%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL081-1 : 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 : n011.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 01:02:48 PM UTC 2026
% Result : Unsatisfiable 0.94s 1.75s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 19 unt; 3 def)
% Number of atoms : 53 ( 26 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 : 25 ( 0 sgn 25 !; 0 ?; 18 :)
% 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(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
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,k(k(b))) != k(k(b)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_124,definition,
iPr_def_10 = k(b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_125,definition,
iPr_def_11 = k(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_126,definition,
iPr_def_12 = apply(abstraction,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_127,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_72,c_124,c_125,c_126]) ).
tcf(c_195,plain,
! [X0: $i] : apply(iPr_def_10,X0) = b,
inference(superposition,[status(thm)],[c_124,c_61]) ).
tcf(c_196,plain,
! [X0: $i] : apply(iPr_def_11,X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_125,c_61]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] : apply(apply(apply(abstraction,iPr_def_11),X0),X1) = apply(iPr_def_10,apply(X0,X1)),
inference(superposition,[status(thm)],[c_196,c_66]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(iPr_def_10,apply(X0,X1)),
inference(light_normalisation,[status(thm)],[c_421,c_126]) ).
tcf(c_523,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ( apply(X0,n(iPr_def_10,X0)) != b ) ),
inference(superposition,[status(thm)],[c_195,c_69]) ).
tcf(c_524,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( apply(X0,n(iPr_def_11,X0)) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_196,c_69]) ).
tcf(c_2194,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = b,
inference(demodulation,[status(thm)],[c_449,c_195]) ).
tcf(c_7387,plain,
! [X0: $i] : apply(iPr_def_12,X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_2194,c_523]) ).
tcf(c_8674,plain,
iPr_def_11 = iPr_def_12,
inference(superposition,[status(thm)],[c_7387,c_524]) ).
tcf(c_8741,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_127,c_8674]) ).
tcf(c_8742,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_8741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:30:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.94/1.75 % SZS status Started for theBenchmark.p
% 0.94/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 0.94/1.75
% 0.94/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.75
% 0.94/1.75 % ------ iProver source info
% 0.94/1.75
% 0.94/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.75 % git: non_committed_changes: false
% 0.94/1.75
% 0.94/1.75 % ------ Parsing...% successful
% 0.94/1.75
% 0.94/1.75
% 0.94/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.75
% 0.94/1.75 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.94/1.75
% 0.94/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.75
% 0.94/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.94/1.75 % ------ Proving...
% 0.94/1.75 % ------ Problem Properties
% 0.94/1.75
% 0.94/1.75 %
% 0.94/1.75 % clauses 15
% 0.94/1.75 % conjectures 1
% 0.94/1.75 % EPR 2
% 0.94/1.75 % Horn 14
% 0.94/1.75 % unary 13
% 0.94/1.75 % binary 2
% 0.94/1.75 % lits 17
% 0.94/1.75 % lits eq 17
% 0.94/1.75 % fd_pure 0
% 0.94/1.75 % fd_pseudo 0
% 0.94/1.75 % fd_cond 0
% 0.94/1.75 % fd_pseudo_cond 2
% 0.94/1.75 % AC symbols 0
% 0.94/1.75
% 0.94/1.75 % ------ Schedule dynamic 5 is on
% 0.94/1.75
% 0.94/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.94/1.75
% 0.94/1.75
% 0.94/1.75 % ------
% 0.94/1.75 % Current options:
% 0.94/1.75 % ------
% 0.94/1.75
% 0.94/1.75
% 0.94/1.75 %
% 0.94/1.75
% 0.94/1.75 % ------ Proving...
% 0.94/1.75 %
% 0.94/1.75
% 0.94/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 0.94/1.75
% 0.94/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.75
% 0.94/1.75
%------------------------------------------------------------------------------