%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 : Fri Sep 25 03:16:42 PM UTC 2026
% Result : Theorem 0.92s 1.29s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 312 ( 73 equ)
% Maximal formula atoms : 47 ( 14 avg)
% Number of connectives : 435 ( 145 ~; 126 |; 138 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn 82 !; 6 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X10] :
( ( leq(X10,pred(pv57))
& leq(n0,X10) )
=> ! [X11] :
( ( leq(X11,n5)
& leq(n0,X11) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ( leq(X9,n5)
& leq(X8,n5)
& leq(n0,X9)
& leq(n0,X8) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ( leq(X7,n5)
& leq(X6,n5)
& leq(n0,X7)
& leq(n0,X6) )
=> ( ( gt(pv58,X7)
& X6 = pv57 )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X4,X5] :
( ( leq(X5,n5)
& leq(X4,n5)
& leq(n0,X5)
& leq(n0,X4) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ( leq(X3,n2)
& leq(X2,n2)
& leq(n0,X3)
& leq(n0,X2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ( leq(X1,n5)
& leq(X0,n5)
& leq(n0,X1)
& leq(n0,X0) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [X12] :
( ( leq(X12,pred(pv57))
& leq(n0,X12) )
=> ! [X13] :
( ( leq(X13,n5)
& leq(n0,X13) )
=> ( ( pv57 != X12
& ~ ( X13 = X12
& pv57 = X13 ) )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0401) ).
fof(f54,negated_conjecture,
~ ( ( ! [X10] :
( ( leq(X10,pred(pv57))
& leq(n0,X10) )
=> ! [X11] :
( ( leq(X11,n5)
& leq(n0,X11) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ( leq(X9,n5)
& leq(X8,n5)
& leq(n0,X9)
& leq(n0,X8) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X6,X7] :
( ( leq(X7,n5)
& leq(X6,n5)
& leq(n0,X7)
& leq(n0,X6) )
=> ( ( gt(pv58,X7)
& X6 = pv57 )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X4,X5] :
( ( leq(X5,n5)
& leq(X4,n5)
& leq(n0,X5)
& leq(n0,X4) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ( leq(X3,n2)
& leq(X2,n2)
& leq(n0,X3)
& leq(n0,X2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ( leq(X1,n5)
& leq(X0,n5)
& leq(n0,X1)
& leq(n0,X0) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [X12] :
( ( leq(X12,pred(pv57))
& leq(n0,X12) )
=> ! [X13] :
( ( leq(X13,n5)
& leq(n0,X13) )
=> ( ( pv57 != X12
& ~ ( X13 = X12
& pv57 = X13 ) )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ! [X10] :
( ~ leq(X10,pred(pv57))
| ~ leq(n0,X10)
| ! [X11] :
( ~ leq(X11,n5)
| ~ leq(n0,X11)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ~ leq(X9,n5)
| ~ leq(X8,n5)
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| ~ gt(pv57,X8)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,n5)
| ~ leq(X6,n5)
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| ~ gt(pv58,X7)
| pv57 != X6
| a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,n5)
| ~ leq(X4,n5)
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,n2)
| ~ leq(X2,n2)
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5)
& ? [X12] :
( leq(X12,pred(pv57))
& leq(n0,X12)
& ? [X13] :
( leq(X13,n5)
& leq(n0,X13)
& pv57 != X12
& ( X12 != X13
| pv57 != X13 )
& a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ! [X10] :
( ~ leq(X10,pred(pv57))
| ~ leq(n0,X10)
| ! [X11] :
( ~ leq(X11,n5)
| ~ leq(n0,X11)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) )
& ! [X8,X9] :
( ~ leq(X9,n5)
| ~ leq(X8,n5)
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| ~ gt(pv57,X8)
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,n5)
| ~ leq(X6,n5)
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| ~ gt(pv58,X7)
| pv57 != X6
| a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,n5)
| ~ leq(X4,n5)
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,n2)
| ~ leq(X2,n2)
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X0,X1] :
( ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5)
& ? [X12] :
( leq(X12,pred(pv57))
& leq(n0,X12)
& ? [X13] :
( leq(X13,n5)
& leq(n0,X13)
& pv57 != X12
& ( X12 != X13
| pv57 != X13 )
& a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12) ) ) ),
inference(flattening,[],[f94]) ).
fof(f117,plain,
( ! [X12] :
( ~ leq(X12,pred(pv57))
| ~ leq(n0,X12)
| ! [X13] :
( ~ leq(X13,n5)
| ~ leq(n0,X13)
| a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) )
& ! [X10,X11] :
( ~ leq(X11,n5)
| ~ leq(X10,n5)
| ~ leq(n0,X11)
| ~ leq(n0,X10)
| ~ gt(pv57,X10)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) )
& ! [X8,X9] :
( ~ leq(X9,n5)
| ~ leq(X8,n5)
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| ~ gt(pv58,X9)
| pv57 != X8
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,n5)
| ~ leq(X6,n5)
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,n2)
| ~ leq(X4,n2)
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,n5)
| ~ leq(X2,n5)
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5)
& ? [X0] :
( leq(X0,pred(pv57))
& leq(n0,X0)
& ? [X1] :
( leq(X1,n5)
& leq(n0,X1)
& pv57 != X0
& ( X0 != X1
| pv57 != X1 )
& a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0) ) ) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
( ! [X12] :
( ~ leq(X12,pred(pv57))
| ~ leq(n0,X12)
| ! [X13] :
( ~ leq(X13,n5)
| ~ leq(n0,X13)
| a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) )
& ! [X10,X11] :
( ~ leq(X11,n5)
| ~ leq(X10,n5)
| ~ leq(n0,X11)
| ~ leq(n0,X10)
| ~ gt(pv57,X10)
| a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) )
& ! [X8,X9] :
( ~ leq(X9,n5)
| ~ leq(X8,n5)
| ~ leq(n0,X9)
| ~ leq(n0,X8)
| ~ gt(pv58,X9)
| pv57 != X8
| a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) )
& ! [X6,X7] :
( ~ leq(X7,n5)
| ~ leq(X6,n5)
| ~ leq(n0,X7)
| ~ leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X4,X5] :
( ~ leq(X5,n2)
| ~ leq(X4,n2)
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4) )
& ! [X2,X3] :
( ~ leq(X3,n5)
| ~ leq(X2,n5)
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5)
& leq(sK0,pred(pv57))
& leq(n0,sK0)
& leq(sK1,n5)
& leq(n0,sK1)
& pv57 != sK0
& ( sK0 != sK1
| pv57 != sK1 )
& a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f117]) ).
fof(f122,plain,
! [X12,X13] :
( ~ leq(X12,pred(pv57))
| ~ leq(n0,X12)
| ~ leq(X13,n5)
| ~ leq(n0,X13)
| a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ),
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
leq(sK0,pred(pv57)),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f136,plain,
leq(sK1,n5),
inference(cnf_transformation,[],[f118]) ).
fof(f137,plain,
leq(n0,sK1),
inference(cnf_transformation,[],[f118]) ).
fof(f140,plain,
a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_49,negated_conjecture,
a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0),
inference(cnf_transformation,[],[f140]) ).
tcf(c_52,negated_conjecture,
leq(n0,sK1),
inference(cnf_transformation,[],[f137]) ).
tcf(c_53,negated_conjecture,
leq(sK1,n5),
inference(cnf_transformation,[],[f136]) ).
tcf(c_54,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_55,negated_conjecture,
leq(sK0,pred(pv57)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_67,negated_conjecture,
! [X0: $i,X1: $i] :
( ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0) )
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| ~ leq(X1,n5)
| ~ leq(X0,pred(pv57)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_2010,plain,
! [X0: $i] :
( ( a_select3(id_ds1_filter,X0,sK0) = a_select3(id_ds1_filter,sK0,X0) )
| ~ leq(n0,sK0)
| ~ leq(n0,X0)
| ~ leq(X0,n5) ),
inference(superposition,[status(thm)],[c_55,c_67]) ).
tcf(c_2012,plain,
! [X0: $i] :
( ( a_select3(id_ds1_filter,X0,sK0) = a_select3(id_ds1_filter,sK0,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,n5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2010,c_54]) ).
tcf(c_2182,plain,
( ( a_select3(id_ds1_filter,sK0,sK1) = a_select3(id_ds1_filter,sK1,sK0) )
| ~ leq(sK1,n5) ),
inference(superposition,[status(thm)],[c_52,c_2012]) ).
tcf(c_2192,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2182,c_49,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 18:45:54 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.92/1.29 % SZS status Started for theBenchmark.p
% 0.92/1.29 % SZS status Theorem for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/1.29
% 0.92/1.29 % ------ iProver source info
% 0.92/1.29
% 0.92/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/1.29 % git: non_committed_changes: false
% 0.92/1.29
% 0.92/1.29 % ------ Parsing...
% 0.92/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 % ------ Problem Properties
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29 % clauses 86
% 0.92/1.29 % conjectures 19
% 0.92/1.29 % EPR 52
% 0.92/1.29 % Horn 79
% 0.92/1.29 % unary 60
% 0.92/1.29 % binary 10
% 0.92/1.29 % lits 155
% 0.92/1.29 % lits eq 50
% 0.92/1.29 % fd_pure 0
% 0.92/1.29 % fd_pseudo 0
% 0.92/1.29 % fd_cond 6
% 0.92/1.29 % fd_pseudo_cond 2
% 0.92/1.29 % AC symbols 0
% 0.92/1.29
% 0.92/1.29 % ------ Schedule dynamic 5 is on
% 0.92/1.29
% 0.92/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 % ------
% 0.92/1.29 % Current options:
% 0.92/1.29 % ------
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % SZS status Theorem for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/1.29
% 0.92/1.29
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