%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP730-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:28:18 PM UTC 2026
% Result : Unsatisfiable 25.66s 3.70s
% Output : CNFRefutation 25.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 3 RR)
% Number of literals : 50 ( 49 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 103 ( 30 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t193,plain,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
inference(orient,[status(thm)],[t8]) ).
cnf(t6,axiom,
mult(i(X1),mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t21,axiom,
mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)) = mult(mult(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t59,plain,
mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t21]) ).
cnf(t72,plain,
asoc(X1,X2,X3) = mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)),
inference(cp,[status(thm)],[t23,t59]) ).
cnf(t6188,plain,
mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)) = asoc(X1,X2,X3),
inference(orient,[status(thm)],[t72]) ).
cnf(t3,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t77,plain,
mult(i(X1),X1) = unit,
inference(orient,[status(thm)],[t3]) ).
cnf(t78,plain,
X1 = mult(i(i(X1)),unit),
inference(cp,[status(thm)],[t23,t77]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t11592,plain,
X1 = i(i(X1)),
inference(step,[status(thm)],[t78,t22]) ).
cnf(t202,plain,
i(i(X1)) = X1,
inference(orient,[status(thm)],[t11592]) ).
cnf(t203,plain,
X1 = mult(X2,mult(i(X2),X1)),
inference(cp,[status(thm)],[t23,t202]) ).
cnf(t287,plain,
mult(X1,mult(i(X1),X2)) = X2,
inference(orient,[status(thm)],[t203]) ).
cnf(t9,axiom,
mult(i(X1),i(X2)) = i(mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t101,plain,
mult(i(X1),i(X2)) = i(mult(X1,X2)),
inference(orient,[status(thm)],[t9]) ).
cnf(t289,plain,
i(X1) = mult(X2,i(mult(X2,X1))),
inference(cp,[status(thm)],[t287,t101]) ).
cnf(t463,plain,
mult(X1,i(mult(X1,X2))) = i(X2),
inference(orient,[status(thm)],[t289]) ).
cnf(t11,axiom,
mult(mult(X1,X2),op_k(X2,X1)) = mult(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t35,plain,
mult(mult(X1,X2),op_k(X2,X1)) = mult(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t467,plain,
i(op_k(X1,X2)) = mult(mult(X2,X1),i(mult(X1,X2))),
inference(cp,[status(thm)],[t463,t35]) ).
cnf(t11145,plain,
mult(mult(X1,X2),i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(orient,[status(thm)],[t467]) ).
cnf(t11283,plain,
asoc(X1,X2,i(mult(X2,X1))) = mult(i(mult(X1,mult(X2,i(mult(X2,X1))))),i(op_k(X2,X1))),
inference(cp,[status(thm)],[t6188,t11145]) ).
cnf(t11785,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(mult(mult(X1,mult(X2,i(mult(X2,X1)))),op_k(X2,X1))),
inference(step,[status(thm)],[t11283,t101]) ).
cnf(t11786,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(mult(mult(X1,i(X1)),op_k(X2,X1))),
inference(step,[status(thm)],[t11785,t463]) ).
cnf(t2,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t54,plain,
mult(X1,i(X1)) = unit,
inference(orient,[status(thm)],[t2]) ).
cnf(t11787,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(mult(unit,op_k(X2,X1))),
inference(step,[status(thm)],[t11786,t54]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t11788,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(step,[status(thm)],[t11787,t26]) ).
cnf(t11298,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(orient,[status(thm)],[t11788]) ).
cnf(t11336,plain,
unit = asoc(i(op_k(X1,X2)),X3,X4),
inference(cp,[status(thm)],[t193,t11298]) ).
cnf(t11569,plain,
asoc(i(op_k(X1,X2)),X3,X4) = unit,
inference(orient,[status(thm)],[t11336]) ).
cnf(t40,plain,
op_k(X1,X2) = mult(i(mult(X2,X1)),mult(X1,X2)),
inference(cp,[status(thm)],[t23,t35]) ).
cnf(t1145,plain,
mult(i(mult(X1,X2)),mult(X2,X1)) = op_k(X2,X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t1184,plain,
op_k(i(X1),i(X2)) = mult(i(mult(i(X2),i(X1))),i(mult(X1,X2))),
inference(cp,[status(thm)],[t1145,t101]) ).
cnf(t11663,plain,
op_k(i(X1),i(X2)) = i(mult(mult(i(X2),i(X1)),mult(X1,X2))),
inference(step,[status(thm)],[t1184,t101]) ).
cnf(t11664,plain,
op_k(i(X1),i(X2)) = i(mult(i(mult(X2,X1)),mult(X1,X2))),
inference(step,[status(thm)],[t11663,t101]) ).
cnf(t11665,plain,
op_k(i(X1),i(X2)) = i(op_k(X1,X2)),
inference(step,[status(thm)],[t11664,t1145]) ).
cnf(t1262,plain,
op_k(i(X1),i(X2)) = i(op_k(X1,X2)),
inference(orient,[status(thm)],[t11665]) ).
cnf(t11577,plain,
unit = asoc(i(i(op_k(X1,X2))),X3,X4),
inference(cp,[status(thm)],[t11569,t1262]) ).
cnf(t11791,plain,
unit = asoc(op_k(X1,X2),X3,X4),
inference(step,[status(thm)],[t11577,t202]) ).
cnf(t11584,plain,
asoc(op_k(X1,X2),X3,X4) = unit,
inference(orient,[status(thm)],[t11791]) ).
cnf(goal_0,negated_conjecture,
asoc(op_k(a,b),c,d) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
unit != unit,
inference(rw,[status(thm)],[goal_0,t11584]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP730-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:55:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.66/3.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.66/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------