%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 22.01s 3.84s
% Output : CNFRefutation 22.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 20 unt; 3 def)
% Number of atoms : 51 ( 27 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 12 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f5,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2b) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,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,[],[f2]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,negated_conjecture,
apply(abstraction,apply(abstraction,k(b))) != k(b),
inference(cnf_transformation,[],[f5]) ).
tcf(c_81,definition,
iPr_def_10 = k(b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_82,definition,
iPr_def_11 = apply(abstraction,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_83,definition,
iPr_def_12 = apply(abstraction,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_84,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_58,c_81,c_82,c_83]) ).
tcf(c_29332,plain,
! [X0: $i] : apply(iPr_def_10,X0) = b,
inference(superposition,[status(thm)],[c_81,c_54]) ).
tcf(c_29338,plain,
! [X0: $i,X1: $i] : apply(apply(apply(abstraction,iPr_def_10),X0),X1) = apply(b,apply(X0,X1)),
inference(superposition,[status(thm)],[c_29332,c_55]) ).
tcf(c_29350,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),X1) = apply(b,apply(X0,X1)),
inference(light_normalisation,[status(thm)],[c_29338,c_82]) ).
tcf(c_29362,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ( apply(X0,n(X0,iPr_def_10)) != b ) ),
inference(superposition,[status(thm)],[c_29332,c_56]) ).
tcf(c_29379,plain,
! [X0: $i,X1: $i] : apply(b,apply(k(X0),apply(X1,X0))) = apply(apply(apply(abstraction,iPr_def_11),X1),X0),
inference(superposition,[status(thm)],[c_29350,c_55]) ).
tcf(c_29382,plain,
! [X0: $i,X1: $i] : apply(b,apply(k(X0),apply(X1,X0))) = apply(apply(iPr_def_12,X1),X0),
inference(light_normalisation,[status(thm)],[c_29379,c_83]) ).
tcf(c_29398,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(b,X1),
inference(demodulation,[status(thm)],[c_29382,c_54]) ).
tcf(c_29403,plain,
! [X0: $i,X1: $i] :
( ( apply(iPr_def_12,X1) = X0 )
| ( apply(X0,n(apply(iPr_def_12,X1),X0)) != apply(b,n(apply(iPr_def_12,X1),X0)) ) ),
inference(superposition,[status(thm)],[c_29398,c_56]) ).
tcf(c_30360,plain,
! [X0: $i] : apply(iPr_def_12,X0) = b,
inference(equality_resolution,[status(thm)],[c_29403]) ).
tcf(c_30502,plain,
iPr_def_10 = iPr_def_12,
inference(superposition,[status(thm)],[c_30360,c_29362]) ).
tcf(c_30520,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_84,c_30502]) ).
tcf(c_30521,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_30520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 07:33:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 22.01/3.84 % SZS status Started for theBenchmark.p
% 22.01/3.84 % SZS status Unsatisfiable for theBenchmark.p
% 22.01/3.84
% 22.01/3.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.01/3.84
% 22.01/3.84 % ------ iProver source info
% 22.01/3.84
% 22.01/3.84 % git: date: 2026-07-19 20:42:38 +0200
% 22.01/3.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.01/3.84 % git: non_committed_changes: false
% 22.01/3.84
% 22.01/3.84 % ------ Parsing...% successful
% 22.01/3.84
% 22.01/3.84
% 22.01/3.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.01/3.84
% 22.01/3.84 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.01/3.84
% 22.01/3.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.01/3.84
% 22.01/3.84 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 22.01/3.84 % ------ Proving...
% 22.01/3.84 % ------ Problem Properties
% 22.01/3.84
% 22.01/3.84 %
% 22.01/3.84 % clauses 8
% 22.01/3.84 % conjectures 1
% 22.01/3.84 % EPR 1
% 22.01/3.84 % Horn 8
% 22.01/3.84 % unary 7
% 22.01/3.84 % binary 1
% 22.01/3.84 % lits 9
% 22.01/3.84 % lits eq 9
% 22.01/3.84 % fd_pure 0
% 22.01/3.84 % fd_pseudo 0
% 22.01/3.84 % fd_cond 0
% 22.01/3.84 % fd_pseudo_cond 1
% 22.01/3.84 % AC symbols 0
% 22.01/3.84
% 22.01/3.84 % ------ Schedule dynamic 5 is on
% 22.01/3.84
% 22.01/3.84 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.01/3.84
% 22.01/3.84
% 22.01/3.84 % ------
% 22.01/3.84 % Current options:
% 22.01/3.84 % ------
% 22.01/3.84
% 22.01/3.84
% 22.01/3.84 %
% 22.01/3.84
% 22.01/3.84 % ------ Proving...
% 22.01/3.84 %
% 22.01/3.84
% 22.01/3.84 % SZS status Unsatisfiable for theBenchmark.p
% 22.01/3.84
% 22.01/3.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.01/3.84
% 22.01/3.84
%------------------------------------------------------------------------------