%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 01:01:09 PM UTC 2026
% Result : Unsatisfiable 2.37s 11.29s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 53 unt; 4 def)
% Number of atoms : 107 ( 52 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f9,axiom,
! [X0] : ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f10,plain,
! [X0] : true = ifeq(there_exists(domain(X0)),true,there_exists(X0),true),
inference(reorient_equations,[],[f9]) ).
fof(f13,axiom,
! [X0,X1] : ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f14,plain,
! [X0,X1] : true = ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0,X1] : ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f16,plain,
! [X0,X1] : codomain(X1) = ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f21,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
fof(f22,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
fof(f23,plain,
true = there_exists(compose(a,b)),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_71,plain,
! [X0: $i] : ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : compose(compose(X0,X1),X2) = compose(X0,compose(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,plain,
! [X0: $i] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[],[f21]) ).
tcf(c_79,plain,
there_exists(compose(a,b)) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_80,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
inference(cnf_transformation,[],[f24]) ).
tcf(c_135,definition,
iPr_def_10 = compose(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = codomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = codomain(a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = there_exists(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,negated_conjecture,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_80,c_137,c_135,c_136]) ).
tcf(c_140,plain,
iPr_def_13 = true,
inference(demodulation,[status(thm)],[c_79,c_138]) ).
tcf(c_141,plain,
! [X0: $i] : compose(codomain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : compose(compose(X0,X1),X2) = compose(X0,compose(X1,X2)),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] : ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_148,plain,
! [X0: $i] : ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_265,plain,
! [X0: $i] : ifeq(there_exists(domain(X0)),iPr_def_13,there_exists(X0),iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_148,c_140]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : ifeq(there_exists(compose(X0,X1)),iPr_def_13,there_exists(domain(X0)),iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_146,c_140]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : ifeq2(there_exists(compose(X0,X1)),iPr_def_13,domain(X0),codomain(X1)) = codomain(X1),
inference(demodulation,[status(thm)],[c_145,c_140]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] : compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(superposition,[status(thm)],[c_141,c_143]) ).
tcf(c_304,plain,
ifeq(there_exists(iPr_def_10),iPr_def_13,there_exists(domain(a)),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_135,c_267]) ).
tcf(c_322,plain,
! [X0: $i] : ifeq2(there_exists(X0),iPr_def_13,domain(codomain(X0)),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c_141,c_268]) ).
tcf(c_325,plain,
! [X0: $i] : ifeq2(there_exists(compose(X0,iPr_def_10)),iPr_def_13,domain(X0),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_136,c_268]) ).
tcf(c_345,plain,
there_exists(domain(a)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_304,c_152,c_138]) ).
tcf(c_399,plain,
ifeq(iPr_def_13,iPr_def_13,there_exists(a),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_345,c_265]) ).
tcf(c_465,plain,
compose(codomain(a),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_135,c_297]) ).
tcf(c_588,plain,
ifeq2(there_exists(a),iPr_def_13,domain(iPr_def_12),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_137,c_322]) ).
tcf(c_834,plain,
compose(iPr_def_12,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_465,c_137]) ).
tcf(c_836,plain,
there_exists(a) = iPr_def_13,
inference(demodulation,[status(thm)],[c_399,c_152]) ).
tcf(c_838,plain,
ifeq2(iPr_def_13,iPr_def_13,domain(iPr_def_12),iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_588,c_836]) ).
tcf(c_839,plain,
domain(iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_838,c_153]) ).
tcf(c_1194,plain,
ifeq2(there_exists(iPr_def_10),iPr_def_13,domain(iPr_def_12),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_834,c_325]) ).
tcf(c_1352,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_1194,c_153,c_138,c_839]) ).
tcf(c_1353,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1352,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/10.38 % Computer : n020.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 06:55:15 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.42 Running UEQ theorem proving
% 0.14/10.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/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...
% 2.37/11.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.37/11.29 % SZS status Started for theBenchmark.p
% 2.37/11.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.37/11.29
% 2.37/11.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.37/11.29
% 2.37/11.29 % ------ iProver source info
% 2.37/11.29
% 2.37/11.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.37/11.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.37/11.29 % git: non_committed_changes: false
% 2.37/11.29
% 2.37/11.29 % ------ Parsing...% successful
% 2.37/11.29
% 2.37/11.29
% 2.37/11.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.37/11.29
% 2.37/11.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.37/11.29
% 2.37/11.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.37/11.29
% 2.37/11.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.37/11.29 % ------ Proving...
% 2.37/11.29 % ------ Problem Properties
% 2.37/11.29
% 2.37/11.29 %
% 2.37/11.29 % clauses 20
% 2.37/11.29 % conjectures 1
% 2.37/11.29 % EPR 2
% 2.37/11.29 % Horn 20
% 2.37/11.29 % unary 20
% 2.37/11.29 % binary 0
% 2.37/11.29 % lits 20
% 2.37/11.29 % lits eq 20
% 2.37/11.29 % fd_pure 0
% 2.37/11.29 % fd_pseudo 0
% 2.37/11.29 % fd_cond 0
% 2.37/11.29 % fd_pseudo_cond 0
% 2.37/11.29 % AC symbols 0
% 2.37/11.29
% 2.37/11.29 % ------ Input Options Time Limit: Unbounded
% 2.37/11.29
% 2.37/11.29
% 2.37/11.29 % ------
% 2.37/11.29 % Current options:
% 2.37/11.29 % ------
% 2.37/11.29
% 2.37/11.29
% 2.37/11.29 %
% 2.37/11.29
% 2.37/11.29 % ------ Proving...
% 2.37/11.29 %
% 2.37/11.29
% 2.37/11.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.37/11.29
% 2.37/11.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.37/11.29
% 2.37/11.29
%------------------------------------------------------------------------------