%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 4.00s 1.27s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 25 unt; 5 def)
% Number of atoms : 48 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f4,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
fof(f5,axiom,
! [X0] : weak_fixed_point(X0) = apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f7,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
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_58,plain,
! [X0: $i] : apply(i,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
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(s,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_79,definition,
iPr_def_12 = apply(iPr_def_11,i),
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(fixed_pt,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_82,negated_conjecture,
iPr_def_14 != iPr_def_13,
inference(demodulation,[status(thm)],[c_59,c_77,c_78,c_79,c_80,c_81]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,X0),i),X1) = apply(apply(X0,X1),X1),
inference(superposition,[status(thm)],[c_58,c_55]) ).
tcf(c_158,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_56]) ).
tcf(c_333,plain,
! [X0: $i] : apply(apply(iPr_def_10,X0),X0) = apply(apply(iPr_def_11,i),X0),
inference(superposition,[status(thm)],[c_78,c_148]) ).
tcf(c_370,plain,
! [X0: $i] : apply(fixed_pt,apply(X0,X0)) = apply(apply(iPr_def_11,i),X0),
inference(demodulation,[status(thm)],[c_333,c_158]) ).
tcf(c_371,plain,
! [X0: $i] : apply(fixed_pt,apply(X0,X0)) = apply(iPr_def_12,X0),
inference(light_normalisation,[status(thm)],[c_370,c_79]) ).
tcf(c_447,plain,
apply(fixed_pt,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_80,c_371]) ).
tcf(c_454,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_81,c_447]) ).
tcf(c_455,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_82,c_454]) ).
tcf(c_456,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 07:10:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running UEQ theorem proving
% 0.12/0.38 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 4.00/1.27 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.00/1.27 % SZS status Started for theBenchmark.p
% 4.00/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 4.00/1.27
% 4.00/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.00/1.27
% 4.00/1.27 % ------ iProver source info
% 4.00/1.27
% 4.00/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.00/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.00/1.27 % git: non_committed_changes: false
% 4.00/1.27
% 4.00/1.27 % ------ Parsing...% successful
% 4.00/1.27
% 4.00/1.27
% 4.00/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.00/1.27
% 4.00/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.00/1.27
% 4.00/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.00/1.27
% 4.00/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.00/1.27 % ------ Proving...
% 4.00/1.27 % ------ Problem Properties
% 4.00/1.27
% 4.00/1.27 %
% 4.00/1.27 % clauses 10
% 4.00/1.27 % conjectures 1
% 4.00/1.27 % EPR 1
% 4.00/1.27 % Horn 10
% 4.00/1.27 % unary 10
% 4.00/1.27 % binary 0
% 4.00/1.27 % lits 10
% 4.00/1.27 % lits eq 10
% 4.00/1.27 % fd_pure 0
% 4.00/1.27 % fd_pseudo 0
% 4.00/1.27 % fd_cond 0
% 4.00/1.27 % fd_pseudo_cond 0
% 4.00/1.27 % AC symbols 0
% 4.00/1.27
% 4.00/1.27 % ------ Input Options Time Limit: Unbounded
% 4.00/1.27
% 4.00/1.27
% 4.00/1.27 % ------
% 4.00/1.27 % Current options:
% 4.00/1.27 % ------
% 4.00/1.27
% 4.00/1.27
% 4.00/1.27 %
% 4.00/1.27
% 4.00/1.27 % ------ Proving...
% 4.00/1.27 %
% 4.00/1.27
% 4.00/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 4.00/1.27
% 4.00/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.00/1.27
% 4.00/1.27
%------------------------------------------------------------------------------