%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL077-1 : 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 : n019.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 71.88s 11.37s
% Output : CNFRefutation 71.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 17 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 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(f13,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f14,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1a) ).
fof(f15,plain,
identity != apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),
inference(reorient_equations,[],[f14]) ).
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_71,plain,
! [X0: $i] : apply(identity,X0) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(cnf_transformation,[],[f15]) ).
tcf(c_415,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_839,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(superposition,[status(thm)],[c_66,c_415]) ).
tcf(c_867,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
inference(demodulation,[status(thm)],[c_72,c_839]) ).
tcf(c_2466,plain,
! [X0: $i] :
( ( X0 = identity )
| ( apply(X0,n(X0,identity)) != n(X0,identity) ) ),
inference(superposition,[status(thm)],[c_71,c_69]) ).
tcf(c_2529,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(abstraction,abstraction),X0),k(X1)),apply(X2,X1)) = apply(k(X1),apply(apply(apply(abstraction,X0),X2),X1)),
inference(superposition,[status(thm)],[c_66,c_839]) ).
tcf(c_7995,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
inference(demodulation,[status(thm)],[c_2529,c_61,c_66]) ).
tcf(c_8048,plain,
! [X0: $i,X1: $i] : apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1) = identity,
inference(superposition,[status(thm)],[c_7995,c_2466]) ).
tcf(c_8068,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) = identity,
inference(instantiation,[status(thm)],[c_8048]) ).
tcf(c_8069,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8068,c_867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 07:29:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 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...
% 71.88/11.37 % SZS status Started for theBenchmark.p
% 71.88/11.37 % SZS status Unsatisfiable for theBenchmark.p
% 71.88/11.37
% 71.88/11.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.88/11.37
% 71.88/11.37 % ------ iProver source info
% 71.88/11.37
% 71.88/11.37 % git: date: 2026-07-19 20:42:38 +0200
% 71.88/11.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.88/11.37 % git: non_committed_changes: false
% 71.88/11.37
% 71.88/11.37 % ------ Parsing...% successful
% 71.88/11.37
% 71.88/11.37
% 71.88/11.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 71.88/11.37
% 71.88/11.37 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 71.88/11.37
% 71.88/11.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.88/11.37
% 71.88/11.37 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 71.88/11.37 % ------ Proving...
% 71.88/11.37 % ------ Problem Properties
% 71.88/11.37
% 71.88/11.37 %
% 71.88/11.37 % clauses 12
% 71.88/11.37 % conjectures 1
% 71.88/11.37 % EPR 1
% 71.88/11.37 % Horn 11
% 71.88/11.37 % unary 10
% 71.88/11.37 % binary 2
% 71.88/11.37 % lits 14
% 71.88/11.37 % lits eq 14
% 71.88/11.37 % fd_pure 0
% 71.88/11.37 % fd_pseudo 0
% 71.88/11.37 % fd_cond 0
% 71.88/11.37 % fd_pseudo_cond 2
% 71.88/11.37 % AC symbols 0
% 71.88/11.37
% 71.88/11.37 % ------ Input Options Time Limit: Unbounded
% 71.88/11.37
% 71.88/11.37
% 71.88/11.37 % ------
% 71.88/11.37 % Current options:
% 71.88/11.37 % ------
% 71.88/11.37
% 71.88/11.37
% 71.88/11.37 %
% 71.88/11.37
% 71.88/11.37 % ------ Proving...
% 71.88/11.37 %
% 71.88/11.37
% 71.88/11.37 % SZS status Unsatisfiable for theBenchmark.p
% 71.88/11.37
% 71.88/11.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.88/11.37
% 71.88/11.37
%------------------------------------------------------------------------------