%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 01:02:28 PM UTC 2026
% Result : Unsatisfiable 3.44s 1.20s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 28 unt; 6 def)
% Number of atoms : 56 ( 27 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,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(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
fof(f5,axiom,
! [X0] : weak_fixed_point(X0) = apply(apply(apply(s,apply(c,apply(b,X0))),apply(s,apply(c,apply(b,X0)))),apply(s,apply(c,apply(b,X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f7,plain,
apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(definition_unfolding,[],[f6,f5,f5]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,definition,
iPr_def_10 = apply(b,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_78,definition,
iPr_def_11 = apply(c,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_79,definition,
iPr_def_12 = apply(s,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_80,definition,
iPr_def_13 = apply(iPr_def_12,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_81,definition,
iPr_def_14 = apply(iPr_def_13,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_82,definition,
iPr_def_15 = apply(fixed_pt,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_83,negated_conjecture,
iPr_def_15 != iPr_def_14,
inference(demodulation,[status(thm)],[c_59,c_77,c_78,c_79,c_80,c_81,c_82]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,X0),X1) = apply(apply(iPr_def_11,X1),X0),
inference(superposition,[status(thm)],[c_78,c_85]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(superposition,[status(thm)],[c_77,c_86]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),apply(X1,X0)) = apply(apply(iPr_def_12,X1),X0),
inference(superposition,[status(thm)],[c_79,c_87]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),X1) = apply(fixed_pt,apply(X1,X0)),
inference(demodulation,[status(thm)],[c_129,c_130]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : apply(fixed_pt,apply(apply(X0,X1),X1)) = apply(apply(iPr_def_12,X0),X1),
inference(demodulation,[status(thm)],[c_144,c_155]) ).
tcf(c_298,plain,
apply(fixed_pt,apply(iPr_def_13,iPr_def_12)) = apply(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_80,c_156]) ).
tcf(c_546,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_298,c_81,c_82]) ).
tcf(c_1064,plain,
$false,
inference(superposition,[status(thm)],[c_546,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 07:08:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.44/1.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.44/1.20 % SZS status Started for theBenchmark.p
% 3.44/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.44/1.20
% 3.44/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.44/1.20
% 3.44/1.20 % ------ iProver source info
% 3.44/1.20
% 3.44/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.44/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.44/1.20 % git: non_committed_changes: false
% 3.44/1.20
% 3.44/1.20 % ------ Parsing...% successful
% 3.44/1.20
% 3.44/1.20
% 3.44/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.44/1.20
% 3.44/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.44/1.20
% 3.44/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.44/1.20
% 3.44/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.44/1.20 % ------ Proving...
% 3.44/1.20 % ------ Problem Properties
% 3.44/1.20
% 3.44/1.20 %
% 3.44/1.20 % clauses 11
% 3.44/1.20 % conjectures 1
% 3.44/1.20 % EPR 1
% 3.44/1.20 % Horn 11
% 3.44/1.20 % unary 11
% 3.44/1.20 % binary 0
% 3.44/1.20 % lits 11
% 3.44/1.20 % lits eq 11
% 3.44/1.20 % fd_pure 0
% 3.44/1.20 % fd_pseudo 0
% 3.44/1.20 % fd_cond 0
% 3.44/1.20 % fd_pseudo_cond 0
% 3.44/1.20 % AC symbols 0
% 3.44/1.20
% 3.44/1.20 % ------ Input Options Time Limit: Unbounded
% 3.44/1.20
% 3.44/1.20
% 3.44/1.20 % ------
% 3.44/1.20 % Current options:
% 3.44/1.20 % ------
% 3.44/1.20
% 3.44/1.20
% 3.44/1.20 %
% 3.44/1.20
% 3.44/1.20 % ------ Proving...
% 3.44/1.20 %
% 3.44/1.20
% 3.44/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.44/1.20
% 3.44/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.44/1.20
% 3.44/1.20
%------------------------------------------------------------------------------