%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 01:01:12 PM UTC 2026
% Result : Unsatisfiable 0.56s 1.79s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 22 unt; 2 def)
% Number of atoms : 87 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 53 ( 28 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).
fof(f8,axiom,
! [X0,X1] :
( there_exists(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition2) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_codomain) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f13,axiom,
there_exists(compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f14,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
tcf(c_66,plain,
! [X0: $i] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( domain(X0) = codomain(X1) )
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( there_exists(compose(X0,X1))
| ~ there_exists(domain(X0))
| ( domain(X0) != codomain(X1) ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : compose(compose(X0,X1),X2) = compose(X0,compose(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_73,plain,
! [X0: $i] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
there_exists(compose(b,c)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
inference(cnf_transformation,[],[f14]) ).
tcf(c_234,definition,
iPr_def_10 = compose(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_235,definition,
iPr_def_11 = compose(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_236,negated_conjecture,
~ there_exists(iPr_def_11),
inference(demodulation,[status(thm)],[c_76,c_234,c_235]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( there_exists(X0)
| ~ there_exists(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_363,plain,
there_exists(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_75,c_234]) ).
tcf(c_388,plain,
there_exists(domain(a)),
inference(superposition,[status(thm)],[c_74,c_68]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i,X2: $i] :
( there_exists(domain(compose(X0,X1)))
| ~ there_exists(compose(X0,compose(X1,X2))) ),
inference(superposition,[status(thm)],[c_71,c_68]) ).
tcf(c_407,plain,
domain(a) = codomain(b),
inference(superposition,[status(thm)],[c_74,c_69]) ).
tcf(c_411,plain,
! [X0: $i] :
( ( domain(codomain(X0)) = codomain(X0) )
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c_73,c_69]) ).
tcf(c_472,plain,
! [X0: $i] :
( there_exists(iPr_def_11)
| ~ there_exists(X0)
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_241]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i] :
( there_exists(domain(compose(codomain(compose(X0,X1)),X0)))
| ~ there_exists(compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_73,c_390]) ).
tcf(c_569,plain,
( there_exists(iPr_def_11)
| ~ there_exists(compose(a,iPr_def_10))
| ( iPr_def_11 != compose(a,iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_472]) ).
tcf(c_872,plain,
domain(codomain(iPr_def_10)) = codomain(iPr_def_10),
inference(superposition,[status(thm)],[c_363,c_411]) ).
tcf(c_970,plain,
( there_exists(domain(compose(codomain(iPr_def_10),b)))
| ~ there_exists(compose(b,c)) ),
inference(superposition,[status(thm)],[c_234,c_488]) ).
tcf(c_988,plain,
( there_exists(domain(compose(codomain(iPr_def_10),b)))
| ~ there_exists(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_970,c_234]) ).
tcf(c_989,plain,
there_exists(domain(compose(codomain(iPr_def_10),b))),
inference(forward_subsumption_resolution,[status(thm)],[c_988,c_363]) ).
tcf(c_1019,plain,
! [X0: $i] :
( there_exists(compose(a,X0))
| ~ there_exists(domain(a))
| ( domain(a) != codomain(X0) ) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1032,plain,
there_exists(compose(codomain(iPr_def_10),b)),
inference(superposition,[status(thm)],[c_989,c_66]) ).
tcf(c_1042,plain,
domain(codomain(iPr_def_10)) = codomain(b),
inference(superposition,[status(thm)],[c_1032,c_69]) ).
tcf(c_1045,plain,
domain(a) = codomain(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1042,c_407,c_872]) ).
tcf(c_2467,plain,
( there_exists(compose(a,iPr_def_10))
| ~ there_exists(domain(a))
| ( domain(a) != codomain(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_2468,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2467,c_1045,c_569,c_388,c_236,c_235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.81 % Computer : n016.cluster.edu
% 0.13/0.81 % Model : x86_64 x86_64
% 0.13/0.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.81 % Memory : 8046.5625MB
% 0.13/0.81 % OS : Linux 6.8.0-71-generic
% 0.13/0.81 % CPULimit : 300
% 0.13/0.81 % WCLimit : 300
% 0.13/0.81 % DateTime : Fri Sep 25 07:02:33 UTC 2026
% 0.13/0.82 % CPUTime :
% 0.13/0.82 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.88 Running first-order theorem proving
% 0.13/0.88 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
% 0.13/0.89
% 0.13/0.89 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.89
% 0.13/0.89 % Detected problem language: tptp
% 0.17/0.90 % Proving...
% 0.56/1.79 % SZS status Started for theBenchmark.p
% 0.56/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 0.56/1.79
% 0.56/1.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.56/1.79
% 0.56/1.79 % ------ iProver source info
% 0.56/1.79
% 0.56/1.79 % git: date: 2026-07-19 20:42:38 +0200
% 0.56/1.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.56/1.79 % git: non_committed_changes: false
% 0.56/1.79
% 0.56/1.79 % ------ Parsing...% successful
% 0.56/1.79
% 0.56/1.79
% 0.56/1.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.56/1.79
% 0.56/1.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.56/1.79
% 0.56/1.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.56/1.79
% 0.56/1.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.56/1.79 % ------ Proving...
% 0.56/1.79 % ------ Problem Properties
% 0.56/1.79
% 0.56/1.79 %
% 0.56/1.79 % clauses 13
% 0.56/1.79 % conjectures 1
% 0.56/1.79 % EPR 1
% 0.56/1.79 % Horn 13
% 0.56/1.79 % unary 8
% 0.56/1.79 % binary 4
% 0.56/1.79 % lits 19
% 0.56/1.79 % lits eq 7
% 0.56/1.79 % fd_pure 0
% 0.56/1.79 % fd_pseudo 0
% 0.56/1.79 % fd_cond 0
% 0.56/1.79 % fd_pseudo_cond 0
% 0.56/1.79 % AC symbols 0
% 0.56/1.79
% 0.56/1.79 % ------ Schedule dynamic 5 is on
% 0.56/1.79
% 0.56/1.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.56/1.79
% 0.56/1.79
% 0.56/1.79 % ------
% 0.56/1.79 % Current options:
% 0.56/1.79 % ------
% 0.56/1.79
% 0.56/1.79
% 0.56/1.79 %
% 0.56/1.79
% 0.56/1.79 % ------ Proving...
% 0.56/1.79 %
% 0.56/1.79
% 0.56/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 0.56/1.79
% 0.56/1.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.56/1.79
% 0.56/1.79
%------------------------------------------------------------------------------