%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL003-17 : 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 : n003.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 71.82s 11.39s
% Output : CNFRefutation 71.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 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; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?; 28 :)
% 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(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),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(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),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_102,plain,
! [X0: $i,X1: $i] : apply(apply(apply(w,X0),X1),X1) = apply(apply(w,apply(X0,X1)),X1),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_104,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(apply(w,w),X0),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(w,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1),
inference(superposition,[status(thm)],[c_120,c_54]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(X0,X1)),X1) = apply(apply(w,apply(w,X0)),X1),
inference(demodulation,[status(thm)],[c_102,c_54]) ).
tcf(c_470,plain,
! [X0: $i] : apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(apply(b,w),X0)),X1) = apply(apply(w,apply(w,X0)),X1),
inference(superposition,[status(thm)],[c_119,c_387]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1) = apply(X0,apply(apply(X1,X1),X1)),
inference(superposition,[status(thm)],[c_207,c_53]) ).
tcf(c_1588,plain,
! [X0: $i] : apply(apply(w,apply(w,X0)),apply(apply(b,w),X0)) = apply(apply(w,w),apply(apply(b,w),X0)),
inference(superposition,[status(thm)],[c_557,c_54]) ).
tcf(c_20668,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1) = apply(X0,apply(apply(w,w),X1)),
inference(superposition,[status(thm)],[c_104,c_1185]) ).
tcf(c_63543,plain,
! [X0: $i] : apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(demodulation,[status(thm)],[c_470,c_53]) ).
tcf(c_122065,plain,
! [X0: $i] : apply(X0,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))),
inference(superposition,[status(thm)],[c_1588,c_20668]) ).
tcf(c_122066,plain,
! [X0: $i] : apply(X0,apply(strong_fixed_point,X0)) = apply(strong_fixed_point,X0),
inference(light_normalisation,[status(thm)],[c_122065,c_63543]) ).
tcf(c_122068,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_122066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-17 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Sep 25 07:09:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running UEQ theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 71.82/11.39 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 71.82/11.39 % SZS status Started for theBenchmark.p
% 71.82/11.39 % SZS status Unsatisfiable for theBenchmark.p
% 71.82/11.39
% 71.82/11.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.82/11.39
% 71.82/11.39 % ------ iProver source info
% 71.82/11.39
% 71.82/11.39 % git: date: 2026-07-19 20:42:38 +0200
% 71.82/11.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.82/11.39 % git: non_committed_changes: false
% 71.82/11.39
% 71.82/11.39 % ------ Parsing...% successful
% 71.82/11.39
% 71.82/11.39
% 71.82/11.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 71.82/11.39
% 71.82/11.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 71.82/11.39
% 71.82/11.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.82/11.39
% 71.82/11.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 71.82/11.39 % ------ Proving...
% 71.82/11.39 % ------ Problem Properties
% 71.82/11.39
% 71.82/11.39 %
% 71.82/11.39 % clauses 4
% 71.82/11.39 % conjectures 1
% 71.82/11.39 % EPR 0
% 71.82/11.39 % Horn 4
% 71.82/11.39 % unary 4
% 71.82/11.39 % binary 0
% 71.82/11.39 % lits 4
% 71.82/11.39 % lits eq 4
% 71.82/11.39 % fd_pure 0
% 71.82/11.39 % fd_pseudo 0
% 71.82/11.39 % fd_cond 0
% 71.82/11.39 % fd_pseudo_cond 0
% 71.82/11.39 % AC symbols 0
% 71.82/11.39
% 71.82/11.39 % ------ Input Options Time Limit: Unbounded
% 71.82/11.39
% 71.82/11.39
% 71.82/11.39 % ------
% 71.82/11.39 % Current options:
% 71.82/11.39 % ------
% 71.82/11.39
% 71.82/11.39
% 71.82/11.39 %
% 71.82/11.39
% 71.82/11.39 % ------ Proving...
% 71.82/11.39 %
% 71.82/11.39
% 71.82/11.39 % SZS status Unsatisfiable for theBenchmark.p
% 71.82/11.39
% 71.82/11.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.82/11.39
% 71.82/11.39
%------------------------------------------------------------------------------