%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL079-2 : 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 158.49s 39.70s
% Output : CNFRefutation 158.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 26 unt; 3 def)
% Number of atoms : 68 ( 33 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 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,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2a) ).
fof(f5,plain,
apply(abstraction,b) != apply(abstraction,apply(abstraction,apply(abstraction,b))),
inference(reorient_equations,[],[f4]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,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_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(cnf_transformation,[],[f5]) ).
tcf(c_75,definition,
iPr_def_10 = apply(abstraction,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_76,definition,
iPr_def_11 = apply(abstraction,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_77,definition,
iPr_def_12 = apply(abstraction,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_78,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_56,c_75,c_76,c_77]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,X0),k(X1)),X2) = apply(apply(X0,k(X2)),X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_3728,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,k(X0)),X1) = apply(apply(iPr_def_11,k(X1)),X0),
inference(superposition,[status(thm)],[c_76,c_1972]) ).
tcf(c_3732,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,apply(abstraction,X0)),X1),X2) = apply(apply(X0,k(apply(X1,X2))),X2),
inference(superposition,[status(thm)],[c_1972,c_54]) ).
tcf(c_7793,plain,
! [X0: $i,X1: $i] : apply(apply(apply(abstraction,apply(abstraction,iPr_def_10)),X0),X1) = apply(apply(iPr_def_11,k(X1)),apply(X0,X1)),
inference(superposition,[status(thm)],[c_3728,c_3732]) ).
tcf(c_7810,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,k(X0)),apply(X1,X0)) = apply(apply(iPr_def_12,X1),X0),
inference(light_normalisation,[status(thm)],[c_7793,c_76,c_77]) ).
tcf(c_125354,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(abstraction,X0),k(X1)),X2) = apply(apply(X0,k(X2)),X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_272992,plain,
! [X0: $i,X1: $i] : apply(apply(b,k(X0)),X1) = apply(apply(iPr_def_10,k(X1)),X0),
inference(superposition,[status(thm)],[c_75,c_125354]) ).
tcf(c_272993,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,k(X0)),X1) = apply(apply(iPr_def_11,k(X1)),X0),
inference(superposition,[status(thm)],[c_76,c_125354]) ).
tcf(c_273133,plain,
! [X0: $i,X1: $i] : apply(apply(b,k(X0)),X1) = apply(apply(iPr_def_11,k(X0)),X1),
inference(superposition,[status(thm)],[c_272993,c_272992]) ).
tcf(c_277740,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,k(X0)),apply(X1,X0)) = apply(apply(apply(abstraction,b),X1),X0),
inference(superposition,[status(thm)],[c_273133,c_54]) ).
tcf(c_277780,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,X0),X1) = apply(apply(iPr_def_12,X0),X1),
inference(light_normalisation,[status(thm)],[c_277740,c_75,c_7810]) ).
tcf(c_277927,plain,
! [X0: $i,X1: $i] :
( ( apply(iPr_def_12,X0) = X1 )
| ( apply(apply(iPr_def_10,X0),n(apply(iPr_def_12,X0),X1)) != apply(X1,n(apply(iPr_def_12,X0),X1)) ) ),
inference(superposition,[status(thm)],[c_277780,c_55]) ).
tcf(c_359603,plain,
! [X0: $i] : apply(iPr_def_10,X0) = apply(iPr_def_12,X0),
inference(equality_resolution,[status(thm)],[c_277927]) ).
tcf(c_362249,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ( apply(X0,n(iPr_def_12,X0)) != apply(iPr_def_10,n(iPr_def_12,X0)) ) ),
inference(superposition,[status(thm)],[c_359603,c_55]) ).
tcf(c_394891,plain,
iPr_def_10 = iPr_def_12,
inference(equality_resolution,[status(thm)],[c_362249]) ).
tcf(c_394941,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_78,c_394891]) ).
tcf(c_394942,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_394941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 07:30:19 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.41 Running first-order theorem proving
% 0.02/0.41 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
% 0.02/0.42
% 0.02/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.42
% 0.02/0.42 % Detected problem language: tptp
% 0.02/0.43 % Proving...
% 158.49/39.70 % SZS status Started for theBenchmark.p
% 158.49/39.70 % SZS status Unsatisfiable for theBenchmark.p
% 158.49/39.70
% 158.49/39.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 158.49/39.70
% 158.49/39.70 % ------ iProver source info
% 158.49/39.70
% 158.49/39.70 % git: date: 2026-07-19 20:42:38 +0200
% 158.49/39.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 158.49/39.70 % git: non_committed_changes: false
% 158.49/39.70
% 158.49/39.70 % ------ Parsing...% successful
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 158.49/39.70
% 158.49/39.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 158.49/39.70
% 158.49/39.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 158.49/39.70
% 158.49/39.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 158.49/39.70 % ------ Proving...
% 158.49/39.70 % ------ Problem Properties
% 158.49/39.70
% 158.49/39.70 %
% 158.49/39.70 % clauses 7
% 158.49/39.70 % conjectures 1
% 158.49/39.70 % EPR 1
% 158.49/39.70 % Horn 7
% 158.49/39.70 % unary 6
% 158.49/39.70 % binary 1
% 158.49/39.70 % lits 8
% 158.49/39.70 % lits eq 8
% 158.49/39.70 % fd_pure 0
% 158.49/39.70 % fd_pseudo 0
% 158.49/39.70 % fd_cond 0
% 158.49/39.70 % fd_pseudo_cond 1
% 158.49/39.70 % AC symbols 0
% 158.49/39.70
% 158.49/39.70 % ------ Schedule dynamic 5 is on
% 158.49/39.70
% 158.49/39.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 % ------
% 158.49/39.70 % Current options:
% 158.49/39.70 % ------
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 %
% 158.49/39.70
% 158.49/39.70 % ------ Proving...
% 158.49/39.70 % Proof_search_loop: time out after: 4967 full_loop iterations
% 158.49/39.70
% 158.49/39.70 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 % ------
% 158.49/39.70 % Current options:
% 158.49/39.70 % ------
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 %
% 158.49/39.70
% 158.49/39.70 % ------ Proving...
% 158.49/39.70 % Proof_search_loop: time out after: 6043 full_loop iterations
% 158.49/39.70
% 158.49/39.70 % ------ Option_1: Negative Selections Time Limit: 35.
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 % ------
% 158.49/39.70 % Current options:
% 158.49/39.70 % ------
% 158.49/39.70
% 158.49/39.70
% 158.49/39.70 %
% 158.49/39.70
% 158.49/39.70 % ------ Proving...
% 158.49/39.70 %
% 158.49/39.70
% 158.49/39.70 % SZS status Unsatisfiable for theBenchmark.p
% 158.49/39.70
% 158.49/39.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 158.49/39.71
% 158.49/39.71
%------------------------------------------------------------------------------