%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:29:58 PM UTC 2026
% Result : Theorem 2.59s 6.18s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 80 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 49 ~; 33 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 62 !; 15 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( X2 = X1
& r2(X0,X2) )
| ( X2 != X1
& ~ r2(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r3(X0,X1,X3) )
| ( X3 != X2
& ~ r3(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& r3(X0,X3,X2) )
& X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoeqy) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& r3(X0,X3,X2) )
& X2 = X1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ r1(X5) )
| ~ r2(X4,X3) )
| ~ r3(X0,X3,X2) )
| X1 != X2 ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f17,plain,
! [X0,X1,X3] :
( ( sK2(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK2(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f25,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X3,X0,X1] :
( r3(X0,X1,X3)
| sK2(X0,X1) != X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r3(X0,X3,X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f71,plain,
! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
inference(equality_resolution,[],[f33]) ).
fof(f77,plain,
! [X2,X3,X0,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r3(X0,X3,X2) ),
inference(equality_resolution,[],[f63]) ).
tcf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK2(X0,X1)),
inference(cnf_transformation,[],[f71]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ r1(X4)
| ~ r2(X4,X3)
| ~ r2(X3,X1)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ r1(X6)
| ~ r2(X6,X5)
| ~ r2(X5,X2)
| ( X2 != X3 )
| ( X0 != X1 )
| ( sK2(X1,X3) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_54]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(unflattening,[status(thm)],[c_271]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(demodulation,[status(thm)],[c_272]) ).
tcf(c_983,plain,
! [X0: $i,X1: $i] :
( ~ r1(X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_758]) ).
tcf(c_990,plain,
! [X0: $i] : ~ r1(X0),
inference(superposition,[status(thm)],[c_52,c_983]) ).
tcf(c_991,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n005.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 05:57:38 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 2.59/6.18 % SZS status Started for theBenchmark.p
% 2.59/6.18 % SZS status Theorem for theBenchmark.p
% 2.59/6.18
% 2.59/6.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.59/6.18
% 2.59/6.18 % ------ iProver source info
% 2.59/6.18
% 2.59/6.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.59/6.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.59/6.18 % git: non_committed_changes: false
% 2.59/6.18
% 2.59/6.18 % ------ Parsing...
% 2.59/6.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.59/6.18
% 2.59/6.18 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 2 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.59/6.18
% 2.59/6.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.59/6.18
% 2.59/6.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.59/6.18 % ------ Proving...
% 2.59/6.18 % ------ Problem Properties
% 2.59/6.18
% 2.59/6.18 %
% 2.59/6.18 % clauses 25
% 2.59/6.18 % conjectures 0
% 2.59/6.18 % EPR 5
% 2.59/6.18 % Horn 21
% 2.59/6.18 % unary 16
% 2.59/6.18 % binary 7
% 2.59/6.18 % lits 36
% 2.59/6.18 % lits eq 15
% 2.59/6.18 % fd_pure 0
% 2.59/6.18 % fd_pseudo 0
% 2.59/6.18 % fd_cond 1
% 2.59/6.18 % fd_pseudo_cond 2
% 2.59/6.18 % AC symbols 0
% 2.59/6.18
% 2.59/6.18 % ------ Schedule dynamic 5 is on
% 2.59/6.18
% 2.59/6.18 % ------ no conjectures: strip conj schedule
% 2.59/6.18
% 2.59/6.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.59/6.18
% 2.59/6.18
% 2.59/6.18 % ------
% 2.59/6.18 % Current options:
% 2.59/6.18 % ------
% 2.59/6.18
% 2.59/6.18
% 2.59/6.18 %
% 2.59/6.18
% 2.59/6.18 % ------ Proving...
% 2.59/6.18 %
% 2.59/6.18
% 2.59/6.18 % SZS status Theorem for theBenchmark.p
% 2.59/6.18
% 2.59/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.59/6.18
% 2.59/6.18
%------------------------------------------------------------------------------