%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV220+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 05:21:06 PM UTC 2026
% Result : Theorem 1.95s 1.91s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 55 unt; 0 def)
% Number of atoms : 251 ( 183 equ)
% Maximal formula atoms : 53 ( 3 avg)
% Number of connectives : 292 ( 112 ~; 43 |; 129 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 57 ( 3 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(quaternion_ds1_symm_0361,conjecture,
! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n5)
& leq(X18,n5) )
=> ( ( ~ ( n0 = X18
& n4 = X14 )
& ~ ( n0 = X18
& n5 = X14 )
& ~ ( n1 = X18
& n4 = X14 )
& ~ ( n1 = X18
& n5 = X14 )
& ~ ( n2 = X14
& n5 = X18 )
& ~ ( n2 = X18
& n4 = X14 )
& ~ ( n2 = X18
& n5 = X14 )
& ~ ( n3 = X14
& n4 = X18 )
& ~ ( n3 = X14
& n5 = X18 )
& ~ ( n3 = X18
& n4 = X14 )
& ~ ( n3 = X18
& n5 = X14 )
& ~ ( n4 = X14
& n4 = X18 )
& ~ ( n4 = X14
& n5 = X18 )
& ~ ( n4 = X18
& n5 = X14 )
& ~ ( n5 = X14
& n5 = X18 )
& n1 = X14
& n3 = X14
& n3 = X18
& n5 = X18 )
=> times(divide(n1,n400),a_select2(sigma,n3)) = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0361) ).
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(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_3_l) ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(leq_gt1,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(gt_5_4,axiom,
gt(n5,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
fof(c_0_14,plain,
! [X14,X18] :
( epred2_2(X18,X14)
<=> ( ~ ( n0 = X18
& n4 = X14 )
& ~ ( n0 = X18
& n5 = X14 )
& ~ ( n1 = X18
& n4 = X14 )
& ~ ( n1 = X18
& n5 = X14 )
& ~ ( n2 = X14
& n5 = X18 )
& ~ ( n2 = X18
& n4 = X14 )
& ~ ( n2 = X18
& n5 = X14 )
& ~ ( n3 = X14
& n4 = X18 )
& ~ ( n3 = X14
& n5 = X18 )
& ~ ( n3 = X18
& n4 = X14 )
& ~ ( n3 = X18
& n5 = X14 )
& ~ ( n4 = X14
& n4 = X18 )
& ~ ( n4 = X14
& n5 = X18 )
& ~ ( n4 = X18
& n5 = X14 )
& ~ ( n5 = X14
& n5 = X18 )
& n1 = X14
& n3 = X14
& n3 = X18
& n5 = X18 ) ),
introduced(definition) ).
fof(c_0_15,plain,
! [X307] : plus(X307,n2) = succ(succ(X307)),
inference(variable_rename,[status(thm)],[succ_plus_2_r]) ).
fof(c_0_16,plain,
! [X305] : plus(X305,n1) = succ(X305),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_17,plain,
! [X306] : plus(n1,X306) = succ(X306),
inference(variable_rename,[status(thm)],[succ_plus_1_l]) ).
fof(c_0_18,plain,
! [X14,X18] :
( epred2_2(X18,X14)
=> ( ~ ( n0 = X18
& n4 = X14 )
& ~ ( n0 = X18
& n5 = X14 )
& ~ ( n1 = X18
& n4 = X14 )
& ~ ( n1 = X18
& n5 = X14 )
& ~ ( n2 = X14
& n5 = X18 )
& ~ ( n2 = X18
& n4 = X14 )
& ~ ( n2 = X18
& n5 = X14 )
& ~ ( n3 = X14
& n4 = X18 )
& ~ ( n3 = X14
& n5 = X18 )
& ~ ( n3 = X18
& n4 = X14 )
& ~ ( n3 = X18
& n5 = X14 )
& ~ ( n4 = X14
& n4 = X18 )
& ~ ( n4 = X14
& n5 = X18 )
& ~ ( n4 = X18
& n5 = X14 )
& ~ ( n5 = X14
& n5 = X18 )
& n1 = X14
& n3 = X14
& n3 = X18
& n5 = X18 ) ),
inference(split_equiv,[status(thm)],[c_0_14]) ).
fof(c_0_19,negated_conjecture,
~ ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n5)
& leq(X18,n5) )
=> ( epred2_2(X18,X14)
=> times(divide(n1,n400),a_select2(sigma,n3)) = n0 ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0361]),c_0_14]) ).
fof(c_0_20,plain,
! [X309] : plus(X309,n3) = succ(succ(succ(X309))),
inference(variable_rename,[status(thm)],[succ_plus_3_r]) ).
cnf(c_0_21,plain,
plus(X1,n2) = succ(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
succ(succ(n0)) = n2,
inference(split_conjunct,[status(thm)],[successor_2]) ).
cnf(c_0_25,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
fof(c_0_26,plain,
! [X372,X373] :
( ( n0 != X373
| n4 != X372
| ~ epred2_2(X373,X372) )
& ( n0 != X373
| n5 != X372
| ~ epred2_2(X373,X372) )
& ( n1 != X373
| n4 != X372
| ~ epred2_2(X373,X372) )
& ( n1 != X373
| n5 != X372
| ~ epred2_2(X373,X372) )
& ( n2 != X372
| n5 != X373
| ~ epred2_2(X373,X372) )
& ( n2 != X373
| n4 != X372
| ~ epred2_2(X373,X372) )
& ( n2 != X373
| n5 != X372
| ~ epred2_2(X373,X372) )
& ( n3 != X372
| n4 != X373
| ~ epred2_2(X373,X372) )
& ( n3 != X372
| n5 != X373
| ~ epred2_2(X373,X372) )
& ( n3 != X373
| n4 != X372
| ~ epred2_2(X373,X372) )
& ( n3 != X373
| n5 != X372
| ~ epred2_2(X373,X372) )
& ( n4 != X372
| n4 != X373
| ~ epred2_2(X373,X372) )
& ( n4 != X372
| n5 != X373
| ~ epred2_2(X373,X372) )
& ( n4 != X373
| n5 != X372
| ~ epred2_2(X373,X372) )
& ( n5 != X372
| n5 != X373
| ~ epred2_2(X373,X372) )
& ( n1 = X372
| ~ epred2_2(X373,X372) )
& ( n3 = X372
| ~ epred2_2(X373,X372) )
& ( n3 = X373
| ~ epred2_2(X373,X372) )
& ( n5 = X373
| ~ epred2_2(X373,X372) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_27,negated_conjecture,
( leq(n0,esk24_0)
& leq(n0,esk25_0)
& leq(esk24_0,n5)
& leq(esk25_0,n5)
& epred2_2(esk25_0,esk24_0)
& times(divide(n1,n400),a_select2(sigma,n3)) != n0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_28,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_29,plain,
! [X221,X222] :
( ( ~ leq(X221,X222)
| gt(succ(X222),X221) )
& ( ~ gt(succ(X222),X221)
| leq(X221,X222) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
fof(c_0_30,plain,
! [X310] : plus(n3,X310) = succ(succ(succ(X310))),
inference(variable_rename,[status(thm)],[succ_plus_3_l]) ).
cnf(c_0_31,plain,
plus(X1,n3) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
plus(X1,n2) = plus(plus(X1,n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_33,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_34,plain,
succ(succ(succ(n0))) = n3,
inference(split_conjunct,[status(thm)],[successor_3]) ).
cnf(c_0_35,plain,
plus(plus(n0,n1),n1) = n2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_22]) ).
cnf(c_0_36,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_37,plain,
( n1 = X1
| ~ epred2_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
epred2_2(esk25_0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_39,plain,
! [X203] : ~ gt(X203,X203),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
plus(n3,X1) = succ(succ(succ(X1))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,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_31,c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_43,plain,
plus(n1,plus(X1,n1)) = plus(X1,n2),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(split_conjunct,[status(thm)],[successor_4]) ).
cnf(c_0_45,plain,
plus(plus(plus(n0,n1),n1),n1) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_46,plain,
plus(n1,n1) = n2,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_47,negated_conjecture,
esk24_0 = n1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( gt(plus(X2,n1),X1)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_50,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_41,c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_51,plain,
plus(n1,plus(X1,n2)) = plus(X1,n3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_33]),c_0_43]),c_0_33]) ).
cnf(c_0_52,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_44,c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_53,plain,
plus(n2,n1) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_36]),c_0_46]) ).
cnf(c_0_54,plain,
( n3 = X1
| ~ epred2_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,negated_conjecture,
epred2_2(esk25_0,n1),
inference(rw,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_56,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,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_50,c_0_33]),c_0_43]),c_0_33]),c_0_51]) ).
cnf(c_0_58,plain,
plus(n3,n1) = n4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_36]),c_0_46]),c_0_53]) ).
cnf(c_0_59,plain,
esk25_0 = n3,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_60,plain,
! [X212,X213] :
( ~ gt(X213,X212)
| leq(X212,X213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt1])]) ).
cnf(c_0_61,plain,
~ leq(plus(n1,n3),n3),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
plus(n1,n3) = n4,
inference(rw,[status(thm)],[c_0_58,c_0_33]) ).
cnf(c_0_63,plain,
( n5 = X1
| ~ epred2_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_64,negated_conjecture,
epred2_2(n3,n1),
inference(rw,[status(thm)],[c_0_55,c_0_59]) ).
cnf(c_0_65,plain,
( leq(X2,X1)
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
gt(n5,n4),
inference(split_conjunct,[status(thm)],[gt_5_4]) ).
cnf(c_0_67,plain,
~ leq(n4,n3),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
n3 = n5,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
leq(n4,n5),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV220+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:57:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.95/1.91 % Version : CSE_E---1.7
% 1.95/1.91 % Problem : theBenchmark.p
% 1.95/1.91 % SZS status Theorem for theBenchmark.p
% 1.95/1.91 % SZS output start CNFRefutation
% See solution above
% 1.95/1.91 % Total time : 1.374s
%------------------------------------------------------------------------------