%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:02:36 PM UTC 2026
% Result : Unsatisfiable 1.84s 0.96s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(apply(o,X0),X1) = apply(X1,apply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o_definition) ).
fof(f4,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i] : apply(X0,X0) = apply(m,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = apply(apply(o,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] : apply(f(X0),apply(X0,f(X0))) != apply(X0,f(X0)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i] : apply(apply(o,X0),f(X0)) != apply(X0,f(X0)),
inference(demodulation,[status(thm)],[c_56,c_55]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,apply(apply(b,X0),X1))) = apply(m,apply(apply(b,X0),X1)),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_2772,plain,
! [X0: $i] : apply(apply(X0,apply(apply(b,o),X0)),f(apply(X0,apply(apply(b,o),X0)))) != apply(apply(m,apply(apply(b,o),X0)),f(apply(X0,apply(apply(b,o),X0)))),
inference(superposition,[status(thm)],[c_254,c_69]) ).
tcf(c_4335,plain,
$false,
inference(equality_resolution,[status(thm)],[c_2772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/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 07:15:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running UEQ theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 1.84/0.96 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.84/0.96 % SZS status Started for theBenchmark.p
% 1.84/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/0.96
% 1.84/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/0.96
% 1.84/0.96 % ------ iProver source info
% 1.84/0.96
% 1.84/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/0.96 % git: non_committed_changes: false
% 1.84/0.96
% 1.84/0.96 % ------ Parsing...% successful
% 1.84/0.96
% 1.84/0.96
% 1.84/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/0.96
% 1.84/0.96 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.84/0.96
% 1.84/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/0.96
% 1.84/0.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.84/0.96 % ------ Proving...
% 1.84/0.96 % ------ Problem Properties
% 1.84/0.96
% 1.84/0.96 %
% 1.84/0.96 % clauses 4
% 1.84/0.96 % conjectures 0
% 1.84/0.96 % EPR 0
% 1.84/0.96 % Horn 4
% 1.84/0.96 % unary 4
% 1.84/0.96 % binary 0
% 1.84/0.96 % lits 4
% 1.84/0.96 % lits eq 4
% 1.84/0.96 % fd_pure 0
% 1.84/0.96 % fd_pseudo 0
% 1.84/0.96 % fd_cond 0
% 1.84/0.96 % fd_pseudo_cond 0
% 1.84/0.96 % AC symbols 0
% 1.84/0.96
% 1.84/0.96 % ------ Input Options Time Limit: Unbounded
% 1.84/0.96
% 1.84/0.96
% 1.84/0.96 % ------
% 1.84/0.96 % Current options:
% 1.84/0.96 % ------
% 1.84/0.96
% 1.84/0.96
% 1.84/0.96 %
% 1.84/0.96
% 1.84/0.96 % ------ Proving...
% 1.84/0.96 %
% 1.84/0.96
% 1.84/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/0.96
% 1.84/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/0.96
% 1.84/0.96
%------------------------------------------------------------------------------