%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV104+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 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 : n018.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 05:20:50 PM UTC 2026
% Result : Theorem 1.76s 1.87s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 57 unt; 0 def)
% Number of atoms : 142 ( 113 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 100 ( 36 ~; 31 |; 28 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 72 ( 3 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0016,conjecture,
( ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0016) ).
fof(sel2_update_1,axiom,
! [X1,X7,X17] : a_select2(tptp_update2(X1,X7,X17),X7) = X17,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel2_update_1) ).
fof(sel2_update_2,axiom,
! [X5,X7,X1,X17,X25] :
( ( X5 != X7
& a_select2(X1,X7) = X17 )
=> a_select2(tptp_update2(X1,X5,X25),X7) = X17 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sel2_update_2) ).
fof(succ_plus_2_r,axiom,
! [X1] : plus(X1,n2) = succ(succ(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_2_r) ).
fof(succ_plus_1_r,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(succ_plus_1_l,axiom,
! [X1] : plus(n1,X1) = succ(X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_3_r) ).
fof(successor_2,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(leq_succ_gt_equiv,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
fof(succ_plus_3_l,axiom,
! [X1] : plus(n3,X1) = succ(succ(succ(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_3_l) ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(leq_gt1,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(gt_5_4,axiom,
gt(n5,n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
fof(reflexivity_leq,axiom,
! [X1] : leq(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',reflexivity_leq) ).
fof(c_0_17,negated_conjecture,
~ ( ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0016]) ).
fof(c_0_18,negated_conjecture,
( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& ( a_select3(u_defuse,n0,n0) != use
| a_select3(u_defuse,n1,n0) != use
| a_select3(u_defuse,n2,n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) != use ) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( a_select3(u_defuse,n0,n0) != use
| a_select3(u_defuse,n1,n0) != use
| a_select3(u_defuse,n2,n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) != use ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_20,negated_conjecture,
a_select3(u_defuse,n0,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
a_select3(u_defuse,n1,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X341,X342,X343] : a_select2(tptp_update2(X341,X342,X343),X342) = X343,
inference(variable_rename,[status(thm)],[sel2_update_1]) ).
fof(c_0_23,plain,
! [X344,X345,X346,X347,X348] :
( X344 = X345
| a_select2(X346,X345) != X347
| a_select2(tptp_update2(X346,X344,X348),X345) = X347 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sel2_update_2])]) ).
fof(c_0_24,plain,
! [X305] : plus(X305,n2) = succ(succ(X305)),
inference(variable_rename,[status(thm)],[succ_plus_2_r]) ).
fof(c_0_25,plain,
! [X303] : plus(X303,n1) = succ(X303),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_26,plain,
! [X304] : plus(n1,X304) = succ(X304),
inference(variable_rename,[status(thm)],[succ_plus_1_l]) ).
cnf(c_0_27,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) != use
| a_select3(u_defuse,n2,n0) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_28,negated_conjecture,
a_select3(u_defuse,n2,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
a_select2(tptp_update2(X1,X2,X3),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( X1 = X2
| a_select2(tptp_update2(X3,X1,X5),X2) = X4
| a_select2(X3,X2) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X307] : plus(X307,n3) = succ(succ(succ(X307))),
inference(variable_rename,[status(thm)],[succ_plus_3_r]) ).
cnf(c_0_32,plain,
plus(X1,n2) = succ(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
succ(succ(n0)) = n2,
inference(split_conjunct,[status(thm)],[successor_2]) ).
cnf(c_0_36,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
cnf(c_0_37,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),c_0_29])]) ).
cnf(c_0_38,plain,
( a_select2(tptp_update2(X1,X2,X3),X4) = a_select2(X1,X4)
| X2 = X4 ),
inference(er,[status(thm)],[c_0_30]) ).
fof(c_0_39,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_40,plain,
! [X219,X220] :
( ( ~ leq(X219,X220)
| gt(succ(X220),X219) )
& ( ~ gt(succ(X220),X219)
| leq(X219,X220) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
fof(c_0_41,plain,
! [X308] : plus(n3,X308) = succ(succ(succ(X308))),
inference(variable_rename,[status(thm)],[succ_plus_3_l]) ).
cnf(c_0_42,plain,
plus(X1,n3) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
plus(X1,n2) = plus(plus(X1,n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_44,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_45,plain,
succ(succ(succ(n0))) = n3,
inference(split_conjunct,[status(thm)],[successor_3]) ).
cnf(c_0_46,plain,
plus(plus(n0,n1),n1) = n2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33]),c_0_33]) ).
cnf(c_0_47,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_48,negated_conjecture,
( n5 = n4
| a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29])]) ).
fof(c_0_49,plain,
! [X201] : ~ gt(X201,X201),
inference(variable_rename,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
plus(n3,X1) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,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_42,c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_53,plain,
plus(n1,plus(X1,n1)) = plus(X1,n2),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(split_conjunct,[status(thm)],[successor_4]) ).
cnf(c_0_55,plain,
plus(plus(plus(n0,n1),n1),n1) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_56,plain,
plus(n1,n1) = n2,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_57,plain,
! [X210,X211] :
( ~ gt(X211,X210)
| leq(X210,X211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt1])]) ).
cnf(c_0_58,negated_conjecture,
( n5 = n3
| n5 = n4
| a_select2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n3) != use ),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_59,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
( gt(plus(X2,n1),X1)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_61,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_51,c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_62,plain,
plus(n1,plus(X1,n2)) = plus(X1,n3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_44]),c_0_53]),c_0_44]) ).
cnf(c_0_63,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_54,c_0_33]),c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_64,plain,
plus(n1,n2) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_47]),c_0_56]),c_0_44]) ).
cnf(c_0_65,plain,
( leq(X2,X1)
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
gt(n5,n4),
inference(split_conjunct,[status(thm)],[gt_5_4]) ).
cnf(c_0_67,negated_conjecture,
( n4 = n3
| n5 = n4
| n5 = n3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_29])]) ).
cnf(c_0_68,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,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_61,c_0_44]),c_0_53]),c_0_44]),c_0_62]) ).
cnf(c_0_70,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_63,c_0_47]),c_0_56]),c_0_44]),c_0_64]),c_0_44]) ).
cnf(c_0_71,plain,
leq(n4,n5),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( n5 = n3
| n4 = n3 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_59]) ).
cnf(c_0_73,plain,
~ leq(n4,n3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
fof(c_0_74,plain,
! [X202] : leq(X202,X202),
inference(variable_rename,[status(thm)],[reflexivity_leq]) ).
cnf(c_0_75,negated_conjecture,
n4 = n3,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_76,plain,
leq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_77,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_75]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV104+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 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 : n018.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 04:56:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.76/1.87 % Version : CSE_E---1.7
% 1.76/1.87 % Problem : theBenchmark.p
% 1.76/1.87 % SZS status Theorem for theBenchmark.p
% 1.76/1.87 % SZS output start CNFRefutation
% See solution above
% 1.76/1.87 % Total time : 1.373s
%------------------------------------------------------------------------------