%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV089+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Thu Sep 24 02:53:41 PM UTC 2026
% Result : Theorem 54.72s 7.40s
% Output : CNFRefutation 54.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 26
% Syntax : Number of formulae : 121 ( 86 unt; 0 def)
% Number of atoms : 221 ( 185 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 153 ( 53 ~; 75 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 150 ( 9 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0001,conjecture,
( true
=> ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) = use ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0001) ).
fof(sel2_update_2,axiom,
! [X5,X7,X1,X17,X25] :
( ( a_select2(X1,X7) = X17
& X5 != X7 )
=> a_select2(tptp_update2(X1,X5,X25),X7) = X17 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sel2_update_2) ).
fof(sel2_update_1,axiom,
! [X1,X7,X17] : a_select2(tptp_update2(X1,X7,X17),X7) = X17,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sel2_update_1) ).
fof(sel3_update_1,axiom,
! [X1,X7,X24,X17] : a_select3(tptp_update3(X1,X7,X24,X17),X7,X24) = X17,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sel3_update_1) ).
fof(sel3_update_2,axiom,
! [X5,X11,X7,X24,X1,X17,X25] :
( ( a_select3(X1,X7,X24) = X17
& X11 = X24
& X5 != X7 )
=> a_select3(tptp_update3(X1,X5,X11,X25),X7,X24) = X17 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sel3_update_2) ).
fof(succ_plus_2_r,axiom,
! [X1] : plus(X1,n2) = succ(succ(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_2_r) ).
fof(succ_plus_1_r,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(succ_plus_1_l,axiom,
! [X1] : plus(n1,X1) = succ(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
fof(succ_plus_3_r,axiom,
! [X1] : plus(X1,n3) = succ(succ(succ(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_3_r) ).
fof(successor_2,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(succ_plus_4_r,axiom,
! [X1] : plus(X1,n4) = succ(succ(succ(succ(X1)))),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_4_r) ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(leq_succ_gt,axiom,
! [X1,X2] :
( leq(succ(X1),X2)
=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
fof(succ_plus_4_l,axiom,
! [X1] : plus(n4,X1) = succ(succ(succ(succ(X1)))),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_4_l) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(succ_plus_3_l,axiom,
! [X1] : plus(n3,X1) = succ(succ(succ(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_3_l) ).
fof(leq_gt1,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(reflexivity_leq,axiom,
! [X1] : leq(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',reflexivity_leq) ).
fof(pred_succ,axiom,
! [X1] : pred(succ(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(gt_5_4,axiom,
gt(n5,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
fof(gt_4_3,axiom,
gt(n4,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
fof(gt_2_0,axiom,
gt(n2,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
fof(c_0_26,negated_conjecture,
~ ( true
=> ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) = use
& a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0001]) ).
fof(c_0_27,plain,
! [X5,X7,X1,X17,X25] :
( ( a_select2(X1,X7) = X17
& X5 != X7 )
=> a_select2(tptp_update2(X1,X5,X25),X7) = X17 ),
inference(fof_simplification,[status(thm)],[sel2_update_2]) ).
fof(c_0_28,negated_conjecture,
( ( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) != use )
& true ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_29,plain,
! [X173,X174,X175] : a_select2(tptp_update2(X173,X174,X175),X174) = X175,
inference(variable_rename,[status(thm)],[sel2_update_1]) ).
fof(c_0_30,plain,
! [X154,X155,X156,X157] : a_select3(tptp_update3(X154,X155,X156,X157),X155,X156) = X157,
inference(variable_rename,[status(thm)],[sel3_update_1]) ).
fof(c_0_31,plain,
! [X176,X177,X178,X179,X180] :
( a_select2(tptp_update2(X178,X176,X180),X177) = X179
| a_select2(X178,X177) != X179
| X176 = X177 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_32,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n3) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n0,n0) != use ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
a_select2(tptp_update2(X1,X2,X3),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
a_select3(tptp_update3(X1,X2,X3,X4),X2,X3) = X4,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( a_select2(X3,X2) != X4
| a_select2(tptp_update2(X3,X1,X5),X2) = X4
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,plain,
! [X5,X11,X7,X24,X1,X17,X25] :
( ( a_select3(X1,X7,X24) = X17
& X11 = X24
& X5 != X7 )
=> a_select3(tptp_update3(X1,X5,X11,X25),X7,X24) = X17 ),
inference(fof_simplification,[status(thm)],[sel3_update_2]) ).
fof(c_0_37,plain,
! [X137] : plus(X137,n2) = succ(succ(X137)),
inference(variable_rename,[status(thm)],[succ_plus_2_r]) ).
fof(c_0_38,plain,
! [X135] : plus(X135,n1) = succ(X135),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_39,plain,
! [X136] : plus(n1,X136) = succ(X136),
inference(variable_rename,[status(thm)],[succ_plus_1_l]) ).
cnf(c_0_40,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),c_0_34])]) ).
cnf(c_0_41,plain,
( X2 = X4
| a_select2(tptp_update2(X1,X2,X3),X4) = a_select2(X1,X4) ),
inference(er,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X158,X159,X160,X161,X162,X163,X164] :
( a_select3(tptp_update3(X162,X158,X159,X164),X160,X161) = X163
| a_select3(X162,X160,X161) != X163
| X159 != X161
| X158 = X160 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_43,plain,
! [X139] : plus(X139,n3) = succ(succ(succ(X139))),
inference(variable_rename,[status(thm)],[succ_plus_3_r]) ).
cnf(c_0_44,plain,
plus(X1,n2) = succ(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
succ(succ(n0)) = n2,
inference(split_conjunct,[status(thm)],[successor_2]) ).
cnf(c_0_48,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
cnf(c_0_49,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n3,use),n4) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use
| n5 = n3 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( a_select3(X5,X2,X4) != X6
| X3 != X4
| a_select3(tptp_update3(X5,X1,X3,X7),X2,X4) = X6
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_51,plain,
! [X141] : plus(X141,n4) = succ(succ(succ(succ(X141)))),
inference(variable_rename,[status(thm)],[succ_plus_4_r]) ).
cnf(c_0_52,plain,
plus(X1,n3) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
plus(X1,n2) = plus(plus(X1,n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
cnf(c_0_54,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_55,plain,
succ(succ(succ(n0))) = n3,
inference(split_conjunct,[status(thm)],[successor_3]) ).
cnf(c_0_56,plain,
plus(plus(n0,n1),n1) = n2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45]),c_0_45]) ).
cnf(c_0_57,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_58,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n5,use),n4,use),n5,use),n3,use),n4,use),n5) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use
| n5 = n3
| n4 = n3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_33])]) ).
cnf(c_0_59,plain,
( X4 = X2
| a_select2(tptp_update2(tptp_update2(X1,X2,X3),X4,X5),X2) = X3 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33])]) ).
cnf(c_0_60,plain,
( a_select3(X1,X5,X3) != X6
| X2 = X5
| a_select3(tptp_update3(X1,X2,X3,X4),X5,X3) = X6 ),
inference(er,[status(thm)],[c_0_50]) ).
fof(c_0_61,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_62,plain,
! [X150,X151] :
( gt(X151,X150)
| ~ leq(succ(X150),X151) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt])])]) ).
fof(c_0_63,plain,
! [X142] : plus(n4,X142) = succ(succ(succ(succ(X142)))),
inference(variable_rename,[status(thm)],[succ_plus_4_l]) ).
cnf(c_0_64,plain,
plus(X1,n4) = succ(succ(succ(succ(X1)))),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,plain,
plus(X1,n3) = plus(plus(plus(X1,n1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_66,plain,
plus(n1,plus(X1,n1)) = plus(X1,n2),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_67,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(split_conjunct,[status(thm)],[successor_4]) ).
cnf(c_0_68,plain,
plus(plus(plus(n0,n1),n1),n1) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_69,plain,
plus(n1,n1) = n2,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_70,negated_conjecture,
( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n1,n0) != use
| n4 = n3
| n5 = n3
| n5 = n4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_59]) ).
cnf(c_0_71,plain,
( X2 = X5
| a_select3(tptp_update3(X1,X2,X3,X4),X5,X3) = a_select3(X1,X5,X3) ),
inference(er,[status(thm)],[c_0_60]) ).
fof(c_0_72,plain,
! [X33] : ~ gt(X33,X33),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_61])]) ).
cnf(c_0_73,plain,
( ~ leq(succ(X1),X2)
| gt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,plain,
plus(n4,X1) = succ(succ(succ(succ(X1)))),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_75,plain,
plus(X1,n4) = plus(plus(plus(plus(X1,n1),n1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_76,plain,
plus(n1,plus(X1,n2)) = plus(X1,n3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_54]),c_0_66]),c_0_54]) ).
cnf(c_0_77,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(split_conjunct,[status(thm)],[successor_5]) ).
cnf(c_0_78,plain,
plus(plus(plus(plus(n0,n1),n1),n1),n1) = n4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_79,plain,
plus(n1,n2) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_57]),c_0_69]),c_0_54]) ).
cnf(c_0_80,negated_conjecture,
( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n0,n0,use),n2,n0) != use
| n5 = n4
| n5 = n3
| n4 = n3
| n1 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_34])]) ).
fof(c_0_81,plain,
! [X140] : plus(n3,X140) = succ(succ(succ(X140))),
inference(variable_rename,[status(thm)],[succ_plus_3_l]) ).
cnf(c_0_82,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_83,plain,
( ~ leq(plus(X1,n1),X2)
| gt(X2,X1) ),
inference(rw,[status(thm)],[c_0_73,c_0_45]) ).
cnf(c_0_84,plain,
plus(n4,X1) = plus(plus(plus(plus(X1,n1),n1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_85,plain,
plus(n1,plus(X1,n3)) = plus(X1,n4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_54]),c_0_66]),c_0_54]),c_0_76]),c_0_54]) ).
cnf(c_0_86,plain,
plus(plus(plus(plus(plus(n0,n1),n1),n1),n1),n1) = n5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_87,plain,
plus(n1,n3) = n4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_57]),c_0_69]),c_0_54]),c_0_79]),c_0_54]) ).
cnf(c_0_88,negated_conjecture,
( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n1,n0,use),n2,n0) != use
| n1 = n0
| n4 = n3
| n5 = n3
| n5 = n4
| n2 = n0 ),
inference(spm,[status(thm)],[c_0_80,c_0_71]) ).
cnf(c_0_89,plain,
plus(n3,X1) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_90,plain,
! [X42,X43] :
( leq(X42,X43)
| ~ gt(X43,X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt1])])]) ).
cnf(c_0_91,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
plus(X1,n4) = plus(n4,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_54]),c_0_66]),c_0_54]),c_0_76]),c_0_54]),c_0_85]) ).
cnf(c_0_93,plain,
plus(n1,n4) = n5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_57]),c_0_69]),c_0_54]),c_0_79]),c_0_54]),c_0_87]),c_0_54]) ).
cnf(c_0_94,negated_conjecture,
( a_select3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(u_defuse,n2,n0,use),n1,n0,use),n2,n0,use),n0,n0,use),n2,n0) != use
| n2 = n0
| n5 = n4
| n5 = n3
| n4 = n3
| n1 = n0
| n2 = n1 ),
inference(spm,[status(thm)],[c_0_88,c_0_71]) ).
fof(c_0_95,plain,
! [X34] : leq(X34,X34),
inference(variable_rename,[status(thm)],[reflexivity_leq]) ).
cnf(c_0_96,plain,
plus(n3,X1) = plus(plus(plus(X1,n1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_45]),c_0_45]),c_0_45]) ).
fof(c_0_97,plain,
! [X146] : pred(succ(X146)) = X146,
inference(variable_rename,[status(thm)],[pred_succ]) ).
fof(c_0_98,plain,
! [X145] : minus(X145,n1) = pred(X145),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
cnf(c_0_99,plain,
( ~ gt(X1,X2)
| leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_100,plain,
gt(n5,n4),
inference(split_conjunct,[status(thm)],[gt_5_4]) ).
cnf(c_0_101,plain,
~ leq(n5,n4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_102,negated_conjecture,
( n2 = n1
| n1 = n0
| n4 = n3
| n5 = n3
| n5 = n4
| n2 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_71]),c_0_34])]) ).
cnf(c_0_103,plain,
leq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_104,plain,
plus(X1,n3) = plus(n3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_54]),c_0_66]),c_0_54]),c_0_76]) ).
cnf(c_0_105,plain,
pred(succ(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_106,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_107,plain,
leq(n4,n5),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( n2 = n0
| n5 = n3
| n4 = n3
| n1 = n0
| n2 = n1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_109,plain,
~ leq(n4,n3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_104]),c_0_87]) ).
cnf(c_0_110,plain,
minus(plus(X1,n1),n1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_45]),c_0_106]) ).
cnf(c_0_111,plain,
gt(n4,n3),
inference(split_conjunct,[status(thm)],[gt_4_3]) ).
cnf(c_0_112,negated_conjecture,
( n2 = n1
| n1 = n0
| n4 = n3
| n2 = n0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_113,plain,
minus(n2,n1) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_54]),c_0_69]) ).
cnf(c_0_114,negated_conjecture,
( n2 = n0
| n1 = n0
| n2 = n1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_82]) ).
cnf(c_0_115,plain,
minus(n1,n1) = n0,
inference(spm,[status(thm)],[c_0_110,c_0_57]) ).
cnf(c_0_116,plain,
gt(n2,n0),
inference(split_conjunct,[status(thm)],[gt_2_0]) ).
cnf(c_0_117,negated_conjecture,
( n1 = n0
| n2 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_118,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[c_0_91,c_0_57]) ).
cnf(c_0_119,negated_conjecture,
n1 = n0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_82]) ).
cnf(c_0_120,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_103])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV089+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:35:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.72/7.40 % Version: 3.5.1
% 54.72/7.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 54.72/7.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.72/7.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 54.72/7.40 % Starting new_bool_3 with 300s (1) cores
% 54.72/7.40 % Starting new_bool_1 with 300s (1) cores
% 54.72/7.40 % Starting sh5l with 300s (1) cores
% 54.72/7.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2689740 completed with status 0
% 54.72/7.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 54.72/7.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 54.72/7.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.72/7.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 54.72/7.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 54.72/7.40 % No SInE strategy applied
% 54.72/7.40 % Search class: FGHSM-FSLM33-DFFFFFNN
% 54.72/7.40 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 54.72/7.40 % Starting SubtermCWHack with 136s (1) cores
% 54.72/7.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 54.72/7.40 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 54.72/7.40 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 54.72/7.40 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 54.72/7.40 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with pid 2689750 completed with status 0
% 54.72/7.40 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN
% 54.72/7.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 54.72/7.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 54.72/7.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 54.72/7.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 54.72/7.40 % No SInE strategy applied
% 54.72/7.40 % Search class: FGHSM-FSLM33-DFFFFFNN
% 54.72/7.40 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 54.72/7.40 % Starting SubtermCWHack with 136s (1) cores
% 54.72/7.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 54.72/7.40 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 54.72/7.40 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 54.72/7.40 % Preprocessing time : 0.202 s
% 54.72/7.40
% 54.72/7.40 % Proof found!
% 54.72/7.40 % SZS status Theorem
% 54.72/7.40 % SZS output start CNFRefutation
% See solution above
% 54.72/7.40 % Parsed axioms : 85
% 54.72/7.40 % Removed by relevancy pruning/SinE : 0
% 54.72/7.40 % Initial clauses : 194
% 54.72/7.40 % Removed in clause preprocessing : 2
% 54.72/7.40 % Initial clauses in saturation : 192
% 54.72/7.40 % Processed clauses : 5775
% 54.72/7.40 % ...of these trivial : 300
% 54.72/7.40 % ...subsumed : 3293
% 54.72/7.40 % ...remaining for further processing : 2182
% 54.72/7.40 % Other redundant clauses eliminated : 1770
% 54.72/7.40 % Clauses deleted for lack of memory : 0
% 54.72/7.40 % Backward-subsumed : 78
% 54.72/7.40 % Backward-rewritten : 389
% 54.72/7.40 % Generated clauses : 103156
% 54.72/7.40 % ...of the previous two non-redundant : 97632
% 54.72/7.40 % ...aggressively subsumed : 0
% 54.72/7.40 % Contextual simplify-reflections : 155
% 54.72/7.40 % Paramodulations : 100561
% 54.72/7.40 % Factorizations : 801
% 54.72/7.40 % NegExts : 0
% 54.72/7.40 % Equation resolutions : 1794
% 54.72/7.40 % Disequality decompositions : 0
% 54.72/7.40 % Total rewrite steps : 84969
% 54.72/7.40 % ...of those cached : 84485
% 54.72/7.40 % Propositional unsat checks : 0
% 54.72/7.40 % Propositional check models : 0
% 54.72/7.40 % Propositional check unsatisfiable : 0
% 54.72/7.40 % Propositional clauses : 0
% 54.72/7.40 % Propositional clauses after purity: 0
% 54.72/7.40 % Propositional unsat core size : 0
% 54.72/7.40 % Propositional preprocessing time : 0.000
% 54.72/7.40 % Propositional encoding time : 0.000
% 54.72/7.40 % Propositional solver time : 0.000
% 54.72/7.40 % Success case prop preproc time : 0.000
% 54.72/7.40 % Success case prop encoding time : 0.000
% 54.72/7.40 % Success case prop solver time : 0.000
% 54.72/7.40 % Current number of processed clauses : 1714
% 54.72/7.40 % Positive orientable unit clauses : 237
% 54.72/7.40 % Positive unorientable unit clauses: 4
% 54.72/7.40 % Negative unit clauses : 222
% 54.72/7.40 % Non-unit-clauses : 1251
% 54.72/7.40 % Current number of unprocessed clauses: 91672
% 54.72/7.40 % ...number of literals in the above : 698596
% 54.72/7.40 % Current number of archived formulas : 0
% 54.72/7.40 % Current number of archived clauses : 469
% 54.72/7.40 % Clause-clause subsumption calls (NU) : 785954
% 54.72/7.40 % Rec. Clause-clause subsumption calls : 27165
% 54.72/7.40 % Non-unit clause-clause subsumptions : 1069
% 54.72/7.40 % Unit Clause-clause subsumption calls : 89159
% 54.72/7.40 % Rewrite failures with RHS unbound : 0
% 54.72/7.40 % BW rewrite match attempts : 224
% 54.72/7.40 % BW rewrite match successes : 65
% 54.72/7.40 % Condensation attempts : 0
% 54.72/7.40 % Condensation successes : 0
% 54.72/7.40 % Termbank termtop insertions : 3164613
% 54.72/7.40 % Search garbage collected termcells : 2178
% 54.72/7.40
% 54.72/7.40 % -------------------------------------------------
% 54.72/7.40 % User time : 6.667 s
% 54.72/7.40 % System time : 0.173 s
% 54.72/7.40 % Total time : 6.840 s
% 54.72/7.40 % Maximum resident set size: 4252 pages
% 54.72/7.40
% 54.72/7.40 % -------------------------------------------------
% 54.72/7.40 % User time : 32.825 s
% 54.72/7.40 % System time : 0.887 s
% 54.72/7.40 % Total time : 33.713 s
% 54.72/7.40 % Maximum resident set size: 4864 pages
% 54.72/7.40 % E exiting
%------------------------------------------------------------------------------