%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 01:02:29 PM UTC 2026
% Result : Unsatisfiable 9.15s 2.18s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 41 unt; 9 def)
% Number of atoms : 89 ( 40 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 : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 36 :)
% 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,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_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,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w,X0),X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))) = strong_fixed_point,
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,definition,
iPr_def_10 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_71,definition,
iPr_def_11 = apply(fixed_pt,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_72,definition,
iPr_def_12 = apply(w,w),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_73,definition,
iPr_def_13 = apply(b,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_74,definition,
iPr_def_14 = apply(b,w),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_75,definition,
iPr_def_15 = apply(b,b),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_76,definition,
iPr_def_16 = apply(iPr_def_15,b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_77,definition,
iPr_def_17 = apply(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_78,definition,
iPr_def_18 = apply(iPr_def_13,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_79,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_56,c_70,c_71]) ).
tcf(c_80,plain,
iPr_def_18 = strong_fixed_point,
inference(demodulation,[status(thm)],[c_55,c_75,c_76,c_74,c_77,c_72,c_73,c_78]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w,X0),X1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_128,plain,
apply(iPr_def_18,fixed_pt) = iPr_def_10,
inference(demodulation,[status(thm)],[c_70,c_80]) ).
tcf(c_138,plain,
! [X0: $i] : apply(apply(w,X0),X0) = apply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_72,c_81]) ).
tcf(c_142,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(apply(w,w),X0),
inference(superposition,[status(thm)],[c_81,c_81]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_14,X0),X1) = apply(w,apply(X0,X1)),
inference(superposition,[status(thm)],[c_74,c_82]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_15,X0),X1) = apply(b,apply(X0,X1)),
inference(superposition,[status(thm)],[c_75,c_82]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_13,X0),X1) = apply(iPr_def_12,apply(X0,X1)),
inference(superposition,[status(thm)],[c_73,c_82]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[status(thm)],[c_82,c_81]) ).
tcf(c_152,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_142,c_72]) ).
tcf(c_207,plain,
! [X0: $i] : apply(w,apply(iPr_def_16,X0)) = apply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_77,c_145]) ).
tcf(c_214,plain,
! [X0: $i] : apply(b,apply(b,X0)) = apply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_76,c_146]) ).
tcf(c_221,plain,
! [X0: $i] : apply(iPr_def_12,apply(iPr_def_17,X0)) = apply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_78,c_147]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X1),X2)),
inference(superposition,[status(thm)],[c_149,c_82]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(iPr_def_17,X0),X1),X2),
inference(demodulation,[status(thm)],[c_294,c_207,c_214]) ).
tcf(c_3057,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_17,X0),X1),X1) = apply(X0,apply(iPr_def_12,X1)),
inference(superposition,[status(thm)],[c_152,c_601]) ).
tcf(c_3254,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(iPr_def_17,X0)),X1) = apply(X0,apply(iPr_def_12,X1)),
inference(demodulation,[status(thm)],[c_3057,c_81]) ).
tcf(c_11074,plain,
! [X0: $i] : apply(X0,apply(iPr_def_12,apply(iPr_def_17,X0))) = apply(iPr_def_12,apply(iPr_def_17,X0)),
inference(superposition,[status(thm)],[c_3254,c_138]) ).
tcf(c_11120,plain,
! [X0: $i] : apply(X0,apply(iPr_def_18,X0)) = apply(iPr_def_18,X0),
inference(demodulation,[status(thm)],[c_11074,c_221]) ).
tcf(c_11431,plain,
apply(fixed_pt,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_11120]) ).
tcf(c_12035,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_11431,c_71]) ).
tcf(c_12191,plain,
$false,
inference(superposition,[status(thm)],[c_12035,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:07:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running UEQ theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 9.15/2.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.15/2.18 % SZS status Started for theBenchmark.p
% 9.15/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.15/2.18
% 9.15/2.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.15/2.18
% 9.15/2.18 % ------ iProver source info
% 9.15/2.18
% 9.15/2.18 % git: date: 2026-07-19 20:42:38 +0200
% 9.15/2.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.15/2.18 % git: non_committed_changes: false
% 9.15/2.18
% 9.15/2.18 % ------ Parsing...% successful
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.15/2.18 % ------ Proving...
% 9.15/2.18 % ------ Problem Properties
% 9.15/2.18
% 9.15/2.18 %
% 9.15/2.18 % clauses 13
% 9.15/2.18 % conjectures 1
% 9.15/2.18 % EPR 2
% 9.15/2.18 % Horn 13
% 9.15/2.18 % unary 13
% 9.15/2.18 % binary 0
% 9.15/2.18 % lits 13
% 9.15/2.18 % lits eq 13
% 9.15/2.18 % fd_pure 0
% 9.15/2.18 % fd_pseudo 0
% 9.15/2.18 % fd_cond 0
% 9.15/2.18 % fd_pseudo_cond 0
% 9.15/2.18 % AC symbols 0
% 9.15/2.18
% 9.15/2.18 % ------ Input Options Time Limit: Unbounded
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 % ------
% 9.15/2.18 % Current options:
% 9.15/2.18 % ------
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 %
% 9.15/2.18
% 9.15/2.18 % ------ Proving...
% 9.15/2.18 %
% 9.15/2.18
% 9.15/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.15/2.18
% 9.15/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.15/2.18
% 9.15/2.18
%------------------------------------------------------------------------------