%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA019-1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:09:18 PM UTC 2026
% Result : Unsatisfiable 21.56s 16.62s
% Output : CNFRefutation 21.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 44 ( 17 unt; 2 nHn; 35 RR)
% Number of literals : 80 ( 13 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_SetInterval_Ocard__atMost_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat) = c_Suc(X1),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_Ocard__atMost_0) ).
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
| ~ c_less(c_0,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a)
| ~ c_less(c_0,X1,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( c_less(c_0,X1,tc_nat)
| X1 = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_Onot__gr0_0) ).
cnf(cls_conjecture_0,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_OrderedGroup_Oabs__0__eq_1,axiom,
( c_0 = c_HOL_Oabs(c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(c_0_15,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
cls_conjecture_2 ).
cnf(c_0_16,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat) = c_Suc(X1),
cls_SetInterval_Ocard__atMost_0 ).
cnf(c_0_17,axiom,
( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
| ~ c_less(c_0,X1,tc_nat) ),
cls_NatBin_OSuc__pred_H_0 ).
cnf(c_0_18,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat)),t_a),t_a),t_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_19,plain,
( X1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X1,c_1,tc_nat),tc_nat),tc_nat)
| ~ c_less(c_0,X1,tc_nat) ),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a)
| ~ c_less(c_0,X1,t_a) ),
cls_conjecture_3 ).
cnf(c_0_21,negated_conjecture,
( c_lessequals(c_HOL_Oabs(v_f(X1),t_a),c_times(v_x,c_HOL_Oabs(v_h(X1),t_a),t_a),t_a)
| ~ c_less(c_0,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
c_less(c_0,v_x,t_a),
cls_conjecture_1 ).
cnf(c_0_23,negated_conjecture,
~ c_less(c_0,v_xa(v_x),tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_24,axiom,
( c_less(c_0,X1,tc_nat)
| X1 = c_0 ),
cls_Nat_Onot__gr0_0 ).
cnf(c_0_25,negated_conjecture,
v_xa(v_x) = c_0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
v_f(c_0) = c_0,
cls_conjecture_0 ).
cnf(c_0_27,axiom,
( c_0 = c_HOL_Oabs(c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__0__eq_1 ).
cnf(c_0_28,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_29,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_22]),c_0_26])]) ).
cnf(c_0_30,plain,
( c_HOL_Oabs(c_0,X1) = c_0
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
tfree_tcs ).
cnf(c_0_32,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).
cnf(c_0_33,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_40 ).
cnf(c_0_34,negated_conjecture,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
( c_lessequals(c_0,c_times(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X1,X3)
| ~ c_lessequals(c_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ c_lessequals(c_0,v_x,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31])]) ).
cnf(c_0_37,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_38,negated_conjecture,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(c_0,v_x,t_a) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_40,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_44 ).
cnf(c_0_41,negated_conjecture,
~ c_lessequals(c_0,v_x,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_31])]) ).
cnf(c_0_42,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_31]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA019-1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:34:42 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 21.56/16.62 % Version : CSE_E---1.7
% 21.56/16.62 % Problem : theBenchmark.p
% 21.56/16.62 % SZS status Unsatisfiable for theBenchmark.p
% 21.56/16.62 % SZS output start CNFRefutation
% See solution above
% 21.56/16.69 % Total time : 13.724s
%------------------------------------------------------------------------------