%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA117-1 : TPTP v9.3.1. Released v9.3.0.
% 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 01:23:49 PM UTC 2026
% Result : Unsatisfiable 1.41s 6.42s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 20
% Syntax : Number of formulae : 127 ( 35 unt; 0 def)
% Number of atoms : 536 ( 292 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 577 ( 168 ~; 409 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( r(X1,X0)
| ~ r(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rsym) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ r(X1,X2)
| ~ r(X0,X2)
| ~ r(X0,X1)
| X1 = X2
| X0 = X2
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rno3cl) ).
fof(f3,axiom,
! [X2,X0,X1] :
( r(X1,X2)
| r(X0,X2)
| r(X0,X1)
| X1 = X2
| X0 = X2
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rno3acl) ).
fof(f4,axiom,
v0 != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv1) ).
fof(f5,axiom,
v0 != v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv2) ).
fof(f6,axiom,
v1 != v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv2) ).
fof(f7,axiom,
v0 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv3) ).
fof(f8,axiom,
v1 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv3) ).
fof(f9,axiom,
v2 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv3) ).
fof(f10,axiom,
v0 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv4) ).
fof(f11,axiom,
v1 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv4) ).
fof(f12,axiom,
v2 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv4) ).
fof(f13,axiom,
v3 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3nv4) ).
fof(f14,axiom,
v0 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv5) ).
fof(f15,axiom,
v1 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv5) ).
fof(f16,axiom,
v2 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv5) ).
fof(f17,axiom,
v3 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3nv5) ).
fof(f18,axiom,
v4 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4nv5) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( r(X1,X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ r(X1,X2)
| ~ r(X0,X2)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( r(X1,X2)
| r(X0,X2)
| r(X0,X1)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
v0 != v1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
v0 != v2,
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
v1 != v2,
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,plain,
v0 != v3,
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
v1 != v3,
inference(cnf_transformation,[],[f8]) ).
tcf(c_75,plain,
v2 != v3,
inference(cnf_transformation,[],[f9]) ).
tcf(c_76,plain,
v0 != v4,
inference(cnf_transformation,[],[f10]) ).
tcf(c_77,plain,
v1 != v4,
inference(cnf_transformation,[],[f11]) ).
tcf(c_78,plain,
v2 != v4,
inference(cnf_transformation,[],[f12]) ).
tcf(c_79,plain,
v3 != v4,
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,plain,
v0 != v5,
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,plain,
v1 != v5,
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,plain,
v2 != v5,
inference(cnf_transformation,[],[f16]) ).
tcf(c_83,plain,
v3 != v5,
inference(cnf_transformation,[],[f17]) ).
tcf(c_84,plain,
v4 != v5,
inference(cnf_transformation,[],[f18]) ).
tcf(c_152,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_155,plain,
v0 = v0,
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_299,plain,
! [X0: $i] :
( ( v0 = v1 )
| ( v1 != X0 )
| ( v0 != X0 ) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_300,plain,
( ( v0 = v1 )
| ( v1 != v0 )
| ( v0 != v0 ) ),
inference(instantiation,[status(thm)],[c_299]) ).
tcf(c_301,plain,
! [X0: $i] :
( ( v0 = v2 )
| ( v2 != X0 )
| ( v0 != X0 ) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_302,plain,
( ( v0 = v2 )
| ( v2 != v0 )
| ( v0 != v0 ) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_307,plain,
! [X0: $i] :
( ( v1 = v3 )
| ( v3 != X0 )
| ( v1 != X0 ) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_309,plain,
! [X0: $i] :
( ( v2 = v3 )
| ( v3 != X0 )
| ( v2 != X0 ) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_339,plain,
! [X0: $i] :
( ( v0 = v2 )
| ( X0 = v2 )
| ( X0 = v0 )
| ~ r(v0,v2)
| ~ r(X0,v2)
| ~ r(X0,v0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_340,plain,
! [X0: $i] :
( ( v1 = v2 )
| ( X0 = v2 )
| ( X0 = v1 )
| ~ r(v1,v2)
| ~ r(X0,v2)
| ~ r(X0,v1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_341,plain,
( ( v1 = v2 )
| ( v0 = v2 )
| ( v0 = v1 )
| ~ r(v1,v2)
| ~ r(v0,v2)
| ~ r(v0,v1) ),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_347,plain,
! [X0: $i] :
( ( v0 = v4 )
| ( X0 = v4 )
| ( X0 = v0 )
| ~ r(v0,v4)
| ~ r(X0,v4)
| ~ r(X0,v0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_348,plain,
! [X0: $i] :
( ( v1 = v4 )
| ( X0 = v4 )
| ( X0 = v1 )
| ~ r(v1,v4)
| ~ r(X0,v4)
| ~ r(X0,v1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_349,plain,
( ( v1 = v4 )
| ( v0 = v4 )
| ( v0 = v1 )
| ~ r(v1,v4)
| ~ r(v0,v4)
| ~ r(v0,v1) ),
inference(instantiation,[status(thm)],[c_348]) ).
tcf(c_350,plain,
! [X0: $i] :
( ( v2 = v4 )
| ( X0 = v4 )
| ( X0 = v2 )
| ~ r(v2,v4)
| ~ r(X0,v4)
| ~ r(X0,v2) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_351,plain,
( ( v2 = v4 )
| ( v0 = v4 )
| ( v0 = v2 )
| ~ r(v2,v4)
| ~ r(v0,v4)
| ~ r(v0,v2) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_352,plain,
! [X0: $i] :
( ( v3 = v4 )
| ( X0 = v4 )
| ( X0 = v3 )
| ~ r(v3,v4)
| ~ r(X0,v4)
| ~ r(X0,v3) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_353,plain,
( ( v3 = v4 )
| ( v0 = v4 )
| ( v0 = v3 )
| ~ r(v3,v4)
| ~ r(v0,v4)
| ~ r(v0,v3) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_355,plain,
! [X0: $i] :
( ( v1 = v5 )
| ( X0 = v5 )
| ( X0 = v1 )
| ~ r(v1,v5)
| ~ r(X0,v5)
| ~ r(X0,v1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_356,plain,
( ( v1 = v5 )
| ( v0 = v5 )
| ( v0 = v1 )
| ~ r(v1,v5)
| ~ r(v0,v5)
| ~ r(v0,v1) ),
inference(instantiation,[status(thm)],[c_355]) ).
tcf(c_357,plain,
! [X0: $i] :
( ( v2 = v5 )
| ( X0 = v5 )
| ( X0 = v2 )
| ~ r(v2,v5)
| ~ r(X0,v5)
| ~ r(X0,v2) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_358,plain,
( ( v2 = v5 )
| ( v0 = v5 )
| ( v0 = v2 )
| ~ r(v2,v5)
| ~ r(v0,v5)
| ~ r(v0,v2) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_359,plain,
! [X0: $i] :
( ( v3 = v5 )
| ( X0 = v5 )
| ( X0 = v3 )
| ~ r(v3,v5)
| ~ r(X0,v5)
| ~ r(X0,v3) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_360,plain,
( ( v3 = v5 )
| ( v0 = v5 )
| ( v0 = v3 )
| ~ r(v3,v5)
| ~ r(v0,v5)
| ~ r(v0,v3) ),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_361,plain,
! [X0: $i] :
( ( v4 = v5 )
| ( X0 = v5 )
| ( X0 = v4 )
| ~ r(v4,v5)
| ~ r(X0,v5)
| ~ r(X0,v4) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_362,plain,
( ( v4 = v5 )
| ( v0 = v5 )
| ( v0 = v4 )
| ~ r(v4,v5)
| ~ r(v0,v5)
| ~ r(v0,v4) ),
inference(instantiation,[status(thm)],[c_361]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i] :
( ( v3 = X1 )
| ( X0 = v3 )
| ( X0 = X1 )
| ~ r(v3,X1)
| ~ r(X0,v3)
| ~ r(X0,X1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i] :
( ( v4 = X1 )
| ( X0 = v4 )
| ( X0 = X1 )
| ~ r(v4,X1)
| ~ r(X0,v4)
| ~ r(X0,X1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_477,plain,
! [X0: $i] :
( r(v1,v2)
| r(X0,v2)
| r(X0,v1)
| ( v1 = v2 )
| ( X0 = v2 )
| ( X0 = v1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_478,plain,
( r(v1,v2)
| r(v0,v2)
| r(v0,v1)
| ( v1 = v2 )
| ( v0 = v2 )
| ( v0 = v1 ) ),
inference(instantiation,[status(thm)],[c_477]) ).
tcf(c_482,plain,
! [X0: $i] :
( r(v1,v3)
| r(X0,v3)
| r(X0,v1)
| ( v1 = v3 )
| ( X0 = v3 )
| ( X0 = v1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_483,plain,
( r(v1,v3)
| r(v0,v3)
| r(v0,v1)
| ( v1 = v3 )
| ( v0 = v3 )
| ( v0 = v1 ) ),
inference(instantiation,[status(thm)],[c_482]) ).
tcf(c_493,plain,
( r(v2,v3)
| ~ r(v3,v2) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_499,plain,
! [X0: $i] :
( r(v1,v4)
| r(X0,v4)
| r(X0,v1)
| ( v1 = v4 )
| ( X0 = v4 )
| ( X0 = v1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_500,plain,
( r(v1,v4)
| r(v0,v4)
| r(v0,v1)
| ( v1 = v4 )
| ( v0 = v4 )
| ( v0 = v1 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_511,plain,
! [X0: $i] :
( r(v2,v4)
| r(X0,v4)
| r(X0,v2)
| ( v2 = v4 )
| ( X0 = v4 )
| ( X0 = v2 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_512,plain,
( r(v2,v4)
| r(v0,v4)
| r(v0,v2)
| ( v2 = v4 )
| ( v0 = v4 )
| ( v0 = v2 ) ),
inference(instantiation,[status(thm)],[c_511]) ).
tcf(c_556,plain,
! [X0: $i] :
( r(v3,v4)
| r(X0,v4)
| r(X0,v3)
| ( v3 = v4 )
| ( X0 = v4 )
| ( X0 = v3 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_557,plain,
( r(v3,v4)
| r(v0,v4)
| r(v0,v3)
| ( v3 = v4 )
| ( v0 = v4 )
| ( v0 = v3 ) ),
inference(instantiation,[status(thm)],[c_556]) ).
tcf(c_559,plain,
! [X0: $i] :
( r(v0,v5)
| r(X0,v5)
| r(X0,v0)
| ( v0 = v5 )
| ( X0 = v5 )
| ( X0 = v0 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_561,plain,
! [X0: $i] :
( r(v1,v5)
| r(X0,v5)
| r(X0,v1)
| ( v1 = v5 )
| ( X0 = v5 )
| ( X0 = v1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_562,plain,
( r(v1,v5)
| r(v0,v5)
| r(v0,v1)
| ( v1 = v5 )
| ( v0 = v5 )
| ( v0 = v1 ) ),
inference(instantiation,[status(thm)],[c_561]) ).
tcf(c_564,plain,
! [X0: $i] :
( r(v2,v5)
| r(X0,v5)
| r(X0,v2)
| ( v2 = v5 )
| ( X0 = v5 )
| ( X0 = v2 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_565,plain,
( r(v2,v5)
| r(v0,v5)
| r(v0,v2)
| ( v2 = v5 )
| ( v0 = v5 )
| ( v0 = v2 ) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_567,plain,
! [X0: $i] :
( r(v3,v5)
| r(X0,v5)
| r(X0,v3)
| ( v3 = v5 )
| ( X0 = v5 )
| ( X0 = v3 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_568,plain,
( r(v3,v5)
| r(v0,v5)
| r(v0,v3)
| ( v3 = v5 )
| ( v0 = v5 )
| ( v0 = v3 ) ),
inference(instantiation,[status(thm)],[c_567]) ).
tcf(c_570,plain,
! [X0: $i] :
( r(v4,v5)
| r(X0,v5)
| r(X0,v4)
| ( v4 = v5 )
| ( X0 = v5 )
| ( X0 = v4 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_571,plain,
( r(v4,v5)
| r(v0,v5)
| r(v0,v4)
| ( v4 = v5 )
| ( v0 = v5 )
| ( v0 = v4 ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_651,plain,
( r(v3,v1)
| ~ r(v1,v3) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_652,plain,
! [X0: $i] :
( r(v3,v1)
| r(X0,v3)
| r(X0,v1)
| ( v3 = v1 )
| ( X0 = v3 )
| ( X0 = v1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_653,plain,
( r(v3,v1)
| r(v0,v3)
| r(v0,v1)
| ( v3 = v1 )
| ( v0 = v3 )
| ( v0 = v1 ) ),
inference(instantiation,[status(thm)],[c_652]) ).
tcf(c_655,plain,
! [X0: $i] :
( r(v3,v2)
| r(X0,v3)
| r(X0,v2)
| ( v3 = v2 )
| ( X0 = v3 )
| ( X0 = v2 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_656,plain,
( r(v3,v2)
| r(v0,v3)
| r(v0,v2)
| ( v3 = v2 )
| ( v0 = v3 )
| ( v0 = v2 ) ),
inference(instantiation,[status(thm)],[c_655]) ).
tcf(c_724,plain,
v1 = v1,
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_729,plain,
( ( v1 = v2 )
| ( v1 = v0 )
| ( v0 = v2 )
| ~ r(v1,v2)
| ~ r(v1,v0)
| ~ r(v0,v2) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_733,plain,
v2 = v2,
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_736,plain,
( ( v2 = v4 )
| ( v2 = v0 )
| ( v0 = v4 )
| ~ r(v2,v4)
| ~ r(v2,v0)
| ~ r(v0,v4) ),
inference(instantiation,[status(thm)],[c_347]) ).
tcf(c_796,plain,
( r(v3,v2)
| r(v3,v1)
| r(v1,v2)
| ( v3 = v2 )
| ( v3 = v1 )
| ( v1 = v2 ) ),
inference(instantiation,[status(thm)],[c_477]) ).
tcf(c_820,plain,
( r(v3,v4)
| r(v3,v1)
| r(v1,v4)
| ( v3 = v4 )
| ( v3 = v1 )
| ( v1 = v4 ) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_823,plain,
( r(v2,v4)
| r(v1,v4)
| r(v1,v2)
| ( v2 = v4 )
| ( v1 = v4 )
| ( v1 = v2 ) ),
inference(instantiation,[status(thm)],[c_511]) ).
tcf(c_824,plain,
( r(v3,v4)
| r(v3,v2)
| r(v2,v4)
| ( v3 = v4 )
| ( v3 = v2 )
| ( v2 = v4 ) ),
inference(instantiation,[status(thm)],[c_511]) ).
tcf(c_845,plain,
( r(v3,v5)
| r(v3,v1)
| r(v1,v5)
| ( v3 = v5 )
| ( v3 = v1 )
| ( v1 = v5 ) ),
inference(instantiation,[status(thm)],[c_561]) ).
tcf(c_848,plain,
( r(v2,v5)
| r(v1,v5)
| r(v1,v2)
| ( v2 = v5 )
| ( v1 = v5 )
| ( v1 = v2 ) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_849,plain,
( r(v3,v5)
| r(v3,v2)
| r(v2,v5)
| ( v3 = v5 )
| ( v3 = v2 )
| ( v2 = v5 ) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_852,plain,
( r(v3,v5)
| r(v1,v5)
| r(v1,v3)
| ( v3 = v5 )
| ( v1 = v5 )
| ( v1 = v3 ) ),
inference(instantiation,[status(thm)],[c_567]) ).
tcf(c_868,plain,
( r(v4,v5)
| r(v1,v5)
| r(v1,v4)
| ( v4 = v5 )
| ( v1 = v5 )
| ( v1 = v4 ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_869,plain,
( r(v4,v5)
| r(v2,v5)
| r(v2,v4)
| ( v4 = v5 )
| ( v2 = v5 )
| ( v2 = v4 ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_870,plain,
( r(v4,v5)
| r(v3,v5)
| r(v3,v4)
| ( v4 = v5 )
| ( v3 = v5 )
| ( v3 = v4 ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_876,plain,
( r(v1,v5)
| r(v1,v0)
| r(v0,v5)
| ( v1 = v5 )
| ( v1 = v0 )
| ( v0 = v5 ) ),
inference(instantiation,[status(thm)],[c_559]) ).
tcf(c_881,plain,
! [X0: $i] :
( r(v2,X0)
| ~ r(X0,v2) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_882,plain,
( r(v2,v0)
| ~ r(v0,v2) ),
inference(instantiation,[status(thm)],[c_881]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i] :
( r(v3,X1)
| r(X0,v3)
| r(X0,X1)
| ( v3 = X1 )
| ( X0 = v3 )
| ( X0 = X1 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1214,plain,
! [X0: $i] :
( ( v3 = v1 )
| ( X0 = v3 )
| ( X0 = v1 )
| ~ r(v3,v1)
| ~ r(X0,v3)
| ~ r(X0,v1) ),
inference(instantiation,[status(thm)],[c_409]) ).
tcf(c_1215,plain,
( ( v3 = v1 )
| ( v0 = v3 )
| ( v0 = v1 )
| ~ r(v3,v1)
| ~ r(v0,v3)
| ~ r(v0,v1) ),
inference(instantiation,[status(thm)],[c_1214]) ).
tcf(c_1216,plain,
( ( v3 = v4 )
| ( v1 = v4 )
| ( v1 = v3 )
| ~ r(v3,v4)
| ~ r(v1,v4)
| ~ r(v1,v3) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_1254,plain,
( ( v3 = v2 )
| ( v3 = v1 )
| ( v1 = v2 )
| ~ r(v3,v2)
| ~ r(v3,v1)
| ~ r(v1,v2) ),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_1294,plain,
( ( v3 = v5 )
| ( v3 = v1 )
| ( v1 = v5 )
| ~ r(v3,v5)
| ~ r(v3,v1)
| ~ r(v1,v5) ),
inference(instantiation,[status(thm)],[c_355]) ).
tcf(c_1298,plain,
( ( v2 = v5 )
| ( v1 = v5 )
| ( v1 = v2 )
| ~ r(v2,v5)
| ~ r(v1,v5)
| ~ r(v1,v2) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_1330,plain,
( ( v3 = v5 )
| ( v3 = v2 )
| ( v2 = v5 )
| ~ r(v3,v5)
| ~ r(v3,v2)
| ~ r(v2,v5) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_1545,plain,
( ( v3 = v4 )
| ( v2 = v4 )
| ( v2 = v3 )
| ~ r(v3,v4)
| ~ r(v2,v4)
| ~ r(v2,v3) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_1559,plain,
( ( v3 = v4 )
| ( v3 = v2 )
| ( v2 = v4 )
| ~ r(v3,v4)
| ~ r(v3,v2)
| ~ r(v2,v4) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_1561,plain,
! [X0: $i] :
( ( v3 = v2 )
| ( X0 = v3 )
| ( X0 = v2 )
| ~ r(v3,v2)
| ~ r(X0,v3)
| ~ r(X0,v2) ),
inference(instantiation,[status(thm)],[c_409]) ).
tcf(c_1562,plain,
( ( v3 = v2 )
| ( v0 = v3 )
| ( v0 = v2 )
| ~ r(v3,v2)
| ~ r(v0,v3)
| ~ r(v0,v2) ),
inference(instantiation,[status(thm)],[c_1561]) ).
tcf(c_1587,plain,
( ( v2 = v3 )
| ( v3 != v2 )
| ( v2 != v2 ) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_1770,plain,
( ( v4 = v5 )
| ( v1 = v5 )
| ( v1 = v4 )
| ~ r(v4,v5)
| ~ r(v1,v5)
| ~ r(v1,v4) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1771,plain,
( ( v4 = v5 )
| ( v2 = v5 )
| ( v2 = v4 )
| ~ r(v4,v5)
| ~ r(v2,v5)
| ~ r(v2,v4) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1772,plain,
( ( v4 = v5 )
| ( v3 = v5 )
| ( v3 = v4 )
| ~ r(v4,v5)
| ~ r(v3,v5)
| ~ r(v3,v4) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1907,plain,
( r(v3,v2)
| r(v1,v3)
| r(v1,v2)
| ( v3 = v2 )
| ( v1 = v3 )
| ( v1 = v2 ) ),
inference(instantiation,[status(thm)],[c_896]) ).
tcf(c_2062,plain,
( ( v1 = v3 )
| ( v3 != v1 )
| ( v1 != v1 ) ),
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_2086,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2062,c_1907,c_1772,c_1771,c_1770,c_1587,c_1562,c_1559,c_1545,c_1330,c_1298,c_1294,c_1254,c_1216,c_1215,c_882,c_876,c_870,c_869,c_868,c_852,c_849,c_848,c_845,c_824,c_823,c_820,c_796,c_736,c_733,c_729,c_724,c_656,c_653,c_651,c_571,c_568,c_565,c_562,c_557,c_512,c_500,c_493,c_483,c_478,c_362,c_360,c_358,c_356,c_353,c_351,c_349,c_341,c_302,c_300,c_155,c_70,c_71,c_72,c_73,c_74,c_75,c_76,c_77,c_78,c_79,c_80,c_81,c_82,c_83,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.22 % Problem : GRA117-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.24 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.58 % Computer : n001.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Wed Sep 23 12:58:40 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.62 Running EPR theorem proving
% 0.15/5.62 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.63
% 0.15/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.63
% 0.15/5.64 % Detected problem language: tptp
% 0.15/5.65 % Proving...
% 1.41/6.42 % SZS status Started for theBenchmark.p
% 1.41/6.42 % SZS status Unsatisfiable for theBenchmark.p
% 1.41/6.42
% 1.41/6.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.41/6.42
% 1.41/6.42 % ------ iProver source info
% 1.41/6.42
% 1.41/6.42 % git: date: 2026-07-19 20:42:38 +0200
% 1.41/6.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.41/6.42 % git: non_committed_changes: false
% 1.41/6.42
% 1.41/6.42 % ------ Parsing...% successful
% 1.41/6.42
% 1.41/6.42
% 1.41/6.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.41/6.42
% 1.41/6.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.41/6.42
% 1.41/6.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.41/6.42
% 1.41/6.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.41/6.42 % ------ Proving...
% 1.41/6.42 % ------ Problem Properties
% 1.41/6.42
% 1.41/6.42 %
% 1.41/6.42 % clauses 18
% 1.41/6.42 % conjectures 0
% 1.41/6.42 % EPR 18
% 1.41/6.42 % Horn 16
% 1.41/6.42 % unary 15
% 1.41/6.42 % binary 1
% 1.41/6.42 % lits 29
% 1.41/6.42 % lits eq 21
% 1.41/6.42 % fd_pure 0
% 1.41/6.42 % fd_pseudo 0
% 1.41/6.42 % fd_cond 0
% 1.41/6.42 % fd_pseudo_cond 2
% 1.41/6.42 % AC symbols 0
% 1.41/6.42
% 1.41/6.42 % ------ Input Options Time Limit: Unbounded
% 1.41/6.42
% 1.41/6.42
% 1.41/6.42 % ------
% 1.41/6.42 % Current options:
% 1.41/6.42 % ------
% 1.41/6.42
% 1.41/6.42
% 1.41/6.42 %
% 1.41/6.42
% 1.41/6.42 % ------ Proving...
% 1.41/6.42 %
% 1.41/6.42
% 1.41/6.42 % SZS status Unsatisfiable for theBenchmark.p
% 1.41/6.42
% 1.41/6.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.41/6.42
% 1.41/6.42
%------------------------------------------------------------------------------