%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM007+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 : n012.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 1.58s 1.06s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 15 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 205 ( 95 ~; 95 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 101 !; 3 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(f2,axiom,
! [X0] :
( ( reflexive_rewrite(c,X0)
& reflexive_rewrite(b,X0) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
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',symmtery) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( reflexive_rewrite(X1,X2)
& equalish(X0,X1) )
=> reflexive_rewrite(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).
fof(f6,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(f7,axiom,
! [X0,X1] :
( rewrite(X0,X1)
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(f8,axiom,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
=> ( rewrite(X0,X1)
| equalish(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X2)
& rewrite(X0,X1) )
=> ? [X3] :
( rewrite(X2,X3)
& rewrite(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(f10,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f11,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
~ goal,
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0)
| goal ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0)
| goal ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ reflexive_rewrite(X1,X2)
| ~ equalish(X0,X1)
| reflexive_rewrite(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ reflexive_rewrite(X1,X2)
| ~ equalish(X0,X1)
| reflexive_rewrite(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1)
| equalish(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1)
| equalish(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( rewrite(X2,X3)
& rewrite(X1,X3) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ? [X3] :
( rewrite(X2,X3)
& rewrite(X1,X3) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| ( rewrite(X2,sK0(X1,X2))
& rewrite(X1,sK0(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X1,X2))],[f23]) ).
fof(f25,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0)
| goal ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0] : equalish(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ reflexive_rewrite(X1,X2)
| ~ equalish(X0,X1)
| reflexive_rewrite(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X2,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X1,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
~ goal,
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i] :
( goal
| ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i] : equalish(X0,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( reflexive_rewrite(X2,X1)
| ~ equalish(X2,X0)
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( reflexive_rewrite(X0,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( rewrite(X0,X1)
| equalish(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( rewrite(X1,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( rewrite(X2,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,negated_conjecture,
~ goal,
inference(cnf_transformation,[],[f36]) ).
tcf(c_66,plain,
! [X0: $i] :
( ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_60,c_51]) ).
tcf(c_67,plain,
! [X0: $i] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) ),
inference(renaming,[status(thm)],[c_66]) ).
tcf(c_163,plain,
! [X0: $i] :
( reflexive_rewrite(b,X0)
| ~ equalish(b,X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_165,plain,
! [X0: $i] :
( reflexive_rewrite(b,X0)
| ~ rewrite(b,X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( reflexive_rewrite(b,X1)
| ~ equalish(b,X0)
| ~ reflexive_rewrite(X0,X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_168,plain,
( reflexive_rewrite(b,b)
| ~ equalish(b,b) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_169,plain,
equalish(b,b),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_170,plain,
! [X0: $i] :
( equalish(b,X0)
| ~ equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_171,plain,
( equalish(b,a)
| ~ equalish(a,b) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_177,plain,
( ~ reflexive_rewrite(c,b)
| ~ reflexive_rewrite(b,b) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_183,plain,
! [X0: $i] :
( rewrite(X0,b)
| equalish(X0,b)
| ~ reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_184,plain,
( rewrite(a,b)
| equalish(a,b)
| ~ reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_192,plain,
! [X0: $i] :
( reflexive_rewrite(c,b)
| ~ equalish(c,X0)
| ~ reflexive_rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_193,plain,
( reflexive_rewrite(c,b)
| ~ equalish(c,a)
| ~ reflexive_rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_192]) ).
tcf(c_194,plain,
! [X0: $i] :
( reflexive_rewrite(c,X0)
| ~ rewrite(c,X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_195,plain,
! [X0: $i] :
( reflexive_rewrite(c,X0)
| ~ equalish(c,X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_204,plain,
! [X0: $i] :
( equalish(c,X0)
| ~ equalish(X0,c) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_205,plain,
( equalish(c,a)
| ~ equalish(a,c) ),
inference(instantiation,[status(thm)],[c_204]) ).
tcf(c_209,plain,
( reflexive_rewrite(c,c)
| ~ equalish(c,c) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_210,plain,
equalish(c,c),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_227,plain,
( ~ reflexive_rewrite(c,c)
| ~ reflexive_rewrite(b,c) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_234,plain,
! [X0: $i] :
( rewrite(X0,c)
| equalish(X0,c)
| ~ reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_235,plain,
( rewrite(a,c)
| equalish(a,c)
| ~ reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_255,plain,
! [X0: $i] :
( reflexive_rewrite(b,c)
| ~ equalish(b,X0)
| ~ reflexive_rewrite(X0,c) ),
inference(instantiation,[status(thm)],[c_167]) ).
tcf(c_256,plain,
( reflexive_rewrite(b,c)
| ~ equalish(b,a)
| ~ reflexive_rewrite(a,c) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( rewrite(X1,sK0(c,X1))
| ~ rewrite(X0,c)
| ~ rewrite(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] :
( rewrite(c,sK0(c,X1))
| ~ rewrite(X0,c)
| ~ rewrite(X0,X1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_311,plain,
! [X0: $i] :
( rewrite(c,sK0(c,b))
| ~ rewrite(X0,c)
| ~ rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_312,plain,
( rewrite(c,sK0(c,b))
| ~ rewrite(a,c)
| ~ rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_315,plain,
! [X0: $i] :
( rewrite(b,sK0(c,b))
| ~ rewrite(X0,c)
| ~ rewrite(X0,b) ),
inference(instantiation,[status(thm)],[c_262]) ).
tcf(c_316,plain,
( rewrite(b,sK0(c,b))
| ~ rewrite(a,c)
| ~ rewrite(a,b) ),
inference(instantiation,[status(thm)],[c_315]) ).
tcf(c_331,plain,
( reflexive_rewrite(c,sK0(c,b))
| ~ rewrite(c,sK0(c,b)) ),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_355,plain,
( reflexive_rewrite(b,sK0(c,b))
| ~ rewrite(b,sK0(c,b)) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_540,plain,
( ~ reflexive_rewrite(c,sK0(c,b))
| ~ reflexive_rewrite(b,sK0(c,b)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_541,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_540,c_355,c_331,c_316,c_312,c_256,c_235,c_227,c_210,c_209,c_205,c_193,c_184,c_177,c_171,c_169,c_168,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 07:44:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 1.58/1.06 % SZS status Started for theBenchmark.p
% 1.58/1.06 % SZS status Theorem for theBenchmark.p
% 1.58/1.06
% 1.58/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.58/1.06
% 1.58/1.06 % ------ iProver source info
% 1.58/1.06
% 1.58/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 1.58/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.58/1.06 % git: non_committed_changes: false
% 1.58/1.06
% 1.58/1.06 % ------ Parsing...
% 1.58/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.58/1.06
% 1.58/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.58/1.06
% 1.58/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.58/1.06 % ------ Proving...
% 1.58/1.06 % ------ Problem Properties
% 1.58/1.06
% 1.58/1.06 %
% 1.58/1.06 % clauses 11
% 1.58/1.06 % conjectures 0
% 1.58/1.06 % EPR 9
% 1.58/1.06 % Horn 10
% 1.58/1.06 % unary 3
% 1.58/1.06 % binary 4
% 1.58/1.06 % lits 23
% 1.58/1.06 % lits eq 0
% 1.58/1.06 % fd_pure 0
% 1.58/1.06 % fd_pseudo 0
% 1.58/1.06 % fd_cond 0
% 1.58/1.06 % fd_pseudo_cond 0
% 1.58/1.06 % AC symbols 0
% 1.58/1.06
% 1.58/1.06 % ------ Schedule dynamic 5 is on
% 1.58/1.06
% 1.58/1.06 % ------ no conjectures: strip conj schedule
% 1.58/1.06
% 1.58/1.06 % ------ no equalities: superposition off
% 1.58/1.06
% 1.58/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.58/1.06
% 1.58/1.06
% 1.58/1.06 % ------
% 1.58/1.06 % Current options:
% 1.58/1.06 % ------
% 1.58/1.06
% 1.58/1.06
% 1.58/1.06 %
% 1.58/1.06
% 1.58/1.06 % ------ Proving...
% 1.58/1.06 %
% 1.58/1.06
% 1.58/1.06 % SZS status Theorem for theBenchmark.p
% 1.58/1.06
% 1.58/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.58/1.06
% 1.58/1.06
%------------------------------------------------------------------------------