%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA007-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 12:55:03 PM UTC 2026
% Result : Unsatisfiable 5.64s 6.30s
% Output : Proof 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 27 unt; 0 def)
% Number of atoms : 51 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 37 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t9,plain,
eq(c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),t_b),true) = efalse,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t21,plain,
eq(c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),t_b),true) = efalse,
inference(orient,[status(thm)],[t9]) ).
cnf(f3,axiom,
( V_c = c_times(c_1,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f3_nnf,plain,
! [T_a,V_c] :
( V_c = c_times(c_1,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_c] :
( V_c = c_times(c_1,V_c,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X1 = c_times(c_1,X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,X1,c_times(c_1,X1,X0)) = c_times(c_1,X1,X0),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f1,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f1_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi0,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
c_times(c_1,X1,t_b) = X1,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
cnf(t10,plain,
c_times(c_1,X1,t_b) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t22,plain,
efalse = eq(c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),true),
inference(cp,[status(thm)],[t21,t10]) ).
cnf(f4,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f4_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
class_Orderings_Oorder(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0]) ).
cnf(f2,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f2_nnf,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(class_Orderings_Oorder(X0),true,c_lessequals(X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t3,plain,
c_lessequals(X1,X1,t_b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h0]) ).
cnf(t18,plain,
c_lessequals(X1,X1,t_b) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t26,plain,
efalse = eq(true,true),
inference(step,[status(thm)],[t22,t18]) ).
cnf(t2,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t20,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t2]) ).
cnf(t27,plain,
efalse = etrue,
inference(step,[status(thm)],[t26,t20]) ).
cnf(t23,plain,
efalse = etrue,
inference(orient,[status(thm)],[t27]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA007-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.39 % Computer : n008.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 05:45:02 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.64/6.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.64/6.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------