%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 12:55:07 PM UTC 2026
% Result : Unsatisfiable 3.75s 1.07s
% Output : Proof 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 40 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( V_x = c_Suc(c_minus(V_x,c_1,tc_nat))
| ~ c_less(c_0,V_x,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
fof(f0_nnf,plain,
! [V_x] :
( V_x = c_Suc(c_minus(V_x,c_1,tc_nat))
| ~ c_less(c_0,V_x,tc_nat) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_x] :
( V_x = c_Suc(c_minus(V_x,c_1,tc_nat))
| ~ c_less(c_0,V_x,tc_nat) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = c_Suc(c_minus(X0,c_1,tc_nat))
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f1,axiom,
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f1_nnf,plain,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p5,plain,
( X0 = c_0
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
inference(resolution,[status(thm)],[c0,c1]) ).
cnf(f2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X0,c_1,tc_nat))),t_a),t_a),t_a)
| X0 = c_0 ),
inference(superposition,[status(thm)],[p5,c2]) ).
cnf(p10,plain,
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| X0 = c_0
| X0 = c_0 ),
inference(superposition,[status(thm)],[p5,p8]) ).
cnf(p11,plain,
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| X0 = c_0 ),
inference(factoring,[status(thm)],[p10]) ).
cnf(f4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f4_nnf,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p12,plain,
v_x = c_0,
inference(resolution,[status(thm)],[p11,c4]) ).
cnf(f3,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
v_x != c_0,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
v_x != c_0,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
v_x != c_0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p13,plain,
c_0 != c_0,
inference(demodulation,[status(thm)],[p12,c3]) ).
cnf(p15,plain,
$false,
inference(equality_resolution,[status(thm)],[p13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:46:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.75/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.75/1.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------