%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV055+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 : n009.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 05:20:43 PM UTC 2026
% Result : Theorem 1.80s 1.88s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 153 ( 33 equ)
% Maximal formula atoms : 41 ( 3 avg)
% Number of connectives : 163 ( 60 ~; 64 |; 29 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 55 ( 1 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0037,conjecture,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(X14,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X14,X18)) = n1 ) )
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(X4,minus(n0,n1)) )
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X20,n0),a_select2(x,pv10)),minus(a_select3(center,X20,n0),a_select2(x,pv10)))))) )
& ! [X21,X22] :
( ( leq(n0,X21)
& leq(X21,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X21,X22)) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0037) ).
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_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_pred,axiom,
! [X1] : succ(pred(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_pred) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(transitivity_leq,axiom,
! [X1,X2,X3] :
( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
fof(c_0_8,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(X14,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X14,X18)) = n1 ) )
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(X4,minus(n0,n1)) )
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X20,n0),a_select2(x,pv10)),minus(a_select3(center,X20,n0),a_select2(x,pv10)))))) )
& ! [X21,X22] :
( ( leq(n0,X21)
& leq(X21,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X21,X22)) = n1 ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0037]) ).
fof(c_0_9,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_10,plain,
! [X225,X226] :
( ( ~ leq(X225,X226)
| gt(succ(X226),X225) )
& ( ~ gt(succ(X226),X225)
| leq(X225,X226) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
fof(c_0_11,plain,
! [X309] : plus(X309,n1) = succ(X309),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_12,negated_conjecture,
! [X360,X361] :
( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& ( ~ leq(n0,X360)
| ~ leq(X360,minus(pv10,n1))
| sum(n0,minus(n5,n1),a_select3(q,X360,X361)) = n1 )
& ( leq(n0,esk26_0)
| leq(n0,esk24_0)
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( leq(esk26_0,minus(pv10,n1))
| leq(n0,esk24_0)
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1
| leq(n0,esk24_0)
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( leq(n0,esk26_0)
| leq(esk24_0,minus(n0,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( leq(esk26_0,minus(pv10,n1))
| leq(esk24_0,minus(n0,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1
| leq(esk24_0,minus(n0,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( leq(n0,esk26_0)
| a_select3(q,pv10,esk24_0) != divide(sqrt(times(minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,esk25_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk25_0,n0),a_select2(x,pv10))))))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( leq(esk26_0,minus(pv10,n1))
| a_select3(q,pv10,esk24_0) != divide(sqrt(times(minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,esk25_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk25_0,n0),a_select2(x,pv10))))))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) )
& ( sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1
| a_select3(q,pv10,esk24_0) != divide(sqrt(times(minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk24_0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,esk25_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk25_0,n0),a_select2(x,pv10))))))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_13,plain,
! [X207] : ~ gt(X207,X207),
inference(variable_rename,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X310] : plus(n1,X310) = succ(X310),
inference(variable_rename,[status(thm)],[succ_plus_1_l]) ).
cnf(c_0_17,negated_conjecture,
( leq(esk24_0,minus(n0,n1))
| sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
leq(n0,pv10),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
leq(pv10,minus(n135300,n1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( leq(n0,esk26_0)
| leq(esk24_0,minus(n0,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( leq(esk26_0,minus(pv10,n1))
| leq(esk24_0,minus(n0,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_22,plain,
! [X321] : succ(pred(X321)) = X321,
inference(variable_rename,[status(thm)],[succ_pred]) ).
fof(c_0_23,plain,
! [X319] : minus(X319,n1) = pred(X319),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
cnf(c_0_24,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( gt(plus(X2,n1),X1)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_26,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X209,X210,X211] :
( ~ leq(X209,X210)
| ~ leq(X210,X211)
| leq(X209,X211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_leq])]) ).
cnf(c_0_28,negated_conjecture,
( leq(esk24_0,minus(n0,n1))
| sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_29,negated_conjecture,
( sum(n0,minus(n5,n1),a_select3(q,X1,X2)) = n1
| ~ leq(n0,X1)
| ~ leq(X1,minus(pv10,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
( leq(esk24_0,minus(n0,n1))
| leq(n0,esk26_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_18]),c_0_19])]) ).
cnf(c_0_31,negated_conjecture,
( leq(esk26_0,minus(pv10,n1))
| leq(esk24_0,minus(n0,n1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_19])]) ).
cnf(c_0_32,plain,
succ(pred(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( leq(n0,esk24_0)
| sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( leq(n0,esk26_0)
| leq(n0,esk24_0)
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
( leq(esk26_0,minus(pv10,n1))
| leq(n0,esk24_0)
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_38,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_39,plain,
( leq(X1,X3)
| ~ leq(X1,X2)
| ~ leq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,negated_conjecture,
leq(esk24_0,minus(n0,n1)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_41,plain,
plus(minus(X1,n1),n1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_15]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( leq(n0,esk24_0)
| sum(n0,minus(n5,n1),a_select3(q,esk26_0,esk27_0)) != n1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_18]),c_0_19])]) ).
cnf(c_0_43,negated_conjecture,
( leq(n0,esk26_0)
| leq(n0,esk24_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_18]),c_0_19])]) ).
cnf(c_0_44,negated_conjecture,
( leq(esk26_0,minus(pv10,n1))
| leq(n0,esk24_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_18]),c_0_19])]) ).
cnf(c_0_45,plain,
~ leq(plus(n1,X1),X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( leq(X1,minus(n0,n1))
| ~ leq(X1,esk24_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
plus(n1,minus(X1,n1)) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
leq(n0,esk24_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_29]),c_0_43]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV055+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 04:54:41 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.80/1.88 % Version : CSE_E---1.7
% 1.80/1.88 % Problem : theBenchmark.p
% 1.80/1.88 % SZS status Theorem for theBenchmark.p
% 1.80/1.88 % SZS output start CNFRefutation
% See solution above
% 1.80/1.88 % Total time : 1.370s
%------------------------------------------------------------------------------