%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM008+2 : TPTP v9.3.1. Released v3.2.0.
% 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 01:04:17 PM UTC 2026
% Result : Theorem 42.07s 17.78s
% Output : CNFRefutation 42.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 20 unt; 0 def)
% Number of atoms : 324 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 395 ( 182 ~; 189 |; 18 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 148 !; 9 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( transitive_reflexive_rewrite(c,X0)
& transitive_reflexive_rewrite(b,X0) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',found) ).
fof(f2,axiom,
( transitive_reflexive_rewrite(a,c)
& transitive_reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
=> transitive_reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X0,X1) )
=> transitive_reflexive_rewrite(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X2)
& rewrite(X0,X1) )
=> ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lo_cfl) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( transitive_reflexive_rewrite(X0,X2)
& transitive_reflexive_rewrite(X0,X1)
& rewrite(a,X0) )
=> ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ih_cfl) ).
fof(f8,axiom,
! [X0,X1] :
( transitive_reflexive_rewrite(X0,X1)
=> ( ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(f9,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f10,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
~ goal,
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( X0 != X1
| transitive_reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ rewrite(a,X0)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ rewrite(a,X0)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| X0 = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| X0 = X1 ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ( transitive_reflexive_rewrite(X2,sK0(X1,X2))
& transitive_reflexive_rewrite(X1,sK0(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X1,X2))],[f19]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ rewrite(a,X0)
| ( transitive_reflexive_rewrite(X2,sK1(X1,X2))
& transitive_reflexive_rewrite(X1,sK1(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X1,X2))],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ( transitive_reflexive_rewrite(sK2(X0,X1),X1)
& rewrite(X0,sK2(X0,X1)) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f23]) ).
fof(f27,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
transitive_reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
transitive_reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( X0 != X1
| transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| transitive_reflexive_rewrite(X2,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| transitive_reflexive_rewrite(X1,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ rewrite(a,X0)
| transitive_reflexive_rewrite(X2,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ rewrite(a,X0)
| transitive_reflexive_rewrite(X1,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| rewrite(X0,sK2(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
~ goal,
inference(cnf_transformation,[],[f11]) ).
fof(f40,plain,
! [X1] : transitive_reflexive_rewrite(X1,X1),
inference(equality_resolution,[],[f30]) ).
tcf(c_49,plain,
! [X0: $i] :
( goal
| ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
transitive_reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,plain,
transitive_reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : transitive_reflexive_rewrite(X0,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X1,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X2,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X1,sK1(X1,X2))
| ~ rewrite(a,X0)
| ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X2,sK1(X1,X2))
| ~ rewrite(a,X0)
| ~ transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( rewrite(X0,sK2(X0,X1))
| ( X0 = X1 )
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(sK2(X0,X1),X1)
| ( X0 = X1 )
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,negated_conjecture,
~ goal,
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
transitive_reflexive_rewrite(a,a),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_68,plain,
! [X0: $i] :
( ~ transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(c,X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).
tcf(c_69,plain,
! [X0: $i] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_307,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( transitive_reflexive_rewrite(X0,X2)
| ~ transitive_reflexive_rewrite(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_312,plain,
a = a,
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_490,plain,
~ transitive_reflexive_rewrite(c,b),
inference(superposition,[status(thm)],[c_52,c_69]) ).
tcf(c_618,plain,
transitive_reflexive_rewrite(b,b),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(X2,X1)
| ( b != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_711,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(c,b)
| ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_712,plain,
( transitive_reflexive_rewrite(c,b)
| ~ transitive_reflexive_rewrite(a,b)
| ~ transitive_reflexive_rewrite(c,a) ),
inference(instantiation,[status(thm)],[c_711]) ).
tcf(c_724,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(b,X1)
| ( b != b )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_675]) ).
tcf(c_725,plain,
b = b,
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(X2,X1)
| ( c != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(c,X1)
| ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_803,plain,
( transitive_reflexive_rewrite(c,a)
| ~ transitive_reflexive_rewrite(a,a)
| ( a != a )
| ( c != a ) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_986,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(b,b)
| ( b != b )
| ( X0 != b ) ),
inference(instantiation,[status(thm)],[c_724]) ).
tcf(c_987,plain,
( transitive_reflexive_rewrite(b,a)
| ~ transitive_reflexive_rewrite(b,b)
| ( a != b )
| ( b != b ) ),
inference(instantiation,[status(thm)],[c_986]) ).
tcf(c_1025,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(X0,b),b)
| ( X0 = b )
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1026,plain,
! [X0: $i] :
( rewrite(X0,sK2(X0,b))
| ( X0 = b )
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1027,plain,
( rewrite(a,sK2(a,b))
| ( a = b )
| ~ transitive_reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_1026]) ).
tcf(c_1028,plain,
( transitive_reflexive_rewrite(sK2(a,b),b)
| ( a = b )
| ~ transitive_reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] :
( ( c = X0 )
| ( c != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_1137,plain,
c = c,
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_1220,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X1,sK0(sK2(X0,b),X1))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,sK2(X0,b)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(sK2(X0,b),sK0(sK2(X0,b),X1))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,sK2(X0,b)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1225,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X1,sK1(X0,X1))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),X1)
| ~ transitive_reflexive_rewrite(sK2(a,b),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X0,sK1(X0,X1))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),X1)
| ~ transitive_reflexive_rewrite(sK2(a,b),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1365,plain,
! [X0: $i] :
( ( c = X0 )
| ( c != c )
| ( X0 != c ) ),
inference(instantiation,[status(thm)],[c_1073]) ).
tcf(c_1366,plain,
( ( c = a )
| ( a != c )
| ( c != c ) ),
inference(instantiation,[status(thm)],[c_1365]) ).
tcf(c_1368,plain,
transitive_reflexive_rewrite(c,c),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1608,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(X0,c),c)
| ( X0 = c )
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1609,plain,
! [X0: $i] :
( rewrite(X0,sK2(X0,c))
| ( X0 = c )
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1610,plain,
( rewrite(a,sK2(a,c))
| ( a = c )
| ~ transitive_reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_1609]) ).
tcf(c_1611,plain,
( transitive_reflexive_rewrite(sK2(a,c),c)
| ( a = c )
| ~ transitive_reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_1608]) ).
tcf(c_1937,plain,
( ~ transitive_reflexive_rewrite(c,c)
| ~ transitive_reflexive_rewrite(b,c) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2247,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,c)
| ~ transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_650]) ).
tcf(c_2248,plain,
( transitive_reflexive_rewrite(b,c)
| ~ transitive_reflexive_rewrite(a,c)
| ~ transitive_reflexive_rewrite(b,a) ),
inference(instantiation,[status(thm)],[c_2247]) ).
tcf(c_2591,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(X0,b),sK0(sK2(X0,b),sK2(X0,c)))
| ~ rewrite(X0,sK2(X0,c))
| ~ rewrite(X0,sK2(X0,b)) ),
inference(instantiation,[status(thm)],[c_1221]) ).
tcf(c_2592,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(X0,c),sK0(sK2(X0,b),sK2(X0,c)))
| ~ rewrite(X0,sK2(X0,c))
| ~ rewrite(X0,sK2(X0,b)) ),
inference(instantiation,[status(thm)],[c_1220]) ).
tcf(c_2595,plain,
( transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,b),sK2(a,c)))
| ~ rewrite(a,sK2(a,c))
| ~ rewrite(a,sK2(a,b)) ),
inference(instantiation,[status(thm)],[c_2592]) ).
tcf(c_2596,plain,
( transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c)))
| ~ rewrite(a,sK2(a,c))
| ~ rewrite(a,sK2(a,b)) ),
inference(instantiation,[status(thm)],[c_2591]) ).
tcf(c_2598,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X1,sK1(X0,X1))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),X1)
| ~ transitive_reflexive_rewrite(sK2(a,c),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2599,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X0,sK1(X0,X1))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),X1)
| ~ transitive_reflexive_rewrite(sK2(a,c),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_3167,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(sK2(a,b),X1)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ transitive_reflexive_rewrite(sK2(a,b),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_3169,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(X0,sK1(b,X0))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),X0) ),
inference(instantiation,[status(thm)],[c_1225]) ).
tcf(c_3300,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(X0,sK1(c,X0))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),X0) ),
inference(instantiation,[status(thm)],[c_2598]) ).
tcf(c_3866,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,sK1(b,X0))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),X0) ),
inference(instantiation,[status(thm)],[c_1226]) ).
tcf(c_3984,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(c,sK1(c,X0))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),X0) ),
inference(instantiation,[status(thm)],[c_2599]) ).
tcf(c_4516,plain,
( transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),sK1(c,sK0(sK2(a,b),sK2(a,c))))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_3300]) ).
tcf(c_4886,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(a,b),X0)
| ~ transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),X0)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_3167]) ).
tcf(c_11831,plain,
( transitive_reflexive_rewrite(c,sK1(c,sK0(sK2(a,b),sK2(a,c))))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_3984]) ).
tcf(c_12111,plain,
( transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,b),sK2(a,c))))
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c)))
| ~ transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),sK1(c,sK0(sK2(a,b),sK2(a,c)))) ),
inference(instantiation,[status(thm)],[c_4886]) ).
tcf(c_34589,plain,
( transitive_reflexive_rewrite(b,sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c)))))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,b),sK2(a,c)))) ),
inference(instantiation,[status(thm)],[c_3866]) ).
tcf(c_34594,plain,
( transitive_reflexive_rewrite(sK1(c,sK0(sK2(a,b),sK2(a,c))),sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c)))))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,b),sK2(a,c)))) ),
inference(instantiation,[status(thm)],[c_3169]) ).
tcf(c_37770,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(c,X1)
| ~ transitive_reflexive_rewrite(c,sK1(c,X0))
| ~ transitive_reflexive_rewrite(sK1(c,X0),X1) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_43495,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(c,sK1(b,sK1(c,X0)))
| ~ transitive_reflexive_rewrite(c,sK1(c,X0))
| ~ transitive_reflexive_rewrite(sK1(c,X0),sK1(b,sK1(c,X0))) ),
inference(instantiation,[status(thm)],[c_37770]) ).
tcf(c_76492,plain,
( transitive_reflexive_rewrite(c,sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c)))))
| ~ transitive_reflexive_rewrite(c,sK1(c,sK0(sK2(a,b),sK2(a,c))))
| ~ transitive_reflexive_rewrite(sK1(c,sK0(sK2(a,b),sK2(a,c))),sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c))))) ),
inference(instantiation,[status(thm)],[c_43495]) ).
tcf(c_118433,plain,
( ~ transitive_reflexive_rewrite(c,sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c)))))
| ~ transitive_reflexive_rewrite(b,sK1(b,sK1(c,sK0(sK2(a,b),sK2(a,c))))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_118439,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_118433,c_76492,c_34589,c_34594,c_12111,c_11831,c_4516,c_2596,c_2595,c_2248,c_1937,c_1611,c_1610,c_1368,c_1366,c_1137,c_1028,c_1027,c_987,c_803,c_725,c_712,c_618,c_490,c_312,c_50,c_51,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM008+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.37 % Computer : n001.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Fri Sep 25 07:51:22 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.44 % Proving...
% 42.07/17.78 % SZS status Started for theBenchmark.p
% 42.07/17.78 % SZS status Theorem for theBenchmark.p
% 42.07/17.78
% 42.07/17.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 42.07/17.78
% 42.07/17.78 % ------ iProver source info
% 42.07/17.78
% 42.07/17.78 % git: date: 2026-07-19 20:42:38 +0200
% 42.07/17.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 42.07/17.78 % git: non_committed_changes: false
% 42.07/17.78
% 42.07/17.78 % ------ Parsing...
% 42.07/17.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 42.07/17.78
% 42.07/17.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 42.07/17.78
% 42.07/17.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 42.07/17.78
% 42.07/17.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 42.07/17.78 % ------ Proving...
% 42.07/17.78 % ------ Problem Properties
% 42.07/17.78
% 42.07/17.78 %
% 42.07/17.78 % clauses 12
% 42.07/17.78 % conjectures 0
% 42.07/17.78 % EPR 6
% 42.07/17.78 % Horn 10
% 42.07/17.78 % unary 3
% 42.07/17.78 % binary 2
% 42.07/17.78 % lits 30
% 42.07/17.78 % lits eq 2
% 42.07/17.78 % fd_pure 0
% 42.07/17.78 % fd_pseudo 0
% 42.07/17.78 % fd_cond 0
% 42.07/17.78 % fd_pseudo_cond 2
% 42.07/17.78 % AC symbols 0
% 42.07/17.78
% 42.07/17.78 % ------ Schedule dynamic 5 is on
% 42.07/17.78
% 42.07/17.78 % ------ no conjectures: strip conj schedule
% 42.07/17.78
% 42.07/17.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 42.07/17.78
% 42.07/17.78
% 42.07/17.78 % ------
% 42.07/17.78 % Current options:
% 42.07/17.78 % ------
% 42.07/17.78
% 42.07/17.78
% 42.07/17.78 %
% 42.07/17.78
% 42.07/17.78 % ------ Proving...
% 42.07/17.78 %
% 42.07/17.78
% 42.07/17.78 % SZS status Theorem for theBenchmark.p
% 42.07/17.78
% 42.07/17.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.07/17.78
% 42.07/17.78
%------------------------------------------------------------------------------