%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 32.38s 5.47s
% Output : CNFRefutation 32.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 54 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 34 :)
% 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] :
( fixed_point(X0)
| X0 != apply(fixed_pt,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,plain,
! [X0] :
( fixed_point(X0)
| apply(fixed_pt,X0) != X0 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] : ~ fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
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,plain,
! [X0: $i] :
( fixed_point(X0)
| ( apply(fixed_pt,X0) != X0 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] : ~ fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
inference(cnf_transformation,[],[f7]) ).
tcf(c_81,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1364,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_3053,plain,
! [X0: $i,X1: $i] :
( ( apply(fixed_pt,X0) = X0 )
| ( X0 != X1 )
| ( apply(fixed_pt,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i] :
( fixed_point(apply(X0,X1))
| ( apply(fixed_pt,apply(X0,X1)) != apply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_3059,plain,
! [X0: $i] : apply(fixed_pt,X0) = apply(fixed_pt,X0),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_3060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(fixed_pt,X0) = X2 )
| ( X2 != X1 )
| ( apply(fixed_pt,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(fixed_pt,X0) = X0 )
| ( X0 != apply(X1,X2) )
| ( apply(fixed_pt,X0) != apply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_3053]) ).
tcf(c_3075,plain,
! [X0: $i,X1: $i] :
( ( apply(fixed_pt,X0) = X1 )
| ( X1 != apply(fixed_pt,X0) )
| ( apply(fixed_pt,X0) != apply(fixed_pt,X0) ) ),
inference(instantiation,[status(thm)],[c_3060]) ).
tcf(c_3105,plain,
! [X0: $i,X1: $i] :
( ( apply(fixed_pt,apply(X0,X1)) = apply(apply(apply(b,fixed_pt),X0),X1) )
| ( apply(fixed_pt,apply(X0,X1)) != apply(fixed_pt,apply(X0,X1)) )
| ( apply(apply(apply(b,fixed_pt),X0),X1) != apply(fixed_pt,apply(X0,X1)) ) ),
inference(instantiation,[status(thm)],[c_3075]) ).
tcf(c_3106,plain,
! [X0: $i,X1: $i] : apply(apply(apply(b,fixed_pt),X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3149,plain,
! [X0: $i,X1: $i] :
( ( apply(fixed_pt,apply(X0,X1)) = apply(X0,X1) )
| ( apply(X0,X1) != apply(apply(apply(b,fixed_pt),X0),X1) )
| ( apply(fixed_pt,apply(X0,X1)) != apply(apply(apply(b,fixed_pt),X0),X1) ) ),
inference(instantiation,[status(thm)],[c_3061]) ).
tcf(c_3271,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) = apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,fixed_pt)),i)),apply(apply(s,apply(b,fixed_pt)),i)),
inference(instantiation,[status(thm)],[c_1364]) ).
tcf(c_3583,plain,
( ( 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)) )
| ( apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(apply(apply(b,fixed_pt),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))) != apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,fixed_pt)),i)),apply(apply(s,apply(b,fixed_pt)),i)) ) ),
inference(instantiation,[status(thm)],[c_3149]) ).
tcf(c_3772,plain,
( ( apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) = apply(apply(apply(b,fixed_pt),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))) != apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) )
| ( apply(apply(apply(b,fixed_pt),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(instantiation,[status(thm)],[c_3105]) ).
tcf(c_5585,plain,
apply(apply(apply(b,fixed_pt),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(instantiation,[status(thm)],[c_3106]) ).
tcf(c_8609,plain,
apply(fixed_pt,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(instantiation,[status(thm)],[c_3059]) ).
tcf(c_9424,plain,
( fixed_point(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))) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) ) ),
inference(instantiation,[status(thm)],[c_3055]) ).
tcf(c_15063,plain,
~ fixed_point(apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_15064,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15063,c_9424,c_8609,c_5585,c_3772,c_3583,c_3271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n008.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
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 07:08:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 32.38/5.47 % SZS status Started for theBenchmark.p
% 32.38/5.47 % SZS status Unsatisfiable for theBenchmark.p
% 32.38/5.47
% 32.38/5.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.38/5.47
% 32.38/5.47 % ------ iProver source info
% 32.38/5.47
% 32.38/5.47 % git: date: 2026-07-19 20:42:38 +0200
% 32.38/5.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.38/5.47 % git: non_committed_changes: false
% 32.38/5.47
% 32.38/5.47 % ------ Parsing...% successful
% 32.38/5.47
% 32.38/5.47
% 32.38/5.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.38/5.47
% 32.38/5.47 % ------ Preprocessing...%
% 32.38/5.47
% 32.38/5.47 % ------ Preprocessing...%
% 32.38/5.47
% 32.38/5.47 % ------ Preprocessing...
% 32.38/5.47 % ------ Proving...
% 32.38/5.47 % ------ Problem Properties
% 32.38/5.47
% 32.38/5.47 %
% 32.38/5.47 % clauses 6
% 32.38/5.47 % conjectures 1
% 32.38/5.47 % EPR 0
% 32.38/5.47 % Horn 6
% 32.38/5.47 % unary 5
% 32.38/5.47 % binary 1
% 32.38/5.47 % lits 7
% 32.38/5.47 % lits eq 5
% 32.38/5.47 % fd_pure 0
% 32.38/5.47 % fd_pseudo 0
% 32.38/5.47 % fd_cond 0
% 32.38/5.47 % fd_pseudo_cond 0
% 32.38/5.47 % AC symbols 0
% 32.38/5.47
% 32.38/5.47 % ------ Input Options Time Limit: Unbounded
% 32.38/5.47
% 32.38/5.47
% 32.38/5.47 % ------
% 32.38/5.47 % Current options:
% 32.38/5.47 % ------
% 32.38/5.47
% 32.38/5.47
% 32.38/5.47 %
% 32.38/5.47
% 32.38/5.47 % ------ Proving...
% 32.38/5.47 %
% 32.38/5.47
% 32.38/5.47 % SZS status Unsatisfiable for theBenchmark.p
% 32.38/5.47
% 32.38/5.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.38/5.47
% 32.38/5.47
%------------------------------------------------------------------------------