%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:27:55 PM UTC 2026
% Result : Unsatisfiable 2.76s 0.75s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 6 RR)
% Number of literals : 67 ( 66 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
eq(tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)),tuple(x1(X1),x1_2(X1))) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t21,plain,
eq(tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)),tuple(x1(X1),x1_2(X1))) = efalse,
inference(orient,[status(thm)],[t6]) ).
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t4,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
mult(mult(X1,mult(X2,X2)),X3) = mult(mult(X1,X2),mult(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(mult(X1,X2),mult(X2,X3)),
inference(orient,[status(thm)],[t5]) ).
cnf(t3,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t15,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),mult(X2,X3)) = mult(X1,X3),
inference(cp,[status(thm)],[t13,t8]) ).
cnf(t54,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),mult(X2,X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t15]) ).
cnf(t58,plain,
mult(X1,ld(X2,X3)) = mult(mult(rd(X1,mult(X2,X2)),X2),X3),
inference(cp,[status(thm)],[t54,t7]) ).
cnf(t70,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),X3) = mult(X1,ld(X2,X3)),
inference(orient,[status(thm)],[t58]) ).
cnf(t77,plain,
mult(mult(mult(rd(X1,mult(X2,X2)),X2),X3),mult(X3,Y3)) = mult(mult(X1,ld(X2,mult(X3,X3))),Y3),
inference(cp,[status(thm)],[t13,t70]) ).
cnf(t839,plain,
mult(mult(X1,ld(X2,X3)),mult(X3,Y3)) = mult(mult(X1,ld(X2,mult(X3,X3))),Y3),
inference(step,[status(thm)],[t77,t70]) ).
cnf(t132,plain,
mult(mult(X1,ld(X2,mult(X3,X3))),Y3) = mult(mult(X1,ld(X2,X3)),mult(X3,Y3)),
inference(orient,[status(thm)],[t839]) ).
cnf(t1,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t140,plain,
mult(mult(X1,ld(X2,X2)),mult(X2,X3)) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t132,t11]) ).
cnf(t289,plain,
mult(mult(X1,ld(X2,X2)),mult(X2,X3)) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t140]) ).
cnf(t300,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(mult(X1,ld(X2,X2)),X3),
inference(cp,[status(thm)],[t289,t7]) ).
cnf(t319,plain,
mult(mult(X1,ld(X2,X2)),X3) = mult(mult(X1,X2),ld(X2,X3)),
inference(orient,[status(thm)],[t300]) ).
cnf(t335,plain,
mult(X1,ld(X2,X2)) = rd(mult(mult(X1,X2),ld(X2,X3)),X3),
inference(cp,[status(thm)],[t9,t319]) ).
cnf(t437,plain,
rd(mult(mult(X1,X2),ld(X2,X3)),X3) = mult(X1,ld(X2,X2)),
inference(orient,[status(thm)],[t335]) ).
cnf(t328,plain,
mult(mult(rd(X1,ld(X2,X2)),X2),ld(X2,X3)) = mult(X1,X3),
inference(cp,[status(thm)],[t319,t8]) ).
cnf(t637,plain,
mult(mult(rd(X1,ld(X2,X2)),X2),ld(X2,X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t328]) ).
cnf(t136,plain,
mult(mult(X1,ld(X1,X2)),mult(X2,X3)) = mult(mult(X2,X2),X3),
inference(cp,[status(thm)],[t132,t7]) ).
cnf(t840,plain,
mult(X2,mult(X2,X3)) = mult(mult(X2,X2),X3),
inference(step,[status(thm)],[t136,t7]) ).
cnf(t164,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t840]) ).
cnf(t174,plain,
mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2),
inference(cp,[status(thm)],[t9,t164]) ).
cnf(t190,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(orient,[status(thm)],[t174]) ).
cnf(t202,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(cp,[status(thm)],[t190,t8]) ).
cnf(t244,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(orient,[status(thm)],[t202]) ).
cnf(t260,plain,
rd(X1,X2) = ld(rd(X1,X2),rd(mult(rd(X1,X2),X1),X2)),
inference(cp,[status(thm)],[t11,t244]) ).
cnf(t196,plain,
mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t190,t7]) ).
cnf(t208,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(orient,[status(thm)],[t196]) ).
cnf(t215,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),X2)),
inference(cp,[status(thm)],[t208,t8]) ).
cnf(t842,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(step,[status(thm)],[t215,t244]) ).
cnf(t273,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(orient,[status(thm)],[t842]) ).
cnf(t845,plain,
rd(X1,X2) = ld(rd(X1,X2),rd(X1,ld(rd(X1,X2),X2))),
inference(step,[status(thm)],[t260,t273]) ).
cnf(t556,plain,
ld(rd(X1,X2),rd(X1,ld(rd(X1,X2),X2))) = rd(X1,X2),
inference(orient,[status(thm)],[t845]) ).
cnf(t10,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t23,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t571,plain,
rd(X1,X1) = ld(rd(X1,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t556,t23]) ).
cnf(t595,plain,
ld(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t571]) ).
cnf(t646,plain,
mult(X1,X2) = mult(mult(rd(X1,rd(X3,X3)),rd(X3,X3)),ld(rd(X3,X3),X2)),
inference(cp,[status(thm)],[t637,t595]) ).
cnf(t847,plain,
mult(X1,X2) = mult(X1,ld(rd(X3,X3),X2)),
inference(step,[status(thm)],[t646,t8]) ).
cnf(t674,plain,
mult(X1,ld(rd(X2,X2),X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t847]) ).
cnf(t675,plain,
mult(rd(X1,X1),X2) = X2,
inference(cp,[status(thm)],[t674,t7]) ).
cnf(t709,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t675]) ).
cnf(t717,plain,
mult(rd(X1,X1),ld(X2,X2)) = rd(mult(X2,ld(X2,X3)),X3),
inference(cp,[status(thm)],[t437,t709]) ).
cnf(t853,plain,
ld(X2,X2) = rd(mult(X2,ld(X2,X3)),X3),
inference(step,[status(thm)],[t717,t709]) ).
cnf(t854,plain,
ld(X2,X2) = rd(X3,X3),
inference(step,[status(thm)],[t853,t7]) ).
cnf(t764,plain,
ld(X1,X1) = rd(X2,X2),
inference(orient,[status(thm)],[t854]) ).
cnf(t775,plain,
X1 = mult(X1,rd(X2,X2)),
inference(cp,[status(thm)],[t7,t764]) ).
cnf(t809,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t775]) ).
cnf(t832,plain,
efalse = eq(tuple(mult(rd(X1,X1),x1(rd(X1,X1))),x1_2(rd(X1,X1))),tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1)))),
inference(cp,[status(thm)],[t21,t809]) ).
cnf(t867,plain,
efalse = eq(tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1))),tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1)))),
inference(step,[status(thm)],[t832,t709]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t20,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t868,plain,
efalse = etrue,
inference(step,[status(thm)],[t867,t20]) ).
cnf(t836,plain,
efalse = etrue,
inference(orient,[status(thm)],[t868]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t836]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 15:30:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.76/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.76/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------