%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL078-2 : 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 3.08s 1.73s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 30 unt; 5 def)
% Number of atoms : 74 ( 39 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f5,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).
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_57,plain,
! [X0: $i] : apply(identity,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_58,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_81,definition,
iPr_def_10 = apply(abstraction,abstraction),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_82,definition,
iPr_def_11 = apply(iPr_def_10,abstraction),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_83,definition,
iPr_def_12 = apply(iPr_def_11,abstraction),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_84,definition,
iPr_def_13 = k(identity),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_85,definition,
iPr_def_14 = k(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_86,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_58,c_84,c_85,c_81,c_82,c_83]) ).
tcf(c_134,plain,
! [X0: $i] : apply(iPr_def_13,X0) = identity,
inference(superposition,[status(thm)],[c_84,c_54]) ).
tcf(c_135,plain,
! [X0: $i] : apply(iPr_def_14,X0) = iPr_def_13,
inference(superposition,[status(thm)],[c_85,c_54]) ).
tcf(c_138,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_54,c_55]) ).
tcf(c_146,plain,
! [X0: $i] : apply(apply(apply(abstraction,X0),abstraction),abstraction) = apply(apply(X0,k(abstraction)),iPr_def_10),
inference(superposition,[status(thm)],[c_81,c_55]) ).
tcf(c_171,plain,
! [X0: $i] :
( ( X0 = identity )
| ( apply(X0,n(X0,identity)) != n(X0,identity) ) ),
inference(superposition,[status(thm)],[c_57,c_56]) ).
tcf(c_172,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( apply(X0,n(X0,iPr_def_13)) != identity ) ),
inference(superposition,[status(thm)],[c_134,c_56]) ).
tcf(c_205,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ( apply(X0,n(iPr_def_14,X0)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_135,c_56]) ).
tcf(c_305,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_55,c_138]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i] : apply(X0,apply(apply(X1,X0),X2)) = apply(apply(apply(iPr_def_10,X1),X0),X2),
inference(light_normalisation,[status(thm)],[c_305,c_81]) ).
tcf(c_1015,plain,
apply(apply(abstraction,k(abstraction)),iPr_def_10) = apply(apply(iPr_def_10,abstraction),abstraction),
inference(superposition,[status(thm)],[c_81,c_146]) ).
tcf(c_1024,plain,
apply(apply(abstraction,k(abstraction)),iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1015,c_82,c_83]) ).
tcf(c_1047,plain,
! [X0: $i] : apply(abstraction,apply(iPr_def_10,X0)) = apply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1024,c_138]) ).
tcf(c_4412,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_10,X0),k(X1)),X2) = X1,
inference(superposition,[status(thm)],[c_319,c_54]) ).
tcf(c_4968,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,apply(iPr_def_10,X0)),X1),X2) = X2,
inference(superposition,[status(thm)],[c_4412,c_55]) ).
tcf(c_4994,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_12,X0),X1),X2) = X2,
inference(light_normalisation,[status(thm)],[c_4968,c_1047]) ).
tcf(c_5417,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = identity,
inference(superposition,[status(thm)],[c_4994,c_171]) ).
tcf(c_5645,plain,
! [X0: $i] : apply(iPr_def_12,X0) = iPr_def_13,
inference(superposition,[status(thm)],[c_5417,c_172]) ).
tcf(c_5737,plain,
iPr_def_12 = iPr_def_14,
inference(superposition,[status(thm)],[c_5645,c_205]) ).
tcf(c_5743,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5737,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.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 07:30:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 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...
% 3.08/1.73 % SZS status Started for theBenchmark.p
% 3.08/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.08/1.73
% 3.08/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.08/1.73
% 3.08/1.73 % ------ iProver source info
% 3.08/1.73
% 3.08/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 3.08/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.08/1.73 % git: non_committed_changes: false
% 3.08/1.73
% 3.08/1.73 % ------ Parsing...% successful
% 3.08/1.73
% 3.08/1.73
% 3.08/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.08/1.73
% 3.08/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.08/1.73
% 3.08/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.08/1.73
% 3.08/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.08/1.73 % ------ Proving...
% 3.08/1.73 % ------ Problem Properties
% 3.08/1.73
% 3.08/1.73 %
% 3.08/1.73 % clauses 10
% 3.08/1.73 % conjectures 1
% 3.08/1.73 % EPR 1
% 3.08/1.73 % Horn 10
% 3.08/1.73 % unary 9
% 3.08/1.73 % binary 1
% 3.08/1.73 % lits 11
% 3.08/1.73 % lits eq 11
% 3.08/1.73 % fd_pure 0
% 3.08/1.73 % fd_pseudo 0
% 3.08/1.73 % fd_cond 0
% 3.08/1.73 % fd_pseudo_cond 1
% 3.08/1.73 % AC symbols 0
% 3.08/1.73
% 3.08/1.73 % ------ Schedule dynamic 5 is on
% 3.08/1.73
% 3.08/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.08/1.73
% 3.08/1.73
% 3.08/1.73 % ------
% 3.08/1.73 % Current options:
% 3.08/1.73 % ------
% 3.08/1.73
% 3.08/1.73
% 3.08/1.73 %
% 3.08/1.73
% 3.08/1.73 % ------ Proving...
% 3.08/1.73 %
% 3.08/1.73
% 3.08/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.08/1.73
% 3.08/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/1.73
% 3.08/1.73
%------------------------------------------------------------------------------