%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL080-1 : 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 : 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 01:02:47 PM UTC 2026
% Result : Unsatisfiable 75.22s 11.96s
% Output : CNFRefutation 75.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
fof(f14,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2b) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,k(X1)),apply(X2,X1)) = apply(apply(apply(abstraction,X0),X2),X1),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
apply(abstraction,apply(abstraction,k(b))) != k(b),
inference(cnf_transformation,[],[f14]) ).
tcf(c_88,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_103,plain,
( ( apply(abstraction,apply(abstraction,k(b))) = k(b) )
| ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_110,plain,
! [X0: $i] :
( ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) )
| ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != X0 )
| ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != X0 ) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[status(thm)],[c_61,c_66]) ).
tcf(c_193,plain,
! [X0: $i] :
( ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = X0 )
| ( apply(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),X0)) != apply(X0,n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),X0)) ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_195,plain,
( ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) )
| ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) )
| ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) ) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_196,plain,
apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,apply(abstraction,k(X0))),X1),X2) = apply(X0,apply(k(X2),apply(X1,X2))),
inference(superposition,[status(thm)],[c_173,c_66]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,apply(abstraction,k(X0))),X1),X2) = apply(X0,X2),
inference(demodulation,[status(thm)],[c_294,c_61]) ).
tcf(c_317,plain,
! [X0: $i] :
( ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) )
| ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != X0 )
| ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != X0 ) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_781,plain,
( ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) )
| ( apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != b )
| ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != b ) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_782,plain,
apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = b,
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_51392,plain,
( ( apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) = b )
| ( apply(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),b)) != apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),b)) ) ),
inference(instantiation,[status(thm)],[c_193]) ).
tcf(c_60317,plain,
apply(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),b)) = apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),b)),
inference(instantiation,[status(thm)],[c_297]) ).
tcf(c_60318,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_60317,c_51392,c_782,c_781,c_196,c_195,c_103,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL080-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 07:32:08 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.14/0.46
% 0.14/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.46
% 0.14/0.46 % Detected problem language: tptp
% 0.20/0.47 % Proving...
% 75.22/11.96 % SZS status Started for theBenchmark.p
% 75.22/11.96 % SZS status Unsatisfiable for theBenchmark.p
% 75.22/11.96
% 75.22/11.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 75.22/11.96
% 75.22/11.96 % ------ iProver source info
% 75.22/11.96
% 75.22/11.96 % git: date: 2026-07-19 20:42:38 +0200
% 75.22/11.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 75.22/11.96 % git: non_committed_changes: false
% 75.22/11.96
% 75.22/11.96 % ------ Parsing...% successful
% 75.22/11.96
% 75.22/11.96
% 75.22/11.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 75.22/11.96
% 75.22/11.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 75.22/11.96
% 75.22/11.96 % ------ Preprocessing...%
% 75.22/11.96
% 75.22/11.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 75.22/11.96 % ------ Proving...
% 75.22/11.96 % ------ Problem Properties
% 75.22/11.96
% 75.22/11.96 %
% 75.22/11.96 % clauses 12
% 75.22/11.96 % conjectures 1
% 75.22/11.96 % EPR 1
% 75.22/11.96 % Horn 11
% 75.22/11.96 % unary 10
% 75.22/11.96 % binary 2
% 75.22/11.96 % lits 14
% 75.22/11.96 % lits eq 14
% 75.22/11.96 % fd_pure 0
% 75.22/11.96 % fd_pseudo 0
% 75.22/11.96 % fd_cond 0
% 75.22/11.96 % fd_pseudo_cond 2
% 75.22/11.96 % AC symbols 0
% 75.22/11.96
% 75.22/11.96 % ------ Input Options Time Limit: Unbounded
% 75.22/11.96
% 75.22/11.96
% 75.22/11.96 % ------
% 75.22/11.96 % Current options:
% 75.22/11.96 % ------
% 75.22/11.96
% 75.22/11.96
% 75.22/11.96 %
% 75.22/11.96
% 75.22/11.96 % ------ Proving...
% 75.22/11.96 %
% 75.22/11.96
% 75.22/11.96 % SZS status Unsatisfiable for theBenchmark.p
% 75.22/11.96
% 75.22/11.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 75.22/11.96
% 75.22/11.96
%------------------------------------------------------------------------------