%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA019-2 : 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 : n029.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 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 43 ( 15 unt; 2 nHn; 37 RR)
% Number of literals : 77 ( 11 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 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_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_OrderedGroup_Oabs__eq__0_1,axiom,
( c_HOL_Oabs(c_0,X1) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( c_less(c_0,X1,tc_nat)
| X1 = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
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_LOrder_Ojoin__semilorder_1,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
cnf(cls_conjecture_0,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
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(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/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
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,
( 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_17,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_18,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_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
c_less(c_0,v_x,t_a),
cls_conjecture_1 ).
cnf(c_0_20,axiom,
( c_HOL_Oabs(c_0,X1) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__eq__0_1 ).
cnf(c_0_21,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_22,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_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,axiom,
( c_less(c_0,X1,tc_nat)
| X1 = c_0 ),
cls_Nat_Onot__gr0_0 ).
cnf(c_0_24,plain,
( c_HOL_Oabs(c_0,X1) = c_0
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
tfree_tcs ).
cnf(c_0_26,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_27,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
clsrel_LOrder_Ojoin__semilorder_1 ).
cnf(c_0_28,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_35 ).
cnf(c_0_29,negated_conjecture,
v_xa(v_x) = c_0,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
v_f(c_0) = c_0,
cls_conjecture_0 ).
cnf(c_0_31,negated_conjecture,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( c_lessequals(c_0,v_x,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_33,plain,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_30]),c_0_31]),c_0_19])]) ).
cnf(c_0_35,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_36,negated_conjecture,
c_lessequals(c_0,v_x,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25])]) ).
cnf(c_0_37,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_38,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_39,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,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_41,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA019-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:36:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------