%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL044-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 4.10s 1.51s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 13 unt; 0 def)
% Number of atoms : 19 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 14 ( 3 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 : 28 ( 0 sgn 28 !; 0 ?; 21 :)
% 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(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_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(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),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(n,X0),X2),X1),
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(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i] :
( ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) )
| ( apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_56]) ).
tcf(c_76,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt),
inference(unflattening,[status(thm)],[c_75]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X2,X1)),X2),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X3)),X2),X3),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_435,plain,
apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(demodulation,[status(thm)],[c_76,c_53]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(superposition,[status(thm)],[c_217,c_53]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(superposition,[status(thm)],[c_220,c_53]) ).
tcf(c_1249,plain,
$false,
inference(ground_joinability,[status(thm)],[c_435,c_462,c_823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.59 % Computer : n020.cluster.edu
% 0.09/0.59 % Model : x86_64 x86_64
% 0.09/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.59 % Memory : 8046.5625MB
% 0.09/0.59 % OS : Linux 6.8.0-71-generic
% 0.09/0.59 % CPULimit : 300
% 0.09/0.59 % WCLimit : 300
% 0.09/0.59 % DateTime : Fri Sep 25 07:20:21 UTC 2026
% 0.09/0.60 % CPUTime :
% 0.09/0.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.63 Running first-order theorem proving
% 0.14/0.63 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
% 0.14/0.64
% 0.14/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.64
% 0.14/0.65 % Detected problem language: tptp
% 0.14/0.66 % Proving...
% 4.10/1.51 % SZS status Started for theBenchmark.p
% 4.10/1.51 % SZS status Unsatisfiable for theBenchmark.p
% 4.10/1.51
% 4.10/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.10/1.51
% 4.10/1.51 % ------ iProver source info
% 4.10/1.51
% 4.10/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.10/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.10/1.51 % git: non_committed_changes: false
% 4.10/1.51
% 4.10/1.51 % ------ Parsing...% successful
% 4.10/1.51
% 4.10/1.51
% 4.10/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.10/1.51
% 4.10/1.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.10/1.51
% 4.10/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.10/1.51
% 4.10/1.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.10/1.51 % ------ Proving...
% 4.10/1.51 % ------ Problem Properties
% 4.10/1.51
% 4.10/1.51 %
% 4.10/1.51 % clauses 3
% 4.10/1.51 % conjectures 0
% 4.10/1.51 % EPR 0
% 4.10/1.51 % Horn 3
% 4.10/1.51 % unary 3
% 4.10/1.51 % binary 0
% 4.10/1.51 % lits 3
% 4.10/1.51 % lits eq 3
% 4.10/1.51 % fd_pure 0
% 4.10/1.51 % fd_pseudo 0
% 4.10/1.51 % fd_cond 0
% 4.10/1.51 % fd_pseudo_cond 0
% 4.10/1.51 % AC symbols 0
% 4.10/1.51
% 4.10/1.51 % ------ Input Options Time Limit: Unbounded
% 4.10/1.51
% 4.10/1.51
% 4.10/1.51 % ------
% 4.10/1.51 % Current options:
% 4.10/1.51 % ------
% 4.10/1.51
% 4.10/1.51
% 4.10/1.51 %
% 4.10/1.51
% 4.10/1.51 % ------ Proving...
% 4.10/1.51 %
% 4.10/1.51
% 4.10/1.51 % SZS status Unsatisfiable for theBenchmark.p
% 4.10/1.51
% 4.10/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.10/1.51
% 4.10/1.51
%------------------------------------------------------------------------------