%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 03:29:15 PM UTC 2026
% Result : Theorem 3.06s 0.98s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 40 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 8 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 53 !; 2 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
fof(f3,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) = X1
=> hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(f1161,conjecture,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1162,negated_conjecture,
~ ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
inference(negated_conjecture,[status(cth)],[f1161]) ).
fof(f1174,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1177,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) != X1
| hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f2156,plain,
? [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X1)) ),
inference(ennf_transformation,[],[f1162]) ).
fof(f2574,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK55,sK56)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK55),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK56)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56]),skolemize(X0,sK55),skolemize(X1,sK56)],[f2156]) ).
fof(f2576,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1)) ),
inference(cnf_transformation,[],[f1174]) ).
fof(f2577,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1)) ),
inference(cnf_transformation,[],[f1175]) ).
fof(f2583,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2) != X1
| hAPP(X1,X0) = hAPP(X3,hAPP(X2,X0)) ),
inference(cnf_transformation,[],[f1177]) ).
fof(f4189,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK55,sK56),
inference(cnf_transformation,[],[f2574]) ).
fof(f4190,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK55),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK56)),
inference(cnf_transformation,[],[f2574]) ).
fof(f4365,plain,
! [X2,X3,X0,X6,X4,X5] : hAPP(X3,hAPP(X2,X0)) = hAPP(hAPP(c_Fun_Ocomp(X6,X5,X4,X3),X2),X0),
inference(equality_resolution,[],[f2583]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2576]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2577]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP(hAPP(c_Fun_Ocomp(X0,X1,X2,X3),X4),X5) = hAPP(X3,hAPP(X4,X5)),
inference(cnf_transformation,[],[f4365]) ).
tcf(c_1614,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK55),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK56)),
inference(cnf_transformation,[],[f4190]) ).
tcf(c_1615,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK55,sK56),
inference(cnf_transformation,[],[f4189]) ).
tcf(c_1750,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK55)),hAPP(v_f____,hAPP(v_ga____,sK56))),
inference(demodulation,[status(thm)],[c_1614,c_57]) ).
tcf(c_1751,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK55),hAPP(v_ga____,sK56)),
inference(superposition,[status(thm)],[c_50,c_1750]) ).
tcf(c_1790,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK55,sK56),
inference(superposition,[status(thm)],[c_51,c_1751]) ).
tcf(c_1792,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1615,c_1790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Thu Sep 24 21:43:59 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 3.06/0.98 % SZS status Started for theBenchmark.p
% 3.06/0.98 % SZS status Theorem for theBenchmark.p
% 3.06/0.98
% 3.06/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.06/0.98
% 3.06/0.98 % ------ iProver source info
% 3.06/0.98
% 3.06/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 3.06/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.06/0.98 % git: non_committed_changes: false
% 3.06/0.98
% 3.06/0.98 % ------ Parsing...
% 3.06/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.06/0.98 % ------ Proving...
% 3.06/0.98 % ------ Problem Properties
% 3.06/0.98
% 3.06/0.98 %
% 3.06/0.98 % clauses 1567
% 3.06/0.98 % conjectures 2
% 3.06/0.98 % EPR 200
% 3.06/0.98 % Horn 1379
% 3.06/0.98 % unary 407
% 3.06/0.98 % binary 532
% 3.06/0.98 % lits 3633
% 3.06/0.98 % lits eq 821
% 3.06/0.98 % fd_pure 0
% 3.06/0.98 % fd_pseudo 0
% 3.06/0.98 % fd_cond 63
% 3.06/0.98 % fd_pseudo_cond 127
% 3.06/0.98 % AC symbols 0
% 3.06/0.98
% 3.06/0.98 % ------ Input Options Time Limit: Unbounded
% 3.06/0.98
% 3.06/0.98
% 3.06/0.98 % ------
% 3.06/0.98 % Current options:
% 3.06/0.98 % ------
% 3.06/0.98
% 3.06/0.98
% 3.06/0.98 %
% 3.06/0.98
% 3.06/0.98 % ------ Proving...
% 3.06/0.98 %
% 3.06/0.98
% 3.06/0.98 % SZS status Theorem for theBenchmark.p
% 3.06/0.98
% 3.06/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/0.98
% 3.06/0.98
%------------------------------------------------------------------------------