%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO028-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n027.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 04:11:20 PM UTC 2026
% Result : Unsatisfiable 2.10s 1.99s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 4 RR)
% Number of literals : 47 ( 46 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(b1,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(b2,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(prove_multiply_add_property,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c_0_9,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_10,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_12,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
b1 ).
cnf(c_0_15,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_16,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_17,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_19,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
b2 ).
cnf(c_0_21,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,inverse(X1))) = multiply(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_15]) ).
cnf(c_0_26,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
add(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_28,plain,
add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_29,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
add(X1,multiply(add(X2,inverse(X1)),X3)) = add(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_26]) ).
cnf(c_0_31,plain,
multiply(add(X1,X2),multiply(add(X1,inverse(X2)),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_18]),c_0_29]) ).
cnf(c_0_33,plain,
multiply(X1,add(multiply(X2,inverse(X1)),X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_21]) ).
cnf(c_0_34,plain,
add(multiply(X1,X2),add(multiply(X1,inverse(X2)),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_35,plain,
add(X1,multiply(add(X2,X1),X3)) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
multiply(X1,add(multiply(X2,X1),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32]) ).
cnf(c_0_37,plain,
add(multiply(X1,X2),multiply(add(X3,X1),X2)) = multiply(add(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_18]) ).
cnf(c_0_38,plain,
add(X1,multiply(X2,add(X3,X1))) = add(X1,multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_39,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_40,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
prove_multiply_add_property ).
cnf(c_0_41,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_12]),c_0_35]),c_0_38]) ).
cnf(c_0_42,plain,
add(X1,multiply(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_43,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X3,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_44,negated_conjecture,
add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_23]),c_0_23]) ).
cnf(c_0_45,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_23]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO028-1 : TPTP v9.2.1. Released v2.2.0.
% 0.12/0.13 % 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
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 10:45:20 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.10/1.99 % Version : CSE_E---1.7
% 2.10/1.99 % Problem : theBenchmark.p
% 2.10/1.99 % SZS status Unsatisfiable for theBenchmark.p
% 2.10/1.99 % SZS output start CNFRefutation
% See solution above
% 2.10/1.99 % Total time : 1.374s
%------------------------------------------------------------------------------