TSTP Solution File: SWV602-1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWV602-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 : Mon Jun 24 17:16:09 EDT 2024
% Result : Unsatisfiable 28.20s 4.72s
% Output : CNFRefutation 28.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 43 ( 31 unt; 0 nHn; 13 RR)
% Number of literals : 57 ( 41 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_94,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(c_233,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X0),c_Transcendental_Ocos(X1),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X0),c_Transcendental_Osin(X1),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__diff2_0) ).
cnf(c_333,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__eq_H_0) ).
cnf(c_488,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__eq_H_1) ).
cnf(c_526,plain,
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(c_745,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
cnf(c_873,plain,
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
cnf(c_946,plain,
c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__two__neq__zero_0) ).
cnf(c_949,plain,
c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(c_960,plain,
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
cnf(c_963,negated_conjecture,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_964,negated_conjecture,
c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_1055,plain,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(c_1057,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_1071,plain,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
cnf(c_1075,plain,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
cnf(c_1078,plain,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(c_1869,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_2081,plain,
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
inference(prop_impl_just,[status(thm)],[c_526]) ).
cnf(c_2125,plain,
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0) ),
inference(prop_impl_just,[status(thm)],[c_873]) ).
cnf(c_9193,plain,
c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_964,c_949]) ).
cnf(c_9194,plain,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_963,c_949]) ).
cnf(c_12283,plain,
( X0 != tc_RealDef_Oreal
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
inference(resolution_lifted,[status(thm)],[c_2081,c_1075]) ).
cnf(c_12284,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(unflattening,[status(thm)],[c_12283]) ).
cnf(c_12437,plain,
( X0 != tc_RealDef_Oreal
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0) ),
inference(resolution_lifted,[status(thm)],[c_2125,c_1071]) ).
cnf(c_12438,plain,
c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_12437]) ).
cnf(c_16471,plain,
( X0 != tc_RealDef_Oreal
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_1869,c_1057]) ).
cnf(c_16472,plain,
c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_16471]) ).
cnf(c_19825,plain,
( X0 != tc_RealDef_Oreal
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
inference(resolution_lifted,[status(thm)],[c_960,c_1078]) ).
cnf(c_19826,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_19825]) ).
cnf(c_19828,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(global_subsumption_just,[status(thm)],[c_19826,c_1055,c_19826]) ).
cnf(c_51465,plain,
c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_9193,c_949,c_19828]) ).
cnf(c_51466,plain,
c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_9194,c_949,c_19828]) ).
cnf(c_51581,plain,
c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(demodulation,[status(thm)],[c_333,c_16472]) ).
cnf(c_51599,plain,
c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(superposition,[status(thm)],[c_51581,c_488]) ).
cnf(c_60446,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_12438,c_745]) ).
cnf(c_60468,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_745,c_16472]) ).
cnf(c_60487,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(light_normalisation,[status(thm)],[c_60446,c_12438]) ).
cnf(c_63429,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X0),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)),
inference(superposition,[status(thm)],[c_51465,c_233]) ).
cnf(c_63588,plain,
c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(light_normalisation,[status(thm)],[c_63429,c_51466]) ).
cnf(c_65020,plain,
c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_63588,c_12284,c_60468,c_60487]) ).
cnf(c_65023,plain,
c_Transcendental_Ocos(X0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_51599,c_65020]) ).
cnf(c_65043,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_946,c_65023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV602-1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 20 21:00:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.20/4.72 % SZS status Started for theBenchmark.p
% 28.20/4.72 % SZS status Unsatisfiable for theBenchmark.p
% 28.20/4.72
% 28.20/4.72 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 28.20/4.72
% 28.20/4.72 ------ iProver source info
% 28.20/4.72
% 28.20/4.72 git: date: 2024-06-12 09:56:46 +0000
% 28.20/4.72 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 28.20/4.72 git: non_committed_changes: false
% 28.20/4.72
% 28.20/4.72 ------ Parsing...successful
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72 ------ Preprocessing... sup_sim: 34 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e
% 28.20/4.72
% 28.20/4.72 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 28.20/4.72
% 28.20/4.72 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e
% 28.20/4.72 ------ Proving...
% 28.20/4.72 ------ Problem Properties
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72 clauses 1084
% 28.20/4.72 conjectures 0
% 28.20/4.72 EPR 55
% 28.20/4.72 Horn 946
% 28.20/4.72 unary 413
% 28.20/4.72 binary 292
% 28.20/4.72 lits 2238
% 28.20/4.72 lits eq 802
% 28.20/4.72 fd_pure 0
% 28.20/4.72 fd_pseudo 0
% 28.20/4.72 fd_cond 58
% 28.20/4.72 fd_pseudo_cond 71
% 28.20/4.72 AC symbols 0
% 28.20/4.72
% 28.20/4.72 ------ Schedule dynamic 5 is on
% 28.20/4.72
% 28.20/4.72 ------ no conjectures: strip conj schedule
% 28.20/4.72
% 28.20/4.72 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72 ------
% 28.20/4.72 Current options:
% 28.20/4.72 ------
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72 ------ Proving...
% 28.20/4.72
% 28.20/4.72
% 28.20/4.72 % SZS status Unsatisfiable for theBenchmark.p
% 28.20/4.72
% 28.20/4.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.20/4.72
% 28.20/4.73
%------------------------------------------------------------------------------