%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV102+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 : n002.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 1.83s 1.89s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 36 unt; 0 def)
% Number of atoms : 173 ( 149 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 175 ( 56 ~; 51 |; 64 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-3 aty)
% Number of variables : 47 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0014,conjecture,
( ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0014) ).
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(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_1_r,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(gt_2_1,axiom,
gt(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
fof(gt_2_0,axiom,
gt(n2,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
fof(reflexivity_leq,axiom,
! [X1] : leq(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',reflexivity_leq) ).
fof(c_0_10,negated_conjecture,
~ ( ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0014]) ).
fof(c_0_11,negated_conjecture,
( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& ( a_select2(sigma_defuse,n0) != use
| a_select2(sigma_defuse,n1) != use
| a_select2(sigma_defuse,n2) != use
| a_select2(sigma_defuse,n3) != use
| a_select2(sigma_defuse,n4) != use
| a_select2(sigma_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(xinit_defuse,n3) != use
| a_select2(xinit_defuse,n4) != use
| a_select2(xinit_defuse,n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) != use ) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
cnf(c_0_12,negated_conjecture,
( a_select2(sigma_defuse,n0) != use
| a_select2(sigma_defuse,n1) != use
| a_select2(sigma_defuse,n2) != use
| a_select2(sigma_defuse,n3) != use
| a_select2(sigma_defuse,n4) != use
| a_select2(sigma_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(xinit_defuse,n3) != use
| a_select2(xinit_defuse,n4) != use
| a_select2(xinit_defuse,n5) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) != use ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
a_select2(sigma_defuse,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
a_select2(sigma_defuse,n1) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
a_select2(sigma_defuse,n2) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
a_select2(sigma_defuse,n3) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
a_select2(sigma_defuse,n4) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
a_select2(sigma_defuse,n5) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
a_select2(xinit_defuse,n3) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X341,X342,X343] : a_select2(tptp_update2(X341,X342,X343),X342) = X343,
inference(variable_rename,[status(thm)],[sel2_update_1]) ).
fof(c_0_21,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])]) ).
cnf(c_0_22,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) != use
| 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,n4) != use
| a_select2(xinit_defuse,n5) != use ),
inference(cn,[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)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
a_select2(xinit_defuse,n4) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
a_select2(tptp_update2(X1,X2,X3),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
a_select3(u_defuse,n0,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
a_select3(u_defuse,n1,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
a_select3(u_defuse,n2,n0) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
a_select2(xinit_defuse,n5) = use,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,plain,
( X1 = X2
| a_select2(tptp_update2(X3,X1,X5),X2) = X4
| a_select2(X3,X2) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) != use
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
( a_select2(tptp_update2(X1,X2,X3),X4) = a_select2(X1,X4)
| X2 = X4 ),
inference(er,[status(thm)],[c_0_29]) ).
fof(c_0_32,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_33,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_34,plain,
! [X303] : plus(X303,n1) = succ(X303),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
cnf(c_0_35,negated_conjecture,
( n2 = n1
| a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) != use ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24])]) ).
fof(c_0_36,plain,
! [X201] : ~ gt(X201,X201),
inference(variable_rename,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( n2 = n0
| n2 = n1
| a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n0) != use ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_40,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( gt(plus(X2,n1),X1)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
cnf(c_0_43,plain,
gt(n2,n1),
inference(split_conjunct,[status(thm)],[gt_2_1]) ).
cnf(c_0_44,negated_conjecture,
( n1 = n0
| n2 = n1
| n2 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_24])]) ).
cnf(c_0_45,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_47,plain,
gt(n2,n0),
inference(split_conjunct,[status(thm)],[gt_2_0]) ).
cnf(c_0_48,negated_conjecture,
( n2 = n0
| n1 = n0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_40]) ).
fof(c_0_49,plain,
! [X202] : leq(X202,X202),
inference(variable_rename,[status(thm)],[reflexivity_leq]) ).
cnf(c_0_50,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
n1 = n0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]) ).
cnf(c_0_52,plain,
leq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV102+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
% 0.14/0.32 % Computer : n002.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 04:56:16 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.83/1.89 % Version : CSE_E---1.7
% 1.83/1.89 % Problem : theBenchmark.p
% 1.83/1.89 % SZS status Theorem for theBenchmark.p
% 1.83/1.89 % SZS output start CNFRefutation
% See solution above
% 1.83/1.89 % Total time : 1.373s
%------------------------------------------------------------------------------