%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG037-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Thu Sep 24 02:06:08 PM UTC 2026
% Result : Unsatisfiable 0.69s 0.49s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 70 ( 36 unt; 0 nHn; 47 RR)
% Number of literals : 136 ( 19 equ; 69 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_inverse_times_b,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(c_0_13,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_14,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition2]) ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_13 ).
cnf(c_0_16,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_17,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_14 ).
cnf(c_0_18,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_19,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_21,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_24,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_25,plain,
( ~ sum(X3,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
cnf(c_0_26,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_27,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_28,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_24 ).
cnf(c_0_29,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_30,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_31,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_32,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_33,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_34,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_27 ).
cnf(c_0_35,hypothesis,
( ~ sum(X4,X3,b)
| ~ product(a,X4,X1)
| ~ product(a,X3,X2)
| sum(X1,X2,d) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
product(a,additive_inverse(b),c),
a_inverse_times_b ).
cnf(c_0_37,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
cnf(c_0_38,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_39,plain,
( ~ sum(add(X2,additive_inverse(X3)),X3,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_40,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_41,hypothesis,
( ~ sum(X2,additive_inverse(b),b)
| ~ product(a,X2,X1)
| sum(X1,c,d) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_43,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_37 ).
cnf(c_0_44,plain,
( ~ sum(X3,X2,X1)
| sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_45,plain,
( ~ sum(add(X2,X3),additive_inverse(X3),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_46,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_47,hypothesis,
( ~ sum(X1,additive_inverse(b),b)
| sum(multiply(a,X1),c,d) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_49,plain,
( ~ sum(X3,X4,X2)
| ~ sum(X1,X3,additive_inverse(X4))
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_50,plain,
sum(add(X1,X2),additive_inverse(X2),X1),
inference(spm,[status(thm)],[c_0_44,c_0_20]) ).
cnf(c_0_51,plain,
( ~ sum(X6,X5,X4)
| ~ product(X3,X6,X1)
| ~ product(X3,X5,X2)
| sum(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_52,plain,
( ~ sum(add(X3,X2),additive_inverse(X3),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,hypothesis,
sum(multiply(a,add(b,b)),c,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_38]) ).
cnf(c_0_54,plain,
( ~ sum(X1,add(X2,X3),X3)
| sum(X1,X2,additive_identity) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_38]) ).
cnf(c_0_55,hypothesis,
( ~ sum(X3,b,X2)
| ~ product(a,X3,X1)
| sum(X1,d,multiply(a,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_56,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_20]),c_0_46]) ).
cnf(c_0_57,hypothesis,
add(c,multiply(a,add(b,b))) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_53]),c_0_46]) ).
cnf(c_0_58,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_46]) ).
cnf(c_0_59,plain,
( ~ sum(X1,add(X3,X2),X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_60,hypothesis,
( ~ sum(b,b,X1)
| sum(d,d,multiply(a,X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_61,hypothesis,
multiply(a,add(b,b)) = add(d,additive_inverse(c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46]) ).
cnf(c_0_62,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_58,c_0_38]) ).
cnf(c_0_63,plain,
( ~ sum(X1,X2,X3)
| sum(X1,add(X2,additive_inverse(X3)),additive_identity) ),
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_64,hypothesis,
sum(d,d,add(d,additive_inverse(c))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_20]),c_0_61]) ).
cnf(c_0_65,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_62]),c_0_46]) ).
cnf(c_0_66,negated_conjecture,
~ sum(c,d,additive_identity),
inference(fof_simplification,[status(thm)],[prove_sum_is_additive_identity]) ).
cnf(c_0_67,hypothesis,
sum(d,c,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_38]) ).
cnf(c_0_68,negated_conjecture,
~ sum(c,d,additive_identity),
c_0_66 ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n005.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 : Mon Sep 21 04:14:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.49 % Version: 3.5.1
% 0.69/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.49 % Starting sh5l with 300s (1) cores
% 0.69/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2526811 completed with status 0
% 0.69/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.69/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.49 % No SInE strategy applied
% 0.69/0.49 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.69/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.69/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.69/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.69/0.49 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 2526819 completed with status 0
% 0.69/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.69/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.49 % No SInE strategy applied
% 0.69/0.49 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.69/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.69/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.69/0.49 % Preprocessing time : 0.001 s
% 0.69/0.49 % Presaturation interreduction done
% 0.69/0.49
% 0.69/0.49 % Proof found!
% 0.69/0.49 % SZS status Unsatisfiable
% 0.69/0.49 % SZS output start CNFRefutation
% See solution above
% 0.69/0.49 % Parsed axioms : 20
% 0.69/0.49 % Removed by relevancy pruning/SinE : 0
% 0.69/0.49 % Initial clauses : 20
% 0.69/0.49 % Removed in clause preprocessing : 0
% 0.69/0.49 % Initial clauses in saturation : 20
% 0.69/0.49 % Processed clauses : 1049
% 0.69/0.49 % ...of these trivial : 91
% 0.69/0.49 % ...subsumed : 555
% 0.69/0.49 % ...remaining for further processing : 403
% 0.69/0.49 % Other redundant clauses eliminated : 0
% 0.69/0.49 % Clauses deleted for lack of memory : 0
% 0.69/0.49 % Backward-subsumed : 1
% 0.69/0.49 % Backward-rewritten : 36
% 0.69/0.49 % Generated clauses : 3563
% 0.69/0.49 % ...of the previous two non-redundant : 2219
% 0.69/0.49 % ...aggressively subsumed : 0
% 0.69/0.49 % Contextual simplify-reflections : 0
% 0.69/0.49 % Paramodulations : 3563
% 0.69/0.49 % Factorizations : 0
% 0.69/0.49 % NegExts : 0
% 0.69/0.49 % Equation resolutions : 0
% 0.69/0.49 % Disequality decompositions : 0
% 0.69/0.49 % Total rewrite steps : 3086
% 0.69/0.49 % ...of those cached : 2878
% 0.69/0.49 % Propositional unsat checks : 0
% 0.69/0.49 % Propositional check models : 0
% 0.69/0.49 % Propositional check unsatisfiable : 0
% 0.69/0.49 % Propositional clauses : 0
% 0.69/0.49 % Propositional clauses after purity: 0
% 0.69/0.49 % Propositional unsat core size : 0
% 0.69/0.49 % Propositional preprocessing time : 0.000
% 0.69/0.49 % Propositional encoding time : 0.000
% 0.69/0.49 % Propositional solver time : 0.000
% 0.69/0.49 % Success case prop preproc time : 0.000
% 0.69/0.49 % Success case prop encoding time : 0.000
% 0.69/0.49 % Success case prop solver time : 0.000
% 0.69/0.49 % Current number of processed clauses : 346
% 0.69/0.49 % Positive orientable unit clauses : 44
% 0.69/0.49 % Positive unorientable unit clauses: 1
% 0.69/0.49 % Negative unit clauses : 1
% 0.69/0.49 % Non-unit-clauses : 300
% 0.69/0.49 % Current number of unprocessed clauses: 1039
% 0.69/0.49 % ...number of literals in the above : 1819
% 0.69/0.49 % Current number of archived formulas : 0
% 0.69/0.49 % Current number of archived clauses : 57
% 0.69/0.49 % Clause-clause subsumption calls (NU) : 25619
% 0.69/0.49 % Rec. Clause-clause subsumption calls : 20020
% 0.69/0.49 % Non-unit clause-clause subsumptions : 539
% 0.69/0.49 % Unit Clause-clause subsumption calls : 19
% 0.69/0.49 % Rewrite failures with RHS unbound : 0
% 0.69/0.49 % BW rewrite match attempts : 109
% 0.69/0.49 % BW rewrite match successes : 21
% 0.69/0.49 % Condensation attempts : 0
% 0.69/0.49 % Condensation successes : 0
% 0.69/0.49 % Termbank termtop insertions : 34906
% 0.69/0.49 % Search garbage collected termcells : 61
% 0.69/0.49
% 0.69/0.49 % -------------------------------------------------
% 0.69/0.49 % User time : 0.064 s
% 0.69/0.49 % System time : 0.005 s
% 0.69/0.49 % Total time : 0.069 s
% 0.69/0.49 % Maximum resident set size: 3604 pages
% 0.69/0.49
% 0.69/0.49 % -------------------------------------------------
% 0.69/0.49 % User time : 0.285 s
% 0.69/0.49 % System time : 0.028 s
% 0.69/0.49 % Total time : 0.313 s
% 0.69/0.49 % Maximum resident set size: 4864 pages
% 0.69/0.49 % E exiting
%------------------------------------------------------------------------------