%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP729-1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 04:27:10 PM UTC 2026
% Result : Unsatisfiable 2.07s 1.97s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 3 RR)
% Number of literals : 57 ( 56 equ; 2 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; 5 con; 0-3 aty)
% Number of variables : 125 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c07,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c04,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c03,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c05,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c06,axiom,
mult(i(X1),mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c11,axiom,
mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
cnf(c10,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
cnf(c21,axiom,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21) ).
cnf(c02,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c01,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c08,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c22,axiom,
asoc(X1,X2,asoc(X3,X4,X5)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22) ).
cnf(goals,negated_conjecture,
asoc(a,b,op_k(c,d)) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_13,axiom,
rd(mult(X1,X2),X2) = X1,
c07 ).
cnf(c_0_14,axiom,
mult(i(X1),X1) = unit,
c04 ).
cnf(c_0_15,axiom,
mult(X1,i(X1)) = unit,
c03 ).
cnf(c_0_16,plain,
rd(unit,X1) = i(X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
c05 ).
cnf(c_0_18,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
i(mult(i(X1),X2)) = mult(X1,i(X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
mult(i(X1),mult(X1,X2)) = X2,
c06 ).
cnf(c_0_21,axiom,
mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)),
c11 ).
cnf(c_0_22,plain,
mult(X1,i(mult(X1,X2))) = i(X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
mult(i(mult(X1,X2)),op_k(i(X2),i(X1))) = i(mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_17]) ).
cnf(c_0_24,plain,
mult(i(mult(X1,X2)),mult(X2,X1)) = op_k(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
i(op_k(i(X1),i(X2))) = op_k(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_24]) ).
cnf(c_0_26,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)),
c10 ).
cnf(c_0_27,axiom,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
c21 ).
cnf(c_0_28,axiom,
mult(X1,unit) = X1,
c02 ).
cnf(c_0_29,plain,
op_k(i(X1),i(X2)) = i(op_k(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_30,plain,
mult(mult(asoc(X1,X2,X3),X4),X5) = mult(asoc(X1,X2,X3),mult(X4,X5)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
mult(mult(X1,X2),i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_32,plain,
i(op_k(X1,i(X2))) = op_k(i(X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_33,plain,
i(op_k(X1,asoc(X2,X3,X4))) = unit,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_22]),c_0_15]) ).
cnf(c_0_34,axiom,
mult(unit,X1) = X1,
c01 ).
cnf(c_0_35,plain,
mult(op_k(X1,i(X2)),op_k(i(X1),X2)) = unit,
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_36,plain,
op_k(X1,asoc(X2,X3,X4)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_33]),c_0_28]) ).
cnf(c_0_37,plain,
asoc(i(mult(X1,X2)),X1,X2) = mult(mult(i(mult(X1,X2)),X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_34]) ).
cnf(c_0_38,plain,
op_k(X1,i(asoc(X2,X3,X4))) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]) ).
cnf(c_0_39,plain,
asoc(X1,X2,i(mult(X2,X1))) = mult(mult(X1,X2),i(mult(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_18]),c_0_18]) ).
cnf(c_0_40,plain,
i(mult(X1,i(X2))) = mult(i(X1),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_41,axiom,
mult(rd(X1,X2),X2) = X1,
c08 ).
cnf(c_0_42,plain,
rd(mult(X1,X2),op_k(X1,X2)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_43,plain,
op_k(X1,op_k(X2,X3)) = unit,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_24]) ).
cnf(c_0_44,plain,
rd(X1,unit) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
cnf(c_0_45,plain,
mult(X1,op_k(X2,X3)) = mult(op_k(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_46,plain,
rd(X1,mult(X2,X1)) = i(X2),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_47,plain,
rd(mult(X1,op_k(X2,X3)),X1) = op_k(X2,X3),
inference(spm,[status(thm)],[c_0_13,c_0_45]) ).
cnf(c_0_48,plain,
i(rd(X1,X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_49,plain,
rd(mult(X1,X2),mult(X2,X1)) = op_k(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_50,plain,
i(op_k(X1,X2)) = op_k(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49]) ).
cnf(c_0_51,plain,
mult(mult(X1,X2),i(mult(X2,X1))) = op_k(X1,X2),
inference(rw,[status(thm)],[c_0_31,c_0_50]) ).
cnf(c_0_52,axiom,
asoc(X1,X2,asoc(X3,X4,X5)) = unit,
c22 ).
cnf(c_0_53,plain,
asoc(X1,X2,i(mult(X2,X1))) = op_k(X1,X2),
inference(rw,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
asoc(a,b,op_k(c,d)) != unit,
goals ).
cnf(c_0_55,plain,
asoc(X1,X2,op_k(X3,X4)) = unit,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP729-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 19:03:47 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 2.07/1.97 % Version : CSE_E---1.7
% 2.07/1.97 % Problem : theBenchmark.p
% 2.07/1.97 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.97 % SZS output start CNFRefutation
% See solution above
% 2.07/1.98 % Total time : 1.372s
%------------------------------------------------------------------------------