%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:02:38 PM UTC 2026
% Result : Unsatisfiable 111.60s 17.45s
% Output : CNFRefutation 111.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 13 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?; 30 :)
% 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,
! [X2,X0,X1] : apply(apply(apply(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_definition) ).
fof(f3,axiom,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)),
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,X2: $i] : apply(apply(apply(X0,X1),X2),X1) = apply(apply(apply(h,X0),X1),X2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i] :
( fixed_point(X0)
| ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i] :
( fixed_point(X0)
| ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) ) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_79,plain,
! [X0: $i] :
( ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) )
| ( apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_56]) ).
tcf(c_80,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt),
inference(unflattening,[status(thm)],[c_79]) ).
tcf(c_91,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(demodulation,[status(thm)],[c_80,c_53]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(h,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(h,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(h,X0),X1),X2),X2) = apply(apply(apply(h,apply(X0,X1)),X2),X1),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_168,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(demodulation,[status(thm)],[c_91,c_53,c_135]) ).
tcf(c_4930,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(h,apply(b,b)),X0),X1),X2) = apply(apply(X0,X1),apply(X0,X2)),
inference(superposition,[status(thm)],[c_132,c_53]) ).
tcf(c_4931,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X2),X1)),
inference(superposition,[status(thm)],[c_132,c_53]) ).
tcf(c_34221,plain,
! [X0: $i,X1: $i] : apply(apply(apply(h,apply(apply(b,b),X0)),X1),X0) = apply(apply(X0,X1),apply(X0,X1)),
inference(superposition,[status(thm)],[c_4930,c_142]) ).
tcf(c_175760,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(h,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X1),apply(X2,X1)),
inference(superposition,[status(thm)],[c_135,c_53]) ).
tcf(c_180213,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),
inference(superposition,[status(thm)],[c_175760,c_168]) ).
tcf(c_188827,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(superposition,[status(thm)],[c_135,c_180213]) ).
tcf(c_188832,plain,
apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))),
inference(superposition,[status(thm)],[c_34221,c_188827]) ).
tcf(c_188847,plain,
$false,
inference(superposition,[status(thm)],[c_4931,c_188832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 07:18:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.40
% 0.10/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.40
% 0.10/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 111.60/17.45 % SZS status Started for theBenchmark.p
% 111.60/17.45 % SZS status Unsatisfiable for theBenchmark.p
% 111.60/17.45
% 111.60/17.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 111.60/17.45
% 111.60/17.45 % ------ iProver source info
% 111.60/17.45
% 111.60/17.45 % git: date: 2026-07-19 20:42:38 +0200
% 111.60/17.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 111.60/17.45 % git: non_committed_changes: false
% 111.60/17.45
% 111.60/17.45 % ------ Parsing...% successful
% 111.60/17.45
% 111.60/17.45
% 111.60/17.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 111.60/17.45
% 111.60/17.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 111.60/17.45
% 111.60/17.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 111.60/17.45
% 111.60/17.45 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 111.60/17.45 % ------ Proving...
% 111.60/17.45 % ------ Problem Properties
% 111.60/17.45
% 111.60/17.45 %
% 111.60/17.45 % clauses 3
% 111.60/17.45 % conjectures 0
% 111.60/17.45 % EPR 0
% 111.60/17.45 % Horn 3
% 111.60/17.45 % unary 3
% 111.60/17.45 % binary 0
% 111.60/17.45 % lits 3
% 111.60/17.45 % lits eq 3
% 111.60/17.45 % fd_pure 0
% 111.60/17.45 % fd_pseudo 0
% 111.60/17.45 % fd_cond 0
% 111.60/17.45 % fd_pseudo_cond 0
% 111.60/17.45 % AC symbols 0
% 111.60/17.45
% 111.60/17.45 % ------ Input Options Time Limit: Unbounded
% 111.60/17.45
% 111.60/17.45
% 111.60/17.45 % ------
% 111.60/17.45 % Current options:
% 111.60/17.45 % ------
% 111.60/17.45
% 111.60/17.45
% 111.60/17.45 %
% 111.60/17.45
% 111.60/17.45 % ------ Proving...
% 111.60/17.45 %
% 111.60/17.45
% 111.60/17.45 % SZS status Unsatisfiable for theBenchmark.p
% 111.60/17.45
% 111.60/17.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 111.60/17.45
% 111.60/17.45
%------------------------------------------------------------------------------