%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM008+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 7.01s 11.79s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 109 ( 15 unt; 0 def)
% Number of atoms : 305 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 360 ( 164 ~; 171 |; 18 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 139 !; 9 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( transitive_reflexive_rewrite(c,X0)
& transitive_reflexive_rewrite(b,X0) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',found) ).
fof(f2,axiom,
( transitive_reflexive_rewrite(a,c)
& transitive_reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(f3,axiom,
! [X0] : equalish(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f4,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
fof(f5,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> transitive_reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X0,X1) )
=> transitive_reflexive_rewrite(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X2)
& rewrite(X0,X1) )
=> ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lo_cfl) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',ih_cfl) ).
fof(f10,axiom,
! [X0,X1] :
( transitive_reflexive_rewrite(X0,X1)
=> ( ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| equalish(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(f11,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f12,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
~ goal,
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(ennf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| transitive_reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( transitive_reflexive_rewrite(X2,X3)
& transitive_reflexive_rewrite(X1,X3) ) ),
inference(flattening,[],[f21]) ).
fof(f23,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,[],[f9]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| equalish(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ? [X2] :
( transitive_reflexive_rewrite(X2,X1)
& rewrite(X0,X2) )
| equalish(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,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))],[f22]) ).
fof(f28,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))],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| ( transitive_reflexive_rewrite(sK2(X0,X1),X1)
& rewrite(X0,sK2(X0,X1)) )
| equalish(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f26]) ).
fof(f30,plain,
! [X0] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0)
| goal ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
transitive_reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
transitive_reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : equalish(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| transitive_reflexive_rewrite(X2,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| transitive_reflexive_rewrite(X1,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,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,[],[f28]) ).
fof(f41,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,[],[f28]) ).
fof(f42,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| transitive_reflexive_rewrite(sK2(X0,X1),X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
! [X0,X1] :
( ~ transitive_reflexive_rewrite(X0,X1)
| rewrite(X0,sK2(X0,X1))
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
~ goal,
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i] :
( goal
| ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
transitive_reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
transitive_reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i] : equalish(X0,X0),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(X0,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,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,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X1,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive_reflexive_rewrite(X2,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,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,[],[f41]) ).
tcf(c_60,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,[],[f40]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| rewrite(X0,sK2(X0,X1))
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| transitive_reflexive_rewrite(sK2(X0,X1),X1)
| ~ transitive_reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
~ goal,
inference(cnf_transformation,[],[f44]) ).
tcf(c_70,plain,
! [X0: $i] :
( ~ transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(c,X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_63,c_49]) ).
tcf(c_71,plain,
! [X0: $i] :
( ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(b,X0) ),
inference(renaming,[status(thm)],[c_70]) ).
tcf(c_211,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,X0)
| ~ equalish(b,X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_212,plain,
( transitive_reflexive_rewrite(b,a)
| ~ equalish(b,a) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_215,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_56]) ).
tcf(c_216,plain,
( transitive_reflexive_rewrite(b,b)
| ~ equalish(b,b) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_217,plain,
equalish(b,b),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_218,plain,
! [X0: $i] :
( equalish(b,X0)
| ~ equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_219,plain,
( equalish(b,a)
| ~ equalish(a,b) ),
inference(instantiation,[status(thm)],[c_218]) ).
tcf(c_228,plain,
( ~ transitive_reflexive_rewrite(c,b)
| ~ transitive_reflexive_rewrite(b,b) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_233,plain,
! [X0: $i] :
( equalish(X0,b)
| transitive_reflexive_rewrite(sK2(X0,b),b)
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_234,plain,
! [X0: $i] :
( equalish(X0,b)
| rewrite(X0,sK2(X0,b))
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_235,plain,
( equalish(a,b)
| rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_236,plain,
( equalish(a,b)
| transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_248,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(c,b)
| ~ transitive_reflexive_rewrite(c,X0)
| ~ transitive_reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_249,plain,
( transitive_reflexive_rewrite(c,b)
| ~ transitive_reflexive_rewrite(a,b)
| ~ transitive_reflexive_rewrite(c,a) ),
inference(instantiation,[status(thm)],[c_248]) ).
tcf(c_255,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_58]) ).
tcf(c_256,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_57]) ).
tcf(c_260,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_60]) ).
tcf(c_261,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_59]) ).
tcf(c_268,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(c,X0)
| ~ equalish(c,X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_269,plain,
( transitive_reflexive_rewrite(c,a)
| ~ equalish(c,a) ),
inference(instantiation,[status(thm)],[c_268]) ).
tcf(c_286,plain,
( transitive_reflexive_rewrite(c,c)
| ~ equalish(c,c) ),
inference(instantiation,[status(thm)],[c_268]) ).
tcf(c_287,plain,
equalish(c,c),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_288,plain,
! [X0: $i] :
( equalish(c,X0)
| ~ equalish(X0,c) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_289,plain,
( equalish(c,a)
| ~ equalish(a,c) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_312,plain,
( ~ transitive_reflexive_rewrite(c,c)
| ~ transitive_reflexive_rewrite(b,c) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_317,plain,
! [X0: $i] :
( equalish(X0,c)
| transitive_reflexive_rewrite(sK2(X0,c),c)
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_318,plain,
! [X0: $i] :
( equalish(X0,c)
| rewrite(X0,sK2(X0,c))
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_319,plain,
( equalish(a,c)
| rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_318]) ).
tcf(c_320,plain,
( equalish(a,c)
| transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_335,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,c)
| ~ transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_336,plain,
( transitive_reflexive_rewrite(b,c)
| ~ transitive_reflexive_rewrite(a,c)
| ~ transitive_reflexive_rewrite(b,a) ),
inference(instantiation,[status(thm)],[c_335]) ).
tcf(c_348,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_256]) ).
tcf(c_349,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_255]) ).
tcf(c_354,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_349]) ).
tcf(c_355,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_348]) ).
tcf(c_357,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_60]) ).
tcf(c_358,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_59]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] :
( transitive_reflexive_rewrite(sK2(a,c),X1)
| ~ transitive_reflexive_rewrite(X0,X1)
| ~ transitive_reflexive_rewrite(sK2(a,c),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_455,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_357]) ).
tcf(c_519,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),sK1(sK0(sK2(a,b),sK2(a,c)),X0))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),X0)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_261]) ).
tcf(c_520,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(X0,sK1(sK0(sK2(a,b),sK2(a,c)),X0))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),X0)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_260]) ).
tcf(c_535,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_358]) ).
tcf(c_657,plain,
( transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),sK1(sK0(sK2(a,b),sK2(a,c)),b))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_764,plain,
( transitive_reflexive_rewrite(b,sK1(sK0(sK2(a,b),sK2(a,c)),b))
| ~ rewrite(a,sK2(a,b))
| ~ transitive_reflexive_rewrite(sK2(a,b),b)
| ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_520]) ).
tcf(c_798,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(sK2(a,c),X0)
| ~ transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),X0)
| ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,b),sK2(a,c))) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_1241,plain,
! [X0: $i] :
( transitive_reflexive_rewrite(b,X0)
| ~ transitive_reflexive_rewrite(b,sK1(sK0(sK2(a,b),sK2(a,c)),b))
| ~ transitive_reflexive_rewrite(sK1(sK0(sK2(a,b),sK2(a,c)),b),X0) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_1473,plain,
( transitive_reflexive_rewrite(sK2(a,c),sK1(sK0(sK2(a,b),sK2(a,c)),b))
| ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,b),sK2(a,c)))
| ~ transitive_reflexive_rewrite(sK0(sK2(a,b),sK2(a,c)),sK1(sK0(sK2(a,b),sK2(a,c)),b)) ),
inference(instantiation,[status(thm)],[c_798]) ).
tcf(c_3270,plain,
( transitive_reflexive_rewrite(c,sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b)))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),sK1(sK0(sK2(a,b),sK2(a,c)),b)) ),
inference(instantiation,[status(thm)],[c_535]) ).
tcf(c_3273,plain,
( transitive_reflexive_rewrite(sK1(sK0(sK2(a,b),sK2(a,c)),b),sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b)))
| ~ rewrite(a,sK2(a,c))
| ~ transitive_reflexive_rewrite(sK2(a,c),c)
| ~ transitive_reflexive_rewrite(sK2(a,c),sK1(sK0(sK2(a,b),sK2(a,c)),b)) ),
inference(instantiation,[status(thm)],[c_455]) ).
tcf(c_10798,plain,
( ~ transitive_reflexive_rewrite(c,sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b)))
| ~ transitive_reflexive_rewrite(b,sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_10801,plain,
( transitive_reflexive_rewrite(b,sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b)))
| ~ transitive_reflexive_rewrite(b,sK1(sK0(sK2(a,b),sK2(a,c)),b))
| ~ transitive_reflexive_rewrite(sK1(sK0(sK2(a,b),sK2(a,c)),b),sK1(c,sK1(sK0(sK2(a,b),sK2(a,c)),b))) ),
inference(instantiation,[status(thm)],[c_1241]) ).
tcf(c_10802,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10801,c_10798,c_3270,c_3273,c_1473,c_764,c_657,c_355,c_354,c_336,c_320,c_319,c_312,c_289,c_287,c_286,c_269,c_249,c_236,c_235,c_228,c_219,c_217,c_216,c_212,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/10.44 % Computer : n001.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Fri Sep 25 07:50:51 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/10.51 Running first-order theorem proving
% 0.22/10.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/10.52
% 0.22/10.52 % ======== iProver multi-core TPTP/SMT =========
% 0.22/10.52
% 0.22/10.52 % Detected problem language: tptp
% 0.22/10.54 % Proving...
% 7.01/11.79 % SZS status Started for theBenchmark.p
% 7.01/11.79 % SZS status Theorem for theBenchmark.p
% 7.01/11.79
% 7.01/11.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.01/11.79
% 7.01/11.79 % ------ iProver source info
% 7.01/11.79
% 7.01/11.79 % git: date: 2026-07-19 20:42:38 +0200
% 7.01/11.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.01/11.79 % git: non_committed_changes: false
% 7.01/11.79
% 7.01/11.79 % ------ Parsing...
% 7.01/11.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.01/11.79
% 7.01/11.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.01/11.79
% 7.01/11.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.01/11.79 % ------ Proving...
% 7.01/11.79 % ------ Problem Properties
% 7.01/11.79
% 7.01/11.79 %
% 7.01/11.79 % clauses 14
% 7.01/11.79 % conjectures 0
% 7.01/11.79 % EPR 8
% 7.01/11.79 % Horn 12
% 7.01/11.79 % unary 3
% 7.01/11.79 % binary 4
% 7.01/11.79 % lits 34
% 7.01/11.79 % lits eq 0
% 7.01/11.79 % fd_pure 0
% 7.01/11.79 % fd_pseudo 0
% 7.01/11.79 % fd_cond 0
% 7.01/11.79 % fd_pseudo_cond 0
% 7.01/11.79 % AC symbols 0
% 7.01/11.79
% 7.01/11.79 % ------ Schedule dynamic 5 is on
% 7.01/11.79
% 7.01/11.79 % ------ no conjectures: strip conj schedule
% 7.01/11.79
% 7.01/11.79 % ------ no equalities: superposition off
% 7.01/11.79
% 7.01/11.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 7.01/11.79
% 7.01/11.79
% 7.01/11.79 % ------
% 7.01/11.79 % Current options:
% 7.01/11.79 % ------
% 7.01/11.79
% 7.01/11.79
% 7.01/11.79 %
% 7.01/11.79
% 7.01/11.79 % ------ Proving...
% 7.01/11.79 %
% 7.01/11.79
% 7.01/11.79 % SZS status Theorem for theBenchmark.p
% 7.01/11.79
% 7.01/11.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.01/11.79
% 7.01/11.79
%------------------------------------------------------------------------------