%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:18:13 AM UTC 2026
% Result : Theorem 3.01s 0.80s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 22 unt; 0 def)
% Number of atoms : 71 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 30 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 5 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(281, 0), 0)',axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(goal(130), 0), 2)',axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(goal(130), 0), 3)',axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [Vd120,Vd121] :
( ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 = Vd121 ),
file('theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('ass(cond(goal(88), 0), 3)',axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| Vd120 != Vd121 ),
file('theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof('holds(conseq(307), 490, 0)',conjecture,
greater(vd486,vd488),
file('theBenchmark.p','holds(conseq(307), 490, 0)') ).
fof('holds(conseq(307), 490, 0)_neg',negated_conjecture,
~ greater(vd486,vd488),
inference(assume_negation,[status(cth)],['holds(conseq(307), 490, 0)']) ).
fof('holds(antec(307), 489, 0)',axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('theBenchmark.p','holds(antec(307), 489, 0)') ).
cnf(c_55,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(clausify,[status(thm)],['holds(antec(307), 489, 0)']) ).
cnf(c_60,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_61,plain,
vmul(A,vplus(B,C)) = vplus(vmul(A,B),vmul(A,C)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_99,plain,
( ~ less(A,B)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
cnf(c_100,plain,
( ~ greater(B,A)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 3)']) ).
cnf(c_102,plain,
( vplus(A,C) != B
| less(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)']) ).
cnf(c_104,plain,
( vplus(B,C) != A
| greater(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)']) ).
fof(nnf_38,plain,
! [Vd120,Vd121] :
( ? [Vd125] : vplus(Vd120,Vd125) = Vd121
| ? [Vd123] : vplus(Vd121,Vd123) = Vd120
| Vd121 = Vd120 ),
inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 0)']) ).
fof('sk_ass(cond(goal(88), 0), 0)',plain,
! [Vd120,Vd121] :
( vplus(Vd120,sK1(Vd120,Vd121)) = Vd121
| vplus(Vd121,sK0(Vd120,Vd121)) = Vd120
| Vd121 = Vd120 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Vd123,sK0(Vd120,Vd121)),skolemize(Vd125,sK1(Vd120,Vd121))],[nnf_38]) ).
cnf(c_105,plain,
( vplus(B,sK1(B,A)) = A
| vplus(A,sK0(B,A)) = B
| A = B ),
inference(split_conjunct,[status(thm)],['sk_ass(cond(goal(88), 0), 0)']) ).
cnf(c_108,plain,
( vplus(A,C) != B
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(88), 0), 3)']) ).
cnf(c_125,negated_conjecture,
~ greater(vd486,vd488),
inference(clausify,[status(thm)],['holds(conseq(307), 490, 0)_neg']) ).
cnf(c_2900,plain,
greater(vmul(vd487,vd486),vmul(vd488,vd487)),
inference(paramod,[status(thm)],[c_62,c_55]) ).
cnf(c_126,plain,
greater(vmul(vd487,vd486),vmul(vd487,vd488)),
inference(paramod,[status(thm)],[c_62,c_2900]) ).
cnf(c_2901,plain,
( vmul(C,A) = vplus(vmul(C,B),vmul(C,sK1(B,A)))
| vplus(A,sK0(B,A)) = B
| A = B ),
inference(paramod,[status(thm)],[c_105,c_61]) ).
cnf(c_184,plain,
( vplus(vmul(C,B),vmul(C,sK1(B,A))) = vmul(C,A)
| vplus(A,sK0(B,A)) = B
| A = B ),
inference(copy,[status(thm)],[c_2901]) ).
cnf(c_203,plain,
( A != C
| B != C
| vplus(A,sK0(B,A)) = B
| A = B ),
inference(paramod,[status(thm)],[c_105,c_108]) ).
cnf(c_281,negated_conjecture,
vplus(vd488,A) != vd486,
inference(resolve,[status(thm)],[c_104,c_125]) ).
cnf(c_285,plain,
vmul(vd487,vd488) != vmul(vd487,vd486),
inference(resolve,[status(thm)],[c_126,c_100]) ).
cnf(c_286,plain,
~ less(vmul(vd487,vd486),vmul(vd487,vd488)),
inference(resolve,[status(thm)],[c_126,c_99]) ).
cnf(c_879,plain,
vplus(vmul(vd487,vd486),A) != vmul(vd487,vd488),
inference(resolve,[status(thm)],[c_102,c_286]) ).
cnf(c_2902,plain,
( vplus(vd488,sK0(vd486,vd488)) = vd486
| vd488 = vd486 ),
inference(resolve,[status(thm)],[c_879,c_184]) ).
cnf(c_2897,plain,
vd488 = vd486,
inference(resolve,[status(thm)],[c_281,c_2902]) ).
cnf(c_2903,plain,
vmul(vd487,vd486) != vmul(vd487,vd488),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_2904,plain,
( vmul(vd487,vd486) != A
| vmul(vd487,vd488) != A
| vplus(vmul(vd487,vd486),sK0(vmul(vd487,vd488),vmul(vd487,vd486))) = vmul(vd487,vd488) ),
inference(resolve,[status(thm)],[c_203,c_2903]) ).
cnf(c_2905,plain,
( vmul(vd487,vd486) != A
| vmul(vd487,vd488) != A ),
inference(resolve,[status(thm)],[c_2904,c_879]) ).
cnf(c_2906,plain,
vmul(vd487,vd488) != vmul(vd486,vd487),
inference(resolve,[status(thm)],[c_2905,c_62]) ).
cnf(c_2907,plain,
vmul(vd487,vd486) != vmul(vd486,vd487),
inference(paramod,[status(thm)],[c_2897,c_2906]) ).
cnf(c_2908,plain,
vmul(vd487,vd486) != vmul(vd487,vd486),
inference(paramod,[status(thm)],[c_62,c_2907]) ).
cnf(c_2899,plain,
$false,
inference(copy,[status(thm)],[c_2908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.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 04:13:02 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 1171785 was started by sandbox on n005,
% 0.09/0.36 % Sat Sep 26 04:13:02 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 3.01/0.80
% 3.01/0.80 % SZS status Theorem for theBenchmark
% 3.01/0.80
% 3.01/0.80 % Proof 1 at 0.34 (+ 0.08) seconds.
% 3.01/0.80 % Length of proof is 29.
% 3.01/0.80 % Level of proof is 6.
% 3.01/0.80 % Maximum clause weight is 43.000.
% 3.01/0.80 % Given clauses 352.
% 3.01/0.80
% 3.01/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------