%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG380-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Sun Sep 27 06:50:06 AM UTC 2026
% Result : Unsatisfiable 17.85s 2.75s
% Output : CNFRefutation 17.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 20 unt; 0 def)
% Number of atoms : 24 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 9 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(c_92,plain,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom]) ).
fof(cls_abs__mult__self_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(VAR_1,VAR_0),c_HOL_Oabs__class_Oabs(VAR_1,VAR_0),VAR_0) = c_HOL_Otimes__class_Otimes(VAR_1,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',cls_abs__mult__self_0) ).
cnf(c_93,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[cls_abs__mult__self_0]) ).
cnf(c_787,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_93,c_92]) ).
fof(cls_real__sqrt__mult_0,axiom,
! [VAR_0,VAR_1] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(VAR_0,VAR_1,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(VAR_0),c_NthRoot_Osqrt(VAR_1),tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__sqrt__mult_0) ).
cnf(c_1294,plain,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__sqrt__mult_0]) ).
cnf(c_1295,plain,
c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B),tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal)),
inference(copy,[status(thm)],[c_1294]) ).
fof(cls_rcis__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_HOL_Otimes__class_Otimes(c_Complex_Orcis(VAR_0,VAR_1),c_Complex_Orcis(VAR_2,VAR_3),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(VAR_0,VAR_2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(VAR_1,VAR_3,tc_RealDef_Oreal)),
file('theBenchmark.p',cls_rcis__mult_0) ).
cnf(c_1299,plain,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(A,B),c_Complex_Orcis(C,D),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[cls_rcis__mult_0]) ).
fof(cls_real__sqrt__abs2_0,axiom,
! [VAR_0] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(VAR_0,VAR_0,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(VAR_0,tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__sqrt__abs2_0) ).
cnf(c_1491,plain,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__sqrt__abs2_0]) ).
fof(cls_real__sum__of__halves_0,axiom,
! [VAR_0] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(VAR_0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(VAR_0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = VAR_0,
file('theBenchmark.p',cls_real__sum__of__halves_0) ).
cnf(c_1529,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = A,
inference(clausify,[status(thm)],[cls_real__sum__of__halves_0]) ).
fof(cls_conjecture_0,axiom,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1550,plain,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1552,plain,
c_Complex_Orcis(c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(paramod,[status(thm)],[c_1299,c_1550]) ).
cnf(c_1553,plain,
c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(paramod,[status(thm)],[c_1295,c_1552]) ).
cnf(c_1554,plain,
c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(v_r,v_r,tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(paramod,[status(thm)],[c_787,c_1553]) ).
cnf(c_1555,plain,
c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(paramod,[status(thm)],[c_1491,c_1554]) ).
cnf(c_1556,plain,
c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(paramod,[status(thm)],[c_1529,c_1555]) ).
cnf(c_1551,plain,
$false,
inference(copy,[status(thm)],[c_1556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG380-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 21:56:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 101471 was started by sandbox2 on n010,
% 0.09/0.36 % Sat Sep 26 21:56:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.43
% 0.13/0.43 % From the command line: assign(max_seconds, 300).
% 17.85/2.75
% 17.85/2.75 % SZS status Unsatisfiable for theBenchmark
% 17.85/2.75
% 17.85/2.75 % Proof 1 at 2.24 (+ 0.03) seconds.
% 17.85/2.75 % Length of proof is 10.
% 17.85/2.75 % Level of proof is 2.
% 17.85/2.75 % Maximum clause weight is 32.000.
% 17.85/2.75 % Given clauses 0.
% 17.85/2.75
% 17.85/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------