%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:53:46 PM UTC 2026
% Result : Theorem 0.46s 0.69s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 114 ( 38 unt; 0 def)
% Number of atoms : 461 ( 85 equ)
% Maximal formula atoms : 75 ( 4 avg)
% Number of connectives : 431 ( 84 ~; 202 |; 115 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(pred_succ,axiom,
! [X1] : pred(succ(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(quaternion_ds1_symm_0015,conjecture,
( ( ! [X21,X22] :
( ( leq(X22,minus(n6,n1))
& leq(X21,minus(n6,n1))
& leq(n0,X22)
& leq(n0,X21) )
=> a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
& ! [X4,X20] :
( ( leq(X20,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X20)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
& ! [X14,X18] :
( ( leq(X18,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X18)
& leq(n0,X14) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) ) )
=> ( ! [X16,X6] :
( ( leq(X6,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X6)
& leq(n0,X16) )
=> a_select3(pminus_ds1_filter,X16,X6) = a_select3(pminus_ds1_filter,X6,X16) )
& ! [X5,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X5,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X5) )
=> a_select3(r_ds1_filter,X5,X11) = a_select3(r_ds1_filter,X11,X5) )
& ! [X28,X29] :
( ( leq(X29,minus(n6,n1))
& leq(X28,minus(n6,n1))
& leq(n0,X29)
& leq(n0,X28) )
=> a_select3(q_ds1_filter,X28,X29) = a_select3(q_ds1_filter,X29,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0015) ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
fof(successor_6,axiom,
succ(succ(succ(succ(succ(succ(n0)))))) = n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_6) ).
cnf(c_0_9,plain,
succ(succ(n0)) = n2,
inference(split_conjunct,[status(thm)],[successor_2]) ).
cnf(c_0_10,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
cnf(c_0_11,plain,
succ(succ(succ(n0))) = n3,
inference(split_conjunct,[status(thm)],[successor_3]) ).
cnf(c_0_12,plain,
succ(n1) = n2,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(split_conjunct,[status(thm)],[successor_4]) ).
cnf(c_0_14,plain,
succ(n2) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_12]) ).
fof(c_0_15,plain,
( epred2_0
<=> ( ! [X5,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X5,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X5) )
=> a_select3(r_ds1_filter,X5,X11) = a_select3(r_ds1_filter,X11,X5) )
& ! [X28,X29] :
( ( leq(X29,minus(n6,n1))
& leq(X28,minus(n6,n1))
& leq(n0,X29)
& leq(n0,X28) )
=> a_select3(q_ds1_filter,X28,X29) = a_select3(q_ds1_filter,X29,X28) ) ) ),
introduced(definition) ).
fof(c_0_16,plain,
! [X69] : pred(succ(X69)) = X69,
inference(variable_rename,[status(thm)],[pred_succ]) ).
fof(c_0_17,plain,
! [X49] : minus(X49,n1) = pred(X49),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_18,plain,
( epred1_0
<=> ( ! [X21,X22] :
( ( leq(X22,minus(n6,n1))
& leq(X21,minus(n6,n1))
& leq(n0,X22)
& leq(n0,X21) )
=> a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
& ! [X4,X20] :
( ( leq(X20,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X20)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
& ! [X14,X18] :
( ( leq(X18,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X18)
& leq(n0,X14) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) ) ) ),
introduced(definition) ).
fof(c_0_19,negated_conjecture,
~ ( ( ! [X21,X22] :
( ( leq(X22,minus(n6,n1))
& leq(X21,minus(n6,n1))
& leq(n0,X22)
& leq(n0,X21) )
=> a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
& ! [X4,X20] :
( ( leq(X20,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X20)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
& ! [X14,X18] :
( ( leq(X18,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X18)
& leq(n0,X14) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) ) )
=> ( ! [X16,X6] :
( ( leq(X6,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X6)
& leq(n0,X16) )
=> a_select3(pminus_ds1_filter,X16,X6) = a_select3(pminus_ds1_filter,X6,X16) )
& ! [X5,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X5,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X5) )
=> a_select3(r_ds1_filter,X5,X11) = a_select3(r_ds1_filter,X11,X5) )
& ! [X28,X29] :
( ( leq(X29,minus(n6,n1))
& leq(X28,minus(n6,n1))
& leq(n0,X29)
& leq(n0,X28) )
=> a_select3(q_ds1_filter,X28,X29) = a_select3(q_ds1_filter,X29,X28) ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0015]) ).
cnf(c_0_20,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(split_conjunct,[status(thm)],[successor_5]) ).
cnf(c_0_21,plain,
succ(n3) = n4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_10]),c_0_12]),c_0_14]) ).
fof(c_0_22,plain,
( ( ! [X5,X11] :
( ( leq(X11,minus(n3,n1))
& leq(X5,minus(n3,n1))
& leq(n0,X11)
& leq(n0,X5) )
=> a_select3(r_ds1_filter,X5,X11) = a_select3(r_ds1_filter,X11,X5) )
& ! [X28,X29] :
( ( leq(X29,minus(n6,n1))
& leq(X28,minus(n6,n1))
& leq(n0,X29)
& leq(n0,X28) )
=> a_select3(q_ds1_filter,X28,X29) = a_select3(q_ds1_filter,X29,X28) ) )
=> epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
pred(succ(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
( epred1_0
=> ( ! [X21,X22] :
( ( leq(X22,minus(n6,n1))
& leq(X21,minus(n6,n1))
& leq(n0,X22)
& leq(n0,X21) )
=> a_select3(pminus_ds1_filter,X21,X22) = a_select3(pminus_ds1_filter,X22,X21) )
& ! [X4,X20] :
( ( leq(X20,minus(n3,n1))
& leq(X4,minus(n3,n1))
& leq(n0,X20)
& leq(n0,X4) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) )
& ! [X14,X18] :
( ( leq(X18,minus(n6,n1))
& leq(X14,minus(n6,n1))
& leq(n0,X18)
& leq(n0,X14) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) ) ) ),
inference(split_equiv,[status(thm)],[c_0_18]) ).
fof(c_0_26,negated_conjecture,
~ ( epred1_0
=> ( ! [X16,X6] :
( ( leq(X6,minus(n6,n1))
& leq(X16,minus(n6,n1))
& leq(n0,X6)
& leq(n0,X16) )
=> a_select3(pminus_ds1_filter,X16,X6) = a_select3(pminus_ds1_filter,X6,X16) )
& epred2_0 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_18]),c_0_15]) ).
cnf(c_0_27,plain,
succ(succ(succ(succ(succ(succ(n0)))))) = n6,
inference(split_conjunct,[status(thm)],[successor_6]) ).
cnf(c_0_28,plain,
succ(n4) = n5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_10]),c_0_12]),c_0_14]),c_0_21]) ).
fof(c_0_29,plain,
( ( epred2_0
| a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0) )
& ( epred2_0
| a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| leq(esk6_0,minus(n3,n1)) )
& ( epred2_0
| a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| leq(esk5_0,minus(n3,n1)) )
& ( epred2_0
| a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| leq(n0,esk6_0) )
& ( epred2_0
| a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| leq(n0,esk5_0) )
& ( epred2_0
| leq(esk4_0,minus(n6,n1))
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0) )
& ( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(esk6_0,minus(n3,n1)) )
& ( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(esk5_0,minus(n3,n1)) )
& ( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(n0,esk6_0) )
& ( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(n0,esk5_0) )
& ( epred2_0
| leq(esk3_0,minus(n6,n1))
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0) )
& ( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(esk6_0,minus(n3,n1)) )
& ( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(esk5_0,minus(n3,n1)) )
& ( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(n0,esk6_0) )
& ( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(n0,esk5_0) )
& ( epred2_0
| leq(n0,esk4_0)
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0) )
& ( epred2_0
| leq(n0,esk4_0)
| leq(esk6_0,minus(n3,n1)) )
& ( epred2_0
| leq(n0,esk4_0)
| leq(esk5_0,minus(n3,n1)) )
& ( epred2_0
| leq(n0,esk4_0)
| leq(n0,esk6_0) )
& ( epred2_0
| leq(n0,esk4_0)
| leq(n0,esk5_0) )
& ( epred2_0
| leq(n0,esk3_0)
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0) )
& ( epred2_0
| leq(n0,esk3_0)
| leq(esk6_0,minus(n3,n1)) )
& ( epred2_0
| leq(n0,esk3_0)
| leq(esk5_0,minus(n3,n1)) )
& ( epred2_0
| leq(n0,esk3_0)
| leq(n0,esk6_0) )
& ( epred2_0
| leq(n0,esk3_0)
| leq(n0,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])]) ).
cnf(c_0_30,plain,
minus(succ(X1),n1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_31,plain,
! [X79,X80,X81,X82,X83,X84] :
( ( ~ epred1_0
| a_select3(pminus_ds1_filter,X83,X84) = a_select3(pminus_ds1_filter,X84,X83)
| ~ leq(X84,minus(n6,n1))
| ~ leq(X83,minus(n6,n1))
| ~ leq(n0,X84)
| ~ leq(n0,X83) )
& ( ~ epred1_0
| a_select3(r_ds1_filter,X81,X82) = a_select3(r_ds1_filter,X82,X81)
| ~ leq(X82,minus(n3,n1))
| ~ leq(X81,minus(n3,n1))
| ~ leq(n0,X82)
| ~ leq(n0,X81) )
& ( ~ epred1_0
| a_select3(q_ds1_filter,X79,X80) = a_select3(q_ds1_filter,X80,X79)
| ~ leq(X80,minus(n6,n1))
| ~ leq(X79,minus(n6,n1))
| ~ leq(n0,X80)
| ~ leq(n0,X79) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
fof(c_0_32,negated_conjecture,
( ( ~ epred2_0
| a_select3(pminus_ds1_filter,esk1_0,esk2_0) != a_select3(pminus_ds1_filter,esk2_0,esk1_0) )
& ( ~ epred2_0
| leq(esk2_0,minus(n6,n1)) )
& ( ~ epred2_0
| leq(esk1_0,minus(n6,n1)) )
& ( ~ epred2_0
| leq(n0,esk2_0) )
& ( ~ epred2_0
| leq(n0,esk1_0) )
& epred1_0 ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).
cnf(c_0_33,plain,
succ(n5) = n6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_10]),c_0_12]),c_0_14]),c_0_21]),c_0_28]) ).
cnf(c_0_34,plain,
( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(esk5_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
minus(n3,n1) = n2,
inference(spm,[status(thm)],[c_0_30,c_0_14]) ).
cnf(c_0_36,plain,
( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(esk5_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(esk6_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(esk6_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| epred2_0
| leq(esk5_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
( ~ epred1_0
| ~ leq(X2,minus(n6,n1))
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| a_select3(q_ds1_filter,X1,X2) = a_select3(q_ds1_filter,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
minus(n6,n1) = n5,
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_43,plain,
( leq(esk5_0,n2)
| leq(esk3_0,minus(n6,n1))
| epred2_0 ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
( leq(esk5_0,n2)
| leq(esk4_0,minus(n6,n1))
| epred2_0 ),
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_45,plain,
( epred2_0
| leq(n0,esk3_0)
| leq(esk5_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_46,plain,
( epred2_0
| leq(n0,esk4_0)
| leq(esk5_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47,plain,
( a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| epred2_0
| leq(esk6_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_48,plain,
( leq(esk6_0,n2)
| leq(esk3_0,minus(n6,n1))
| epred2_0 ),
inference(rw,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_49,plain,
( leq(esk6_0,n2)
| leq(esk4_0,minus(n6,n1))
| epred2_0 ),
inference(rw,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_50,plain,
( epred2_0
| leq(n0,esk3_0)
| leq(esk6_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_51,plain,
( epred2_0
| leq(n0,esk4_0)
| leq(esk6_0,minus(n3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_52,plain,
( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(n0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_53,plain,
( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(n0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_54,plain,
( epred2_0
| leq(esk3_0,minus(n6,n1))
| leq(n0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_55,plain,
( epred2_0
| leq(esk4_0,minus(n6,n1))
| leq(n0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_56,plain,
( ~ epred1_0
| ~ leq(X2,minus(n3,n1))
| ~ leq(X1,minus(n3,n1))
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| a_select3(r_ds1_filter,X1,X2) = a_select3(r_ds1_filter,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_57,plain,
( a_select3(q_ds1_filter,esk4_0,esk3_0) != a_select3(q_ds1_filter,esk3_0,esk4_0)
| leq(esk5_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_58,plain,
( ~ leq(X1,n5)
| ~ leq(X2,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X1,X2) = a_select3(q_ds1_filter,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_42])]) ).
cnf(c_0_59,plain,
( leq(esk3_0,n5)
| leq(esk5_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_60,plain,
( leq(esk4_0,n5)
| leq(esk5_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_61,plain,
( leq(n0,esk3_0)
| leq(esk5_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_62,plain,
( leq(n0,esk4_0)
| leq(esk5_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_63,plain,
( a_select3(q_ds1_filter,esk4_0,esk3_0) != a_select3(q_ds1_filter,esk3_0,esk4_0)
| leq(esk6_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_47,c_0_35]) ).
cnf(c_0_64,plain,
( leq(esk3_0,n5)
| leq(esk6_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_65,plain,
( leq(esk4_0,n5)
| leq(esk6_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_66,plain,
( leq(n0,esk3_0)
| leq(esk6_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_67,plain,
( leq(n0,esk4_0)
| leq(esk6_0,n2)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_51,c_0_35]) ).
cnf(c_0_68,plain,
( a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| epred2_0
| leq(n0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_69,plain,
( leq(esk3_0,n5)
| leq(n0,esk5_0)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_70,plain,
( leq(esk4_0,n5)
| leq(n0,esk5_0)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_71,plain,
( epred2_0
| leq(n0,esk3_0)
| leq(n0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_72,plain,
( epred2_0
| leq(n0,esk4_0)
| leq(n0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_73,plain,
( a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| epred2_0
| leq(n0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_74,plain,
( leq(esk3_0,n5)
| leq(n0,esk6_0)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_75,plain,
( leq(esk4_0,n5)
| leq(n0,esk6_0)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_76,plain,
( epred2_0
| leq(n0,esk3_0)
| leq(n0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_77,plain,
( epred2_0
| leq(n0,esk4_0)
| leq(n0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_78,plain,
( ~ epred1_0
| ~ leq(X2,minus(n6,n1))
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| a_select3(pminus_ds1_filter,X1,X2) = a_select3(pminus_ds1_filter,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_79,negated_conjecture,
( ~ epred2_0
| leq(esk1_0,minus(n6,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_80,negated_conjecture,
( ~ epred2_0
| leq(esk2_0,minus(n6,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_81,plain,
( a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0)
| epred2_0
| leq(esk3_0,minus(n6,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_82,plain,
( a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0)
| epred2_0
| leq(esk4_0,minus(n6,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_83,plain,
( a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0)
| epred2_0
| leq(n0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_84,plain,
( ~ leq(X1,n2)
| ~ leq(X2,n2)
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X1,X2) = a_select3(r_ds1_filter,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_41]),c_0_35]),c_0_35])]) ).
cnf(c_0_85,plain,
( leq(esk5_0,n2)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62]) ).
cnf(c_0_86,plain,
( leq(esk6_0,n2)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_58]),c_0_64]),c_0_65]),c_0_66]),c_0_67]) ).
cnf(c_0_87,plain,
( leq(n0,esk5_0)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_58]),c_0_69]),c_0_70]),c_0_71]),c_0_72]) ).
cnf(c_0_88,plain,
( leq(n0,esk6_0)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_58]),c_0_74]),c_0_75]),c_0_76]),c_0_77]) ).
cnf(c_0_89,negated_conjecture,
( ~ epred2_0
| a_select3(pminus_ds1_filter,esk1_0,esk2_0) != a_select3(pminus_ds1_filter,esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_90,plain,
( ~ leq(X1,n5)
| ~ leq(X2,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| a_select3(pminus_ds1_filter,X1,X2) = a_select3(pminus_ds1_filter,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_41]),c_0_42]),c_0_42])]) ).
cnf(c_0_91,negated_conjecture,
( ~ epred2_0
| leq(esk1_0,n5) ),
inference(rw,[status(thm)],[c_0_79,c_0_42]) ).
cnf(c_0_92,negated_conjecture,
( ~ epred2_0
| leq(esk2_0,n5) ),
inference(rw,[status(thm)],[c_0_80,c_0_42]) ).
cnf(c_0_93,negated_conjecture,
( ~ epred2_0
| leq(n0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_94,negated_conjecture,
( ~ epred2_0
| leq(n0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_95,plain,
( a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0)
| epred2_0
| leq(n0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_96,plain,
( a_select3(r_ds1_filter,esk6_0,esk5_0) != a_select3(r_ds1_filter,esk5_0,esk6_0)
| leq(esk3_0,n5)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_81,c_0_42]) ).
cnf(c_0_97,plain,
( a_select3(r_ds1_filter,esk6_0,esk5_0) != a_select3(r_ds1_filter,esk5_0,esk6_0)
| leq(esk4_0,n5)
| epred2_0 ),
inference(rw,[status(thm)],[c_0_82,c_0_42]) ).
cnf(c_0_98,plain,
( leq(n0,esk3_0)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_99,negated_conjecture,
~ epred2_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_100,plain,
( leq(n0,esk4_0)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_101,plain,
( leq(esk3_0,n5)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_102,plain,
( leq(esk4_0,n5)
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_103,plain,
( a_select3(q_ds1_filter,esk3_0,esk4_0) != a_select3(q_ds1_filter,esk4_0,esk3_0)
| a_select3(r_ds1_filter,esk5_0,esk6_0) != a_select3(r_ds1_filter,esk6_0,esk5_0)
| epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_104,plain,
leq(n0,esk3_0),
inference(sr,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,plain,
leq(n0,esk4_0),
inference(sr,[status(thm)],[c_0_100,c_0_99]) ).
cnf(c_0_106,plain,
leq(esk3_0,n5),
inference(sr,[status(thm)],[c_0_101,c_0_99]) ).
cnf(c_0_107,plain,
leq(esk4_0,n5),
inference(sr,[status(thm)],[c_0_102,c_0_99]) ).
cnf(c_0_108,plain,
a_select3(r_ds1_filter,esk6_0,esk5_0) != a_select3(r_ds1_filter,esk5_0,esk6_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_58]),c_0_104]),c_0_105]),c_0_106]),c_0_107])]),c_0_99]) ).
cnf(c_0_109,plain,
leq(n0,esk6_0),
inference(sr,[status(thm)],[c_0_88,c_0_99]) ).
cnf(c_0_110,plain,
leq(n0,esk5_0),
inference(sr,[status(thm)],[c_0_87,c_0_99]) ).
cnf(c_0_111,plain,
leq(esk6_0,n2),
inference(sr,[status(thm)],[c_0_86,c_0_99]) ).
cnf(c_0_112,plain,
leq(esk5_0,n2),
inference(sr,[status(thm)],[c_0_85,c_0_99]) ).
cnf(c_0_113,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_84]),c_0_109]),c_0_110]),c_0_111]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n015.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 08:35:06 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.46/0.69 % Version: 3.5.1
% 0.46/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.46/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.46/0.69 % Starting sh5l with 300s (1) cores
% 0.46/0.69 % new_bool_3 with pid 1049194 completed with status 0
% 0.46/0.69 % Result found by new_bool_3
% 0.46/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.46/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.46/0.69 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.46/0.69 % Search class: FGHSM-FFMM31-DFFFFFNN
% 0.46/0.69 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.46/0.69 % Starting SubtermCWHack with 31s (1) cores
% 0.46/0.69 % SubtermCWHack with pid 1049197 completed with status 0
% 0.46/0.69 % Result found by SubtermCWHack
% 0.46/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.46/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.46/0.69 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.46/0.69 % Search class: FGHSM-FFMM31-DFFFFFNN
% 0.46/0.69 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.46/0.69 % Starting SubtermCWHack with 31s (1) cores
% 0.46/0.69 % Preprocessing time : 0.002 s
% 0.46/0.69
% 0.46/0.69 % Proof found!
% 0.46/0.69 % SZS status Theorem
% 0.46/0.69 % SZS output start CNFRefutation
% See solution above
% 0.46/0.69 % Parsed axioms : 94
% 0.46/0.69 % Removed by relevancy pruning/SinE : 24
% 0.46/0.69 % Initial clauses : 106
% 0.46/0.69 % Removed in clause preprocessing : 0
% 0.46/0.69 % Initial clauses in saturation : 106
% 0.46/0.69 % Processed clauses : 3069
% 0.46/0.69 % ...of these trivial : 38
% 0.46/0.69 % ...subsumed : 2165
% 0.46/0.69 % ...remaining for further processing : 866
% 0.46/0.69 % Other redundant clauses eliminated : 0
% 0.46/0.69 % Clauses deleted for lack of memory : 0
% 0.46/0.69 % Backward-subsumed : 106
% 0.46/0.69 % Backward-rewritten : 30
% 0.46/0.69 % Generated clauses : 11493
% 0.46/0.69 % ...of the previous two non-redundant : 7074
% 0.46/0.69 % ...aggressively subsumed : 0
% 0.46/0.69 % Contextual simplify-reflections : 44
% 0.46/0.69 % Paramodulations : 11455
% 0.46/0.69 % Factorizations : 24
% 0.46/0.69 % NegExts : 0
% 0.46/0.69 % Equation resolutions : 0
% 0.46/0.69 % Disequality decompositions : 0
% 0.46/0.69 % Total rewrite steps : 7549
% 0.46/0.69 % ...of those cached : 7372
% 0.46/0.69 % Propositional unsat checks : 0
% 0.46/0.69 % Propositional check models : 0
% 0.46/0.69 % Propositional check unsatisfiable : 0
% 0.46/0.69 % Propositional clauses : 0
% 0.46/0.69 % Propositional clauses after purity: 0
% 0.46/0.69 % Propositional unsat core size : 0
% 0.46/0.69 % Propositional preprocessing time : 0.000
% 0.46/0.69 % Propositional encoding time : 0.000
% 0.46/0.69 % Propositional solver time : 0.000
% 0.46/0.69 % Success case prop preproc time : 0.000
% 0.46/0.69 % Success case prop encoding time : 0.000
% 0.46/0.69 % Success case prop solver time : 0.000
% 0.46/0.69 % Current number of processed clauses : 716
% 0.46/0.69 % Positive orientable unit clauses : 160
% 0.46/0.69 % Positive unorientable unit clauses: 0
% 0.46/0.69 % Negative unit clauses : 157
% 0.46/0.69 % Non-unit-clauses : 399
% 0.46/0.69 % Current number of unprocessed clauses: 4078
% 0.46/0.69 % ...number of literals in the above : 12406
% 0.46/0.69 % Current number of archived formulas : 0
% 0.46/0.69 % Current number of archived clauses : 150
% 0.46/0.69 % Clause-clause subsumption calls (NU) : 24922
% 0.46/0.69 % Rec. Clause-clause subsumption calls : 20977
% 0.46/0.69 % Non-unit clause-clause subsumptions : 752
% 0.46/0.69 % Unit Clause-clause subsumption calls : 5608
% 0.46/0.69 % Rewrite failures with RHS unbound : 0
% 0.46/0.69 % BW rewrite match attempts : 52
% 0.46/0.69 % BW rewrite match successes : 11
% 0.46/0.69 % Condensation attempts : 0
% 0.46/0.69 % Condensation successes : 0
% 0.46/0.69 % Termbank termtop insertions : 100985
% 0.46/0.69 % Search garbage collected termcells : 1048
% 0.46/0.69
% 0.46/0.69 % -------------------------------------------------
% 0.46/0.69 % User time : 0.122 s
% 0.46/0.69 % System time : 0.006 s
% 0.46/0.69 % Total time : 0.128 s
% 0.46/0.69 % Maximum resident set size: 4008 pages
% 0.46/0.69
% 0.46/0.69 % -------------------------------------------------
% 0.46/0.69 % User time : 0.128 s
% 0.46/0.69 % System time : 0.012 s
% 0.46/0.69 % Total time : 0.140 s
% 0.46/0.69 % Maximum resident set size: 4608 pages
% 0.46/0.69 % E exiting
%------------------------------------------------------------------------------