%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP002-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:31 PM UTC 2026
% Result : Unsatisfiable 1.20s 1.71s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 42 RR)
% Number of literals : 65 ( 64 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(h_times_b_is_j,negated_conjecture,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c_0_12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_13,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_14,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_15,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,hypothesis,
multiply(X1,multiply(X1,X1)) = identity,
x_cubed_is_identity ).
cnf(c_0_17,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_18,negated_conjecture,
multiply(d,inverse(b)) = h,
d_times_inverse_b_is_h ).
cnf(c_0_19,hypothesis,
inverse(X1) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_21,negated_conjecture,
multiply(d,multiply(b,b)) = h,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_17]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
multiply(d,multiply(d,h)) = multiply(b,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_19]),c_0_12]) ).
cnf(c_0_25,hypothesis,
inverse(multiply(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
multiply(h,b) = j,
h_times_b_is_j ).
cnf(c_0_27,negated_conjecture,
multiply(d,multiply(d,j)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_12]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
multiply(d,d) = multiply(d,j),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_19]),c_0_12]),c_0_17]) ).
cnf(c_0_29,hypothesis,
inverse(multiply(d,j)) = d,
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_30,hypothesis,
multiply(d,multiply(j,d)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_12]) ).
cnf(c_0_31,hypothesis,
multiply(d,j) = multiply(j,d),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_19]),c_0_28]),c_0_12]),c_0_17]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_17]) ).
cnf(c_0_33,negated_conjecture,
multiply(c,inverse(a)) = d,
c_times_inverse_a_is_d ).
cnf(c_0_34,negated_conjecture,
multiply(d,d) = multiply(j,d),
inference(rw,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_35,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_22]) ).
cnf(c_0_36,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_37,negated_conjecture,
multiply(c,multiply(a,a)) = d,
inference(rw,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
d = j,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_19]),c_0_28]),c_0_31]),c_0_12]),c_0_30]),c_0_17]) ).
cnf(c_0_39,negated_conjecture,
multiply(c,multiply(c,a)) = multiply(b,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_12]),c_0_19]) ).
cnf(c_0_40,negated_conjecture,
multiply(j,inverse(h)) = k,
j_times_inverse_h_is_k ).
cnf(c_0_41,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_42,negated_conjecture,
multiply(c,multiply(a,a)) = j,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
inverse(multiply(c,a)) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_25]) ).
cnf(c_0_44,negated_conjecture,
multiply(c,multiply(c,d)) = multiply(a,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_37]),c_0_19]),c_0_12]) ).
cnf(c_0_45,negated_conjecture,
multiply(j,multiply(h,h)) = k,
inference(rw,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_46,negated_conjecture,
multiply(h,multiply(b,X1)) = multiply(j,X1),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_47,negated_conjecture,
multiply(b,multiply(c,j)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_12]) ).
cnf(c_0_48,negated_conjecture,
multiply(c,multiply(c,j)) = multiply(a,a),
inference(rw,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
multiply(j,multiply(j,k)) = multiply(h,h),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_45]),c_0_19]),c_0_12]) ).
cnf(c_0_50,negated_conjecture,
multiply(a,multiply(a,c)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_36]),c_0_19]),c_0_12]) ).
cnf(c_0_51,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = inverse(multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_52,negated_conjecture,
multiply(j,multiply(c,j)) = multiply(h,a),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
inverse(multiply(c,j)) = multiply(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_48]),c_0_25]) ).
cnf(c_0_54,negated_conjecture,
multiply(j,multiply(k,h)) = multiply(j,j),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_49]),c_0_25]),c_0_12]),c_0_19]) ).
cnf(c_0_55,negated_conjecture,
multiply(a,multiply(a,multiply(c,X1))) = multiply(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_50]),c_0_12]) ).
cnf(c_0_56,hypothesis,
multiply(c,multiply(h,a)) = multiply(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_57,negated_conjecture,
multiply(k,h) = j,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_54]),c_0_19]),c_0_12]),c_0_16]),c_0_17]) ).
cnf(c_0_58,hypothesis,
multiply(b,multiply(h,a)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_50]),c_0_36]) ).
cnf(c_0_59,negated_conjecture,
multiply(a,multiply(c,c)) = multiply(j,j),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_53]),c_0_12]),c_0_19]) ).
cnf(c_0_60,negated_conjecture,
multiply(h,multiply(j,j)) = multiply(k,k),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_57]),c_0_19]),c_0_19]) ).
cnf(c_0_61,negated_conjecture,
multiply(k,inverse(b)) != identity,
prove_k_times_inverse_b_is_e ).
cnf(c_0_62,hypothesis,
multiply(k,k) = multiply(b,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_19]),c_0_12]),c_0_59]),c_0_60]),c_0_19]) ).
cnf(c_0_63,negated_conjecture,
multiply(k,multiply(b,b)) != identity,
inference(rw,[status(thm)],[c_0_61,c_0_19]) ).
cnf(c_0_64,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP002-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n008.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:16:13 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.20/1.71 % Version : CSE_E---1.7
% 1.20/1.71 % Problem : theBenchmark.p
% 1.20/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.20/1.71 % SZS output start CNFRefutation
% See solution above
% 1.20/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------