,
( use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0)
| use != a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X4] :
( a_select2(X2,X1) != X3
| X0 = X1
| a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
inference(cnf_transformation,[],[f96]) ).
fof(f134,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f48]) ).
fof(f140,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2
| a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
inference(cnf_transformation,[],[f100]) ).
fof(f141,plain,
! [X2,X3,X0,X1] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(cnf_transformation,[],[f45]) ).
fof(f154,plain,
gt(n2,n1),
inference(cnf_transformation,[],[f69]) ).
fof(f157,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f64]) ).
fof(f162,plain,
gt(n2,n0),
inference(cnf_transformation,[],[f65]) ).
fof(f166,plain,
gt(n5,n3),
inference(cnf_transformation,[],[f75]) ).
fof(f167,plain,
gt(n4,n3),
inference(cnf_transformation,[],[f74]) ).
fof(f175,plain,
gt(n5,n4),
inference(cnf_transformation,[],[f55]) ).
fof(f194,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f196,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f225,plain,
! [X2,X0,X1,X4] :
( X0 = X1
| a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1) ),
inference(equality_resolution,[],[f133]) ).
fof(f226,plain,
! [X2,X3,X0,X6,X4,X5] :
( a_select3(X4,X2,X3) != X5
| X0 = X2
| a_select3(tptp_update3(X4,X0,X3,X6),X2,X3) = X5 ),
inference(equality_resolution,[],[f140]) ).
fof(f227,plain,
! [X2,X3,X0,X6,X4] :
( X0 = X2
| a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3) ),
inference(equality_resolution,[],[f226]) ).
tcf(c_49,negated_conjecture,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( a_select2(tptp_update2(X0,X1,X2),X3) = a_select2(X0,X3) ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f134]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( a_select3(tptp_update3(X0,X1,X2,X3),X4,X2) = a_select3(X0,X4,X2) ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(cnf_transformation,[],[f141]) ).
tcf(c_75,plain,
gt(n2,n1),
inference(cnf_transformation,[],[f154]) ).
tcf(c_78,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_83,plain,
gt(n2,n0),
inference(cnf_transformation,[],[f162]) ).
tcf(c_87,plain,
gt(n5,n3),
inference(cnf_transformation,[],[f166]) ).
tcf(c_88,plain,
gt(n4,n3),
inference(cnf_transformation,[],[f167]) ).
tcf(c_96,plain,
gt(n5,n4),
inference(cnf_transformation,[],[f175]) ).
tcf(c_115,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f194]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| gt(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_124,plain,
~ gt(n0,n0),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_130,plain,
( gt(n0,n0)
| ( n0 = n0 ) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_350,plain,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_55]) ).
tcf(c_359,plain,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_350,c_62]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( gt(X0,X2)
| ~ gt(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2678,plain,
! [X0: $i,X1: $i] :
( gt(X0,X1)
| ~ gt(n1,n0)
| ( X1 != n0 )
| ( X0 != n1 ) ),
inference(instantiation,[status(thm)],[c_1006]) ).
tcf(c_2679,plain,
( gt(n0,n0)
| ~ gt(n1,n0)
| ( n0 != n1 )
| ( n0 != n0 ) ),
inference(instantiation,[status(thm)],[c_2678]) ).
tcf(c_2686,plain,
! [X0: $i,X1: $i] :
( gt(X0,X1)
| ~ gt(n2,n0)
| ( X1 != n0 )
| ( X0 != n2 ) ),
inference(instantiation,[status(thm)],[c_1006]) ).
tcf(c_2687,plain,
( gt(n0,n0)
| ~ gt(n2,n0)
| ( n0 != n0 )
| ( n0 != n2 ) ),
inference(instantiation,[status(thm)],[c_2686]) ).
tcf(c_3616,plain,
( ( n2 = n0 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use ) ),
inference(superposition,[status(thm)],[c_61,c_359]) ).
tcf(c_3739,plain,
! [X0: $i,X1: $i] :
( ( X0 = n2 )
| ( n2 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_999]) ).
tcf(c_3740,plain,
( ( n0 = n2 )
| ( n0 != n0 )
| ( n2 != n0 ) ),
inference(instantiation,[status(thm)],[c_3739]) ).
tcf(c_3764,plain,
( ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use ) ),
inference(global_subsumption_just,[status(thm)],[c_3616,c_83,c_124,c_130,c_2687,c_3616,c_3740]) ).
tcf(c_3765,plain,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use ) ),
inference(renaming,[status(thm)],[c_3764]) ).
tcf(c_3774,plain,
( ( n0 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n1,n0) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use ) ),
inference(superposition,[status(thm)],[c_61,c_3765]) ).
tcf(c_3775,plain,
( ( n0 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use ) ),
inference(ground_joinability,[status(thm)],[c_3774,c_62]) ).
tcf(c_3780,plain,
( ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use ) ),
inference(global_subsumption_just,[status(thm)],[c_3775,c_78,c_124,c_130,c_2679,c_3775]) ).
tcf(c_3781,plain,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use ) ),
inference(renaming,[status(thm)],[c_3780]) ).
tcf(c_3788,plain,
( ( n2 = n1 )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n2,n0) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use ) ),
inference(superposition,[status(thm)],[c_61,c_3781]) ).
tcf(c_3801,plain,
( ( n5 = n3 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n2,n0) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use ) ),
inference(superposition,[status(thm)],[c_54,c_3788]) ).
tcf(c_3817,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n4) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n2,n0) != use ) ),
inference(superposition,[status(thm)],[c_54,c_3801]) ).
tcf(c_3818,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n2,n0) != use ) ),
inference(ground_joinability,[status(thm)],[c_3817,c_55]) ).
tcf(c_3834,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 )
| ( n2 = n0 )
| ( a_select3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n2,n0) != use )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use ) ),
inference(superposition,[status(thm)],[c_61,c_3818]) ).
tcf(c_3835,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 )
| ( n2 = n0 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use ) ),
inference(ground_joinability,[status(thm)],[c_3834,c_62]) ).
tcf(c_3841,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use ) ),
inference(global_subsumption_just,[status(thm)],[c_3835,c_83,c_124,c_130,c_2687,c_3740,c_3835]) ).
tcf(c_3851,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n5 = n4 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n5) != use ) ),
inference(superposition,[status(thm)],[c_54,c_3841]) ).
tcf(c_3867,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n5 = n4 )
| ( n2 = n1 )
| ( a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n5) != use ) ),
inference(superposition,[status(thm)],[c_54,c_3851]) ).
tcf(c_3868,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n5 = n4 )
| ( n2 = n1 ) ),
inference(ground_joinability,[status(thm)],[c_3867,c_55]) ).
tcf(c_3906,plain,
( gt(n4,n4)
| ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 ) ),
inference(superposition,[status(thm)],[c_3868,c_96]) ).
tcf(c_3910,plain,
( ( n4 = n3 )
| ( n5 = n3 )
| ( n2 = n1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3906,c_115]) ).
tcf(c_4347,plain,
( gt(n3,n3)
| ( n4 = n3 )
| ( n2 = n1 ) ),
inference(superposition,[status(thm)],[c_3910,c_87]) ).
tcf(c_4350,plain,
( ( n4 = n3 )
| ( n2 = n1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4347,c_115]) ).
tcf(c_4378,plain,
( gt(n3,n3)
| ( n2 = n1 ) ),
inference(superposition,[status(thm)],[c_4350,c_88]) ).
tcf(c_4381,plain,
n2 = n1,
inference(forward_subsumption_resolution,[status(thm)],[c_4378,c_115]) ).
tcf(c_4426,plain,
gt(n1,n1),
inference(demodulation,[status(thm)],[c_75,c_4381]) ).
tcf(c_4431,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4426,c_115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV089+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 18:34:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.74/1.21 % SZS status Started for theBenchmark.p
% 0.74/1.21 % SZS status Theorem for theBenchmark.p
% 0.74/1.21
% 0.74/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.74/1.21
% 0.74/1.21 % ------ iProver source info
% 0.74/1.21
% 0.74/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.74/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.74/1.21 % git: non_committed_changes: false
% 0.74/1.21
% 0.74/1.21 % ------ Parsing...
% 0.74/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.74/1.21
% 0.74/1.21 % ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.74/1.21
% 0.74/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.74/1.21
% 0.74/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.74/1.21 % ------ Proving...
% 0.74/1.21 % ------ Problem Properties
% 0.74/1.21
% 0.74/1.21 %
% 0.74/1.21 % clauses 74
% 0.74/1.21 % conjectures 0
% 0.74/1.21 % EPR 34
% 0.74/1.21 % Horn 55
% 0.74/1.21 % unary 41
% 0.74/1.21 % binary 9
% 0.74/1.21 % lits 190
% 0.74/1.21 % lits eq 64
% 0.74/1.21 % fd_pure 0
% 0.74/1.21 % fd_pseudo 0
% 0.74/1.21 % fd_cond 6
% 0.74/1.21 % fd_pseudo_cond 4
% 0.74/1.21 % AC symbols 0
% 0.74/1.21
% 0.74/1.21 % ------ Schedule dynamic 5 is on
% 0.74/1.21
% 0.74/1.21 % ------ no conjectures: strip conj schedule
% 0.74/1.21
% 0.74/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.74/1.21
% 0.74/1.21
% 0.74/1.21 % ------
% 0.74/1.21 % Current options:
% 0.74/1.21 % ------
% 0.74/1.21
% 0.74/1.21
% 0.74/1.21 %
% 0.74/1.21
% 0.74/1.21 % ------ Proving...
% 0.74/1.21 %
% 0.74/1.21
% 0.74/1.21 % SZS status Theorem for theBenchmark.p
% 0.74/1.21
% 0.74/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.74/1.21
% 0.74/1.21
%------------------------------------------------------------------------------