%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV415+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 03:17:35 PM UTC 2026
% Result : Theorem 11.12s 2.16s
% Output : CNFRefutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 43 unt; 5 def)
% Number of atoms : 119 ( 87 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 26 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-3 aty)
% Number of variables : 258 ( 0 sgn 221 !; 37 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax11) ).
fof(f17,axiom,
! [X0,X1,X2] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax17) ).
fof(f42,axiom,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).
fof(f54,axiom,
! [X0,X1] : i(triple(X0,create_slb,X1)) = create_pq,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax54) ).
fof(f55,axiom,
! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax55) ).
fof(f63,axiom,
( ( ! [X4] :
( ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8))
=> ! [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) = i(triple(X10,insert_slb(X4,pair(X13,X14)),X12)) )
& ! [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) = i(triple(X1,create_slb,X3)) )
=> ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big2_induction) ).
fof(f64,conjecture,
! [X0,X1,X2,X3] : i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X0,X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co2) ).
fof(f65,negated_conjecture,
~ ! [X0,X1,X2,X3] : i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X0,X1,X2)),X3),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f116,plain,
( ? [X4] :
( ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8))
& ? [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) != i(triple(X10,insert_slb(X4,pair(X13,X14)),X12)) )
| ? [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) != i(triple(X1,create_slb,X3))
| ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19)) ),
inference(ennf_transformation,[],[f63]) ).
fof(f117,plain,
( ? [X4] :
( ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8))
& ? [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) != i(triple(X10,insert_slb(X4,pair(X13,X14)),X12)) )
| ? [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) != i(triple(X1,create_slb,X3))
| ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19)) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
? [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) != i(insert_cpq(triple(X0,X1,X2),X3)),
inference(ennf_transformation,[],[f65]) ).
fof(f128,plain,
( ? [X9] :
( ! [X16,X17,X18,X19] : i(triple(X16,X9,X18)) = i(triple(X17,X9,X19))
& ? [X10,X11,X12,X13,X14,X15] : i(triple(X10,insert_slb(X9,pair(X14,X15)),X12)) != i(triple(X11,insert_slb(X9,pair(X14,X15)),X13)) )
| ? [X5,X6,X7,X8] : i(triple(X5,create_slb,X7)) != i(triple(X6,create_slb,X8))
| ! [X0,X1,X2,X3,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
inference(rectify,[],[f117]) ).
fof(f129,plain,
( ( ! [X16,X17,X18,X19] : i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19))
& i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9)) )
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| ! [X0,X1,X2,X3,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3),skolemize(X8,sK4),skolemize(X9,sK5),skolemize(X10,sK6),skolemize(X11,sK7),skolemize(X12,sK8),skolemize(X13,sK9),skolemize(X14,sK10),skolemize(X15,sK11)],[f128]) ).
fof(f130,plain,
insert_pq(i(triple(sK12,sK13,sK14)),sK15) != i(insert_cpq(triple(sK12,sK13,sK14),sK15)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f118]) ).
fof(f144,plain,
! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f11]) ).
fof(f150,plain,
! [X2,X0,X1] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1),
inference(cnf_transformation,[],[f17]) ).
fof(f182,plain,
! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[],[f42]) ).
fof(f194,plain,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f195,plain,
! [X2,X3,X0,X1,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
inference(cnf_transformation,[],[f55]) ).
fof(f196,plain,
! [X2,X3,X0,X1,X18,X19,X16,X4,X17] :
( i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19))
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f197,plain,
! [X2,X3,X0,X1,X4] :
( i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9))
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f198,plain,
insert_pq(i(triple(sK12,sK13,sK14)),sK15) != i(insert_cpq(triple(sK12,sK13,sK14),sK15)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : remove_pq(insert_pq(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f144]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1),
inference(cnf_transformation,[],[f150]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : triple(insert_pqp(X0,X1),insert_slb(X2,pair(X1,bottom)),X3) = insert_cpq(triple(X0,X2,X3),X1),
inference(cnf_transformation,[],[f182]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] : i(triple(X0,create_slb,X1)) = create_pq,
inference(cnf_transformation,[],[f194]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : i(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = insert_pq(i(triple(X0,X1,X4)),X2),
inference(cnf_transformation,[],[f195]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) )
| ( i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4)) )
| ( i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9)) ) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( i(triple(X5,sK5,X6)) = i(triple(X7,sK5,X8)) )
| ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) )
| ( i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4)) ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_114,negated_conjecture,
insert_pq(i(triple(sK12,sK13,sK14)),sK15) != i(insert_cpq(triple(sK12,sK13,sK14),sK15)),
inference(cnf_transformation,[],[f198]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( i(triple(X5,sK5,X6)) = i(triple(X7,sK5,X8)) )
| ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) )
| ( create_pq != create_pq ) ),
inference(demodulation,[status(thm)],[c_113,c_110]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( i(triple(X5,sK5,X6)) = i(triple(X7,sK5,X8)) )
| ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) ) ),
inference(equality_resolution_simp,[status(thm)],[c_616]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) )
| ( create_pq != create_pq )
| ( insert_pq(i(triple(sK6,sK5,sK8)),sK10) != insert_pq(i(triple(sK7,sK5,sK9)),sK10) ) ),
inference(demodulation,[status(thm)],[c_112,c_110,c_111]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) )
| ( insert_pq(i(triple(sK6,sK5,sK8)),sK10) != insert_pq(i(triple(sK7,sK5,sK9)),sK10) ) ),
inference(equality_resolution_simp,[status(thm)],[c_624]) ).
tcf(c_1425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ iPr_def_10
| ( i(triple(X0,sK5,X1)) = i(triple(X2,sK5,X3)) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_617]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ iPr_def_11
| ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_617]) ).
tcf(c_1427,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_617]) ).
tcf(c_1428,definition,
iPr_def_12 = triple(sK12,sK13,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1429,definition,
iPr_def_13 = i(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1430,definition,
iPr_def_14 = insert_pq(iPr_def_13,sK15),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1431,definition,
iPr_def_15 = insert_cpq(iPr_def_12,sK15),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1432,definition,
iPr_def_16 = i(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_1433,negated_conjecture,
iPr_def_14 != iPr_def_16,
inference(demodulation,[status(thm)],[c_114,c_1431,c_1432,c_1428,c_1429,c_1430]) ).
tcf(c_2289,plain,
! [X0: $i] : insert_pq(insert_pq(iPr_def_13,X0),sK15) = insert_pq(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_1430,c_68]) ).
tcf(c_2367,plain,
! [X0: $i] : remove_pq(insert_pq(iPr_def_14,X0),sK15) = insert_pq(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_2289,c_62]) ).
tcf(c_2431,plain,
insert_pq(iPr_def_13,sK15) = iPr_def_14,
inference(superposition,[status(thm)],[c_62,c_2367]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : insert_pq(i(triple(insert_pqp(X0,X1),X2,X3)),X1) = i(insert_cpq(triple(X0,X2,X3),X1)),
inference(superposition,[status(thm)],[c_100,c_111]) ).
tcf(c_3555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( iPr_def_10
| ( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) ) ),
inference(superposition,[status(thm)],[c_1427,c_1426]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : i(triple(X0,sK5,X1)) = i(triple(X2,sK5,X3)),
inference(backward_subsumption_resolution,[status(thm)],[c_1425,c_3555]) ).
tcf(c_7831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : insert_pq(i(triple(X0,sK5,X1)),X2) = i(insert_cpq(triple(X3,sK5,X4),X2)),
inference(superposition,[status(thm)],[c_3563,c_3061]) ).
tcf(c_11258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : insert_pq(i(triple(X0,sK5,X1)),X2) = insert_pq(i(triple(X3,sK5,X4)),X2),
inference(superposition,[status(thm)],[c_7831,c_7831]) ).
tcf(c_11293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)),
inference(backward_subsumption_resolution,[status(thm)],[c_625,c_11258]) ).
tcf(c_11484,plain,
! [X0: $i,X1: $i] : i(triple(X0,sK13,X1)) = i(iPr_def_12),
inference(superposition,[status(thm)],[c_1428,c_11293]) ).
tcf(c_11496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : insert_pq(i(triple(X0,X1,X2)),X3) = i(insert_cpq(triple(X4,X1,X5),X3)),
inference(superposition,[status(thm)],[c_11293,c_3061]) ).
tcf(c_11497,plain,
! [X0: $i,X1: $i] : i(triple(X0,sK13,X1)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_11484,c_1429]) ).
tcf(c_12817,plain,
! [X0: $i,X1: $i,X2: $i] : i(insert_cpq(triple(X0,sK13,X1),X2)) = insert_pq(iPr_def_13,X2),
inference(superposition,[status(thm)],[c_11497,c_11496]) ).
tcf(c_12959,plain,
! [X0: $i] : i(insert_cpq(iPr_def_12,X0)) = insert_pq(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_1428,c_12817]) ).
tcf(c_12990,plain,
insert_pq(iPr_def_13,sK15) = i(iPr_def_15),
inference(superposition,[status(thm)],[c_1431,c_12959]) ).
tcf(c_12991,plain,
iPr_def_14 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_12990,c_1432,c_2431]) ).
tcf(c_12992,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12991,c_1433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV415+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 19:31:26 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 11.12/2.16 % SZS status Started for theBenchmark.p
% 11.12/2.16 % SZS status Theorem for theBenchmark.p
% 11.12/2.16
% 11.12/2.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.12/2.16
% 11.12/2.16 % ------ iProver source info
% 11.12/2.16
% 11.12/2.16 % git: date: 2026-07-19 20:42:38 +0200
% 11.12/2.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.12/2.16 % git: non_committed_changes: false
% 11.12/2.16
% 11.12/2.16 % ------ Parsing...
% 11.12/2.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.12/2.16
% 11.12/2.16 % ------ Preprocessing... sup_sim: 2 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 11.12/2.16
% 11.12/2.16 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.12/2.16
% 11.12/2.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.12/2.16 % ------ Proving...
% 11.12/2.16 % ------ Problem Properties
% 11.12/2.16
% 11.12/2.16 %
% 11.12/2.16 % clauses 65
% 11.12/2.16 % conjectures 1
% 11.12/2.16 % EPR 9
% 11.12/2.16 % Horn 47
% 11.12/2.16 % unary 28
% 11.12/2.16 % binary 19
% 11.12/2.16 % lits 121
% 11.12/2.16 % lits eq 50
% 11.12/2.16 % fd_pure 0
% 11.12/2.16 % fd_pseudo 0
% 11.12/2.16 % fd_cond 5
% 11.12/2.16 % fd_pseudo_cond 7
% 11.12/2.16 % AC symbols 0
% 11.12/2.16
% 11.12/2.16 % ------ Schedule dynamic 5 is on
% 11.12/2.16
% 11.12/2.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 11.12/2.16
% 11.12/2.16 % ------
% 11.12/2.16 % Current options:
% 11.12/2.16 % ------
% 11.12/2.16
% 11.12/2.16
% 11.12/2.16 %
% 11.12/2.16
% 11.12/2.16 % ------ Proving...
% 11.12/2.16 %
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% 11.12/2.16 % SZS status Theorem for theBenchmark.p
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% 11.12/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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