%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:24:53 PM UTC 2026
% Result : Unsatisfiable 6.48s 1.32s
% Output : CNFRefutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 8
% Syntax : Number of clauses : 145 ( 145 unt; 0 nHn; 3 RR)
% Number of literals : 145 ( 144 equ; 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 277 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t5]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t27,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t9,t25]) ).
cnf(t1,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t2429,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t27,t8]) ).
cnf(t56,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t2429]) ).
cnf(t2,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t21,plain,
identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))),
inference(cp,[status(thm)],[t20,t9]) ).
cnf(t63,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(orient,[status(thm)],[t21]) ).
cnf(t70,plain,
multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity),
inference(cp,[status(thm)],[t56,t63]) ).
cnf(t0,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t2430,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(step,[status(thm)],[t70,t7]) ).
cnf(t72,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t2430]) ).
cnf(t78,plain,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inference(cp,[status(thm)],[t56,t72]) ).
cnf(t82,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t78]) ).
cnf(t85,plain,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(cp,[status(thm)],[t9,t82]) ).
cnf(t254,plain,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(orient,[status(thm)],[t85]) ).
cnf(t6,axiom,
multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))) = commutator(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))) = commutator(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t2431,plain,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = commutator(X1,X2),
inference(step,[status(thm)],[t10,t82]) ).
cnf(t87,plain,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = commutator(X1,X2),
inference(rw,[status(thm)],[t2431]) ).
cnf(t120,plain,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = commutator(X1,X2),
inference(orient,[status(thm)],[t87]) ).
cnf(t255,plain,
multiply(inverse(multiply(X1,X2)),inverse(multiply(inverse(X1),inverse(X2)))) = commutator(inverse(X2),inverse(X1)),
inference(cp,[status(thm)],[t254,t120]) ).
cnf(t2470,plain,
inverse(multiply(multiply(inverse(X1),inverse(X2)),multiply(X1,X2))) = commutator(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t255,t82]) ).
cnf(t2471,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(X1,X2)))) = commutator(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t2470,t9]) ).
cnf(t2472,plain,
inverse(multiply(inverse(multiply(X2,X1)),multiply(X1,X2))) = commutator(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t2471,t254]) ).
cnf(t23,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t9,t20]) ).
cnf(t2424,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t23,t8]) ).
cnf(t36,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t2424]) ).
cnf(t38,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t36,t20]) ).
cnf(t2425,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t38,t7]) ).
cnf(t43,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2425]) ).
cnf(t84,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t82,t43]) ).
cnf(t95,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t84]) ).
cnf(t2473,plain,
multiply(inverse(multiply(X1,X2)),multiply(X2,X1)) = commutator(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t2472,t95]) ).
cnf(t1271,plain,
multiply(inverse(multiply(X1,X2)),multiply(X2,X1)) = commutator(inverse(X2),inverse(X1)),
inference(orient,[status(thm)],[t2473]) ).
cnf(t79,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(cp,[status(thm)],[t36,t72]) ).
cnf(t88,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t79]) ).
cnf(t89,plain,
multiply(X1,inverse(multiply(X2,X3))) = inverse(multiply(X2,multiply(X3,inverse(X1)))),
inference(cp,[status(thm)],[t88,t9]) ).
cnf(t275,plain,
inverse(multiply(X1,multiply(X2,inverse(X3)))) = multiply(X3,inverse(multiply(X1,X2))),
inference(orient,[status(thm)],[t89]) ).
cnf(t276,plain,
multiply(multiply(X1,X2),inverse(multiply(X2,X1))) = inverse(commutator(X2,X1)),
inference(cp,[status(thm)],[t275,t120]) ).
cnf(t2441,plain,
multiply(X1,multiply(X2,inverse(multiply(X2,X1)))) = inverse(commutator(X2,X1)),
inference(step,[status(thm)],[t276,t9]) ).
cnf(t2442,plain,
commutator(X1,X2) = inverse(commutator(X2,X1)),
inference(step,[status(thm)],[t2441,t120]) ).
cnf(t310,plain,
inverse(commutator(X1,X2)) = commutator(X2,X1),
inference(orient,[status(thm)],[t2442]) ).
cnf(t313,plain,
inverse(multiply(X1,commutator(X2,X3))) = multiply(commutator(X3,X2),inverse(X1)),
inference(cp,[status(thm)],[t82,t310]) ).
cnf(t340,plain,
inverse(multiply(X1,commutator(X2,X3))) = multiply(commutator(X3,X2),inverse(X1)),
inference(orient,[status(thm)],[t313]) ).
cnf(t75,plain,
inverse(multiply(X1,X2)) = multiply(X3,inverse(multiply(X1,multiply(X2,X3)))),
inference(cp,[status(thm)],[t72,t9]) ).
cnf(t451,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(orient,[status(thm)],[t75]) ).
cnf(t455,plain,
inverse(multiply(X1,X2)) = multiply(inverse(multiply(X2,X1)),inverse(commutator(X1,X2))),
inference(cp,[status(thm)],[t451,t120]) ).
cnf(t2457,plain,
inverse(multiply(X1,X2)) = inverse(multiply(commutator(X1,X2),multiply(X2,X1))),
inference(step,[status(thm)],[t455,t82]) ).
cnf(t314,plain,
inverse(multiply(commutator(X1,X2),X3)) = multiply(inverse(X3),commutator(X2,X1)),
inference(cp,[status(thm)],[t82,t310]) ).
cnf(t371,plain,
inverse(multiply(commutator(X1,X2),X3)) = multiply(inverse(X3),commutator(X2,X1)),
inference(orient,[status(thm)],[t314]) ).
cnf(t2458,plain,
inverse(multiply(X1,X2)) = multiply(inverse(multiply(X2,X1)),commutator(X2,X1)),
inference(step,[status(thm)],[t2457,t371]) ).
cnf(t900,plain,
multiply(inverse(multiply(X1,X2)),commutator(X1,X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t2458]) ).
cnf(t963,plain,
multiply(commutator(X1,X2),inverse(inverse(multiply(X2,X1)))) = inverse(inverse(multiply(X1,X2))),
inference(cp,[status(thm)],[t340,t900]) ).
cnf(t2459,plain,
multiply(commutator(X1,X2),multiply(X2,X1)) = inverse(inverse(multiply(X1,X2))),
inference(step,[status(thm)],[t963,t43]) ).
cnf(t2460,plain,
multiply(commutator(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(step,[status(thm)],[t2459,t43]) ).
cnf(t981,plain,
multiply(commutator(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(orient,[status(thm)],[t2460]) ).
cnf(t471,plain,
commutator(multiply(X1,X2),X2) = multiply(multiply(X1,X2),inverse(multiply(X2,X1))),
inference(cp,[status(thm)],[t120,t451]) ).
cnf(t2443,plain,
commutator(multiply(X1,X2),X2) = multiply(X1,multiply(X2,inverse(multiply(X2,X1)))),
inference(step,[status(thm)],[t471,t9]) ).
cnf(t2444,plain,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(step,[status(thm)],[t2443,t120]) ).
cnf(t474,plain,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(orient,[status(thm)],[t2444]) ).
cnf(t485,plain,
commutator(inverse(X1),multiply(X1,X2)) = commutator(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t474,t56]) ).
cnf(t132,plain,
commutator(multiply(X1,X2),inverse(X1)) = multiply(multiply(X1,X2),multiply(inverse(X1),inverse(X2))),
inference(cp,[status(thm)],[t120,t56]) ).
cnf(t2434,plain,
commutator(multiply(X1,X2),inverse(X1)) = multiply(X1,multiply(X2,multiply(inverse(X1),inverse(X2)))),
inference(step,[status(thm)],[t132,t9]) ).
cnf(t2435,plain,
commutator(multiply(X1,X2),inverse(X1)) = multiply(X1,multiply(X2,inverse(multiply(X2,X1)))),
inference(step,[status(thm)],[t2434,t82]) ).
cnf(t2436,plain,
commutator(multiply(X1,X2),inverse(X1)) = commutator(X1,X2),
inference(step,[status(thm)],[t2435,t120]) ).
cnf(t143,plain,
commutator(multiply(X1,X2),inverse(X1)) = commutator(X1,X2),
inference(orient,[status(thm)],[t2436]) ).
cnf(t151,plain,
commutator(inverse(X1),multiply(X1,X2)) = commutator(X2,inverse(inverse(X1))),
inference(cp,[status(thm)],[t143,t56]) ).
cnf(t2437,plain,
commutator(inverse(X1),multiply(X1,X2)) = commutator(X2,X1),
inference(step,[status(thm)],[t151,t43]) ).
cnf(t156,plain,
commutator(inverse(X1),multiply(X1,X2)) = commutator(X2,X1),
inference(orient,[status(thm)],[t2437]) ).
cnf(t2445,plain,
commutator(X2,X1) = commutator(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t485,t156]) ).
cnf(t497,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(orient,[status(thm)],[t2445]) ).
cnf(t985,plain,
multiply(X1,multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(multiply(X2,X1),X1)),
inference(cp,[status(thm)],[t981,t497]) ).
cnf(t2494,plain,
multiply(X1,multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(X2,multiply(X1,X1))),
inference(step,[status(thm)],[t985,t9]) ).
cnf(t4,axiom,
multiply(X1,multiply(X1,X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
multiply(X1,multiply(X1,X1)) = identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t40,plain,
multiply(inverse(X1),inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t36,t16]) ).
cnf(t2427,plain,
multiply(inverse(X1),inverse(X1)) = X1,
inference(step,[status(thm)],[t40,t7]) ).
cnf(t48,plain,
multiply(inverse(X1),inverse(X1)) = X1,
inference(orient,[status(thm)],[t2427]) ).
cnf(t49,plain,
inverse(X1) = multiply(X1,inverse(inverse(X1))),
inference(cp,[status(thm)],[t48,t43]) ).
cnf(t2428,plain,
inverse(X1) = multiply(X1,X1),
inference(step,[status(thm)],[t49,t43]) ).
cnf(t53,plain,
multiply(X1,X1) = inverse(X1),
inference(orient,[status(thm)],[t2428]) ).
cnf(t2495,plain,
multiply(X1,multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(X2,inverse(X1))),
inference(step,[status(thm)],[t2494,t53]) ).
cnf(t1932,plain,
multiply(commutator(X1,X2),multiply(X2,inverse(X1))) = multiply(X1,multiply(X2,X1)),
inference(orient,[status(thm)],[t2495]) ).
cnf(t80,plain,
inverse(X1) = multiply(inverse(multiply(X2,X1)),inverse(inverse(X2))),
inference(cp,[status(thm)],[t72,t72]) ).
cnf(t2432,plain,
inverse(X1) = inverse(multiply(inverse(X2),multiply(X2,X1))),
inference(step,[status(thm)],[t80,t82]) ).
cnf(t2433,plain,
inverse(X1) = multiply(inverse(multiply(X2,X1)),X2),
inference(step,[status(thm)],[t2432,t95]) ).
cnf(t105,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t2433]) ).
cnf(t482,plain,
commutator(inverse(multiply(X1,X2)),X1) = commutator(inverse(X2),X1),
inference(cp,[status(thm)],[t474,t105]) ).
cnf(t537,plain,
commutator(inverse(multiply(X1,X2)),X1) = commutator(inverse(X2),X1),
inference(orient,[status(thm)],[t482]) ).
cnf(t539,plain,
commutator(inverse(inverse(X1)),X2) = commutator(multiply(X1,inverse(X2)),X2),
inference(cp,[status(thm)],[t537,t88]) ).
cnf(t2446,plain,
commutator(X1,X2) = commutator(multiply(X1,inverse(X2)),X2),
inference(step,[status(thm)],[t539,t43]) ).
cnf(t562,plain,
commutator(multiply(X1,inverse(X2)),X2) = commutator(X1,X2),
inference(orient,[status(thm)],[t2446]) ).
cnf(t1960,plain,
multiply(multiply(X1,inverse(X2)),multiply(X2,multiply(X1,inverse(X2)))) = multiply(commutator(X1,X2),multiply(X2,inverse(multiply(X1,inverse(X2))))),
inference(cp,[status(thm)],[t1932,t562]) ).
cnf(t2496,plain,
multiply(X1,multiply(inverse(X2),multiply(X2,multiply(X1,inverse(X2))))) = multiply(commutator(X1,X2),multiply(X2,inverse(multiply(X1,inverse(X2))))),
inference(step,[status(thm)],[t1960,t9]) ).
cnf(t2497,plain,
multiply(X1,multiply(X1,inverse(X2))) = multiply(commutator(X1,X2),multiply(X2,inverse(multiply(X1,inverse(X2))))),
inference(step,[status(thm)],[t2496,t56]) ).
cnf(t55,plain,
multiply(X1,multiply(X1,X2)) = multiply(inverse(X1),X2),
inference(cp,[status(thm)],[t9,t53]) ).
cnf(t59,plain,
multiply(X1,multiply(X1,X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t55]) ).
cnf(t2498,plain,
multiply(inverse(X1),inverse(X2)) = multiply(commutator(X1,X2),multiply(X2,inverse(multiply(X1,inverse(X2))))),
inference(step,[status(thm)],[t2497,t59]) ).
cnf(t2499,plain,
inverse(multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(X2,inverse(multiply(X1,inverse(X2))))),
inference(step,[status(thm)],[t2498,t82]) ).
cnf(t2500,plain,
inverse(multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(X2,multiply(X2,inverse(X1)))),
inference(step,[status(thm)],[t2499,t88]) ).
cnf(t2501,plain,
inverse(multiply(X2,X1)) = multiply(commutator(X1,X2),multiply(inverse(X2),inverse(X1))),
inference(step,[status(thm)],[t2500,t59]) ).
cnf(t2502,plain,
inverse(multiply(X2,X1)) = multiply(commutator(X1,X2),inverse(multiply(X1,X2))),
inference(step,[status(thm)],[t2501,t82]) ).
cnf(t2025,plain,
multiply(commutator(X1,X2),inverse(multiply(X1,X2))) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t2502]) ).
cnf(t2108,plain,
commutator(inverse(inverse(multiply(X1,X2))),inverse(commutator(X1,X2))) = multiply(inverse(inverse(multiply(X2,X1))),multiply(inverse(multiply(X1,X2)),commutator(X1,X2))),
inference(cp,[status(thm)],[t1271,t2025]) ).
cnf(t2564,plain,
commutator(multiply(X1,X2),inverse(commutator(X1,X2))) = multiply(inverse(inverse(multiply(X2,X1))),multiply(inverse(multiply(X1,X2)),commutator(X1,X2))),
inference(step,[status(thm)],[t2108,t43]) ).
cnf(t2565,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = multiply(inverse(inverse(multiply(X2,X1))),multiply(inverse(multiply(X1,X2)),commutator(X1,X2))),
inference(step,[status(thm)],[t2564,t310]) ).
cnf(t479,plain,
commutator(X1,inverse(multiply(X2,X1))) = commutator(inverse(X2),inverse(multiply(X2,X1))),
inference(cp,[status(thm)],[t474,t72]) ).
cnf(t148,plain,
commutator(X1,inverse(multiply(X2,X1))) = commutator(inverse(X2),inverse(X1)),
inference(cp,[status(thm)],[t143,t72]) ).
cnf(t184,plain,
commutator(X1,inverse(multiply(X2,X1))) = commutator(inverse(X2),inverse(X1)),
inference(orient,[status(thm)],[t148]) ).
cnf(t2450,plain,
commutator(inverse(X2),inverse(X1)) = commutator(inverse(X2),inverse(multiply(X2,X1))),
inference(step,[status(thm)],[t479,t184]) ).
cnf(t649,plain,
commutator(inverse(X1),inverse(multiply(X1,X2))) = commutator(inverse(X1),inverse(X2)),
inference(orient,[status(thm)],[t2450]) ).
cnf(t958,plain,
commutator(inverse(inverse(multiply(X1,X2))),inverse(commutator(X1,X2))) = commutator(inverse(inverse(multiply(X1,X2))),inverse(inverse(multiply(X2,X1)))),
inference(cp,[status(thm)],[t649,t900]) ).
cnf(t2466,plain,
commutator(multiply(X1,X2),inverse(commutator(X1,X2))) = commutator(inverse(inverse(multiply(X1,X2))),inverse(inverse(multiply(X2,X1)))),
inference(step,[status(thm)],[t958,t43]) ).
cnf(t2467,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = commutator(inverse(inverse(multiply(X1,X2))),inverse(inverse(multiply(X2,X1)))),
inference(step,[status(thm)],[t2466,t310]) ).
cnf(t2468,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = commutator(multiply(X1,X2),inverse(inverse(multiply(X2,X1)))),
inference(step,[status(thm)],[t2467,t43]) ).
cnf(t2469,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = commutator(multiply(X1,X2),multiply(X2,X1)),
inference(step,[status(thm)],[t2468,t43]) ).
cnf(t1220,plain,
commutator(multiply(X1,X2),commutator(X2,X1)) = commutator(multiply(X1,X2),multiply(X2,X1)),
inference(orient,[status(thm)],[t2469]) ).
cnf(t2566,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = multiply(inverse(inverse(multiply(X2,X1))),multiply(inverse(multiply(X1,X2)),commutator(X1,X2))),
inference(step,[status(thm)],[t2565,t1220]) ).
cnf(t2567,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X2,X1)))),commutator(X1,X2)),
inference(step,[status(thm)],[t2566,t254]) ).
cnf(t2568,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = multiply(multiply(multiply(X2,X1),inverse(multiply(X1,X2))),commutator(X1,X2)),
inference(step,[status(thm)],[t2567,t88]) ).
cnf(t2569,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = multiply(multiply(X2,multiply(X1,inverse(multiply(X1,X2)))),commutator(X1,X2)),
inference(step,[status(thm)],[t2568,t9]) ).
cnf(t2570,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = multiply(commutator(X2,X1),commutator(X1,X2)),
inference(step,[status(thm)],[t2569,t120]) ).
cnf(t318,plain,
identity = multiply(commutator(X1,X2),commutator(X2,X1)),
inference(cp,[status(thm)],[t25,t310]) ).
cnf(t338,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = identity,
inference(orient,[status(thm)],[t318]) ).
cnf(t2571,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = identity,
inference(step,[status(thm)],[t2570,t338]) ).
cnf(t2331,plain,
commutator(multiply(X1,X2),multiply(X2,X1)) = identity,
inference(orient,[status(thm)],[t2571]) ).
cnf(t2361,plain,
identity = commutator(multiply(multiply(X1,X2),inverse(X1)),X2),
inference(cp,[status(thm)],[t2331,t56]) ).
cnf(t2580,plain,
identity = commutator(multiply(X1,multiply(X2,inverse(X1))),X2),
inference(step,[status(thm)],[t2361,t9]) ).
cnf(t545,plain,
commutator(inverse(multiply(X1,inverse(multiply(X1,X2)))),X2) = commutator(inverse(commutator(X2,X1)),X2),
inference(cp,[status(thm)],[t537,t120]) ).
cnf(t2475,plain,
commutator(multiply(multiply(X1,X2),inverse(X1)),X2) = commutator(inverse(commutator(X2,X1)),X2),
inference(step,[status(thm)],[t545,t88]) ).
cnf(t2476,plain,
commutator(multiply(X1,multiply(X2,inverse(X1))),X2) = commutator(inverse(commutator(X2,X1)),X2),
inference(step,[status(thm)],[t2475,t9]) ).
cnf(t2477,plain,
commutator(multiply(X1,multiply(X2,inverse(X1))),X2) = commutator(commutator(X1,X2),X2),
inference(step,[status(thm)],[t2476,t310]) ).
cnf(t1465,plain,
commutator(multiply(X1,multiply(X2,inverse(X1))),X2) = commutator(commutator(X1,X2),X2),
inference(orient,[status(thm)],[t2477]) ).
cnf(t2581,plain,
identity = commutator(commutator(X1,X2),X2),
inference(step,[status(thm)],[t2580,t1465]) ).
cnf(t2394,plain,
commutator(commutator(X1,X2),X2) = identity,
inference(orient,[status(thm)],[t2581]) ).
cnf(goal_0,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
identity != identity,
inference(rw,[status(thm)],[goal_0,t2394]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 13:16:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.48/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.48/1.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------